Mercurial > repos > public > sbplib
changeset 1072:6468a5f6ec79 feature/grids/LaplaceSquared
Merge with default
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 12 Feb 2019 17:12:42 +0100 |
| parents | 92cb03e64ca4 (current diff) c7b619cf5e34 (diff) |
| children | 95113a592421 |
| files | +sbp/+implementations/intOpAWW_orders_2to2_ratio2to1.m +sbp/+implementations/intOpAWW_orders_2to2_ratio_2to1_accC2F1_accF2C2.m +sbp/+implementations/intOpAWW_orders_2to2_ratio_2to1_accC2F2_accF2C1.m +sbp/+implementations/intOpAWW_orders_4to4_ratio2to1.m +sbp/+implementations/intOpAWW_orders_4to4_ratio_2to1_accC2F2_accF2C3.m +sbp/+implementations/intOpAWW_orders_4to4_ratio_2to1_accC2F3_accF2C2.m +sbp/+implementations/intOpAWW_orders_6to6_ratio2to1.m +sbp/+implementations/intOpAWW_orders_6to6_ratio_2to1_accC2F3_accF2C4.m +sbp/+implementations/intOpAWW_orders_6to6_ratio_2to1_accC2F4_accF2C3.m +sbp/+implementations/intOpAWW_orders_8to8_ratio2to1.m +sbp/+implementations/intOpAWW_orders_8to8_ratio_2to1_accC2F4_accF2C5.m +sbp/+implementations/intOpAWW_orders_8to8_ratio_2to1_accC2F5_accF2C4.m +sbp/InterpAWW.m +sbp/InterpMC.m +scheme/Beam2d.m +scheme/TODO.txt +scheme/Wave.m +scheme/Wave2dCurve.m +scheme/error1d.m +scheme/error2d.m +scheme/errorMax.m +scheme/errorRelative.m +scheme/errorSbp.m +scheme/errorVector.m +time/+cdiff/cdiff.m |
| diffstat | 82 files changed, 3209 insertions(+), 2284 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+grid/Nodes.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,47 @@ +classdef Nodes < grid.Grid + properties + coords + end + + methods + % Creates a grid with one point for each row in coords. + % The dimension equals the number of columns in coords. + function obj = Nodes(coords) + obj.coords = coords; + end + + function o = N(obj) + o = size(obj.coords, 1); + end + + % d returns the spatial dimension of the grid + function o = D(obj) + o = size(obj.coords, 2); + end + + % points returns a n x d matrix containing the coordinates for all points. + function X = points(obj) + X = obj.coords; + end + + % Restricts the grid function gf on obj to the subgrid g. + function gf = restrictFunc(obj, gf, g) + error('Not implemented'); + end + + % Projects the grid function gf on obj to the grid g. + function gf = projectFunc(obj, gf, g) + error('Not implemented'); + end + + % Return the grid.boundaryIdentifiers of all boundaries in a cell array. + function bs = getBoundaryNames(obj) + error('Not implemented'); + end + + % Return coordinates for the given boundary + function b = getBoundary(obj, name) + error('Not implemented'); + end + end +end
--- a/+multiblock/+domain/Circle.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+multiblock/+domain/Circle.m Tue Feb 12 17:12:42 2019 +0100 @@ -65,10 +65,10 @@ conn{5,2} = {'n','s'}; boundaryGroups = struct(); - boundaryGroups.E = multiblock.BoundaryGroup({2,'e'}); - boundaryGroups.N = multiblock.BoundaryGroup({3,'n'}); - boundaryGroups.W = multiblock.BoundaryGroup({4,'n'}); - boundaryGroups.S = multiblock.BoundaryGroup({5,'e'}); + boundaryGroups.E = multiblock.BoundaryGroup({{2,'e'}}); + boundaryGroups.N = multiblock.BoundaryGroup({{3,'n'}}); + boundaryGroups.W = multiblock.BoundaryGroup({{4,'n'}}); + boundaryGroups.S = multiblock.BoundaryGroup({{5,'e'}}); boundaryGroups.all = multiblock.BoundaryGroup({{2,'e'},{3,'n'},{4,'n'},{5,'e'}}); obj = obj@multiblock.DefCurvilinear(blocks, conn, boundaryGroups, blocksNames);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+multiblock/+domain/Line.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,153 @@ +classdef Line < multiblock.Definition + properties + + xlims + blockNames % Cell array of block labels + nBlocks + connections % Cell array specifying connections between blocks + boundaryGroups % Structure of boundaryGroups + + end + + + methods + % Creates a divided line + % x is a vector of boundary and interface positions. + % blockNames: cell array of labels. The id is default. + function obj = Line(x,blockNames) + default_arg('blockNames',[]); + + N = length(x)-1; % number of blocks in the x direction. + + if ~issorted(x) + error('The elements of x seem to be in the wrong order'); + end + + % Dimensions of blocks and number of points + blockTi = cell(N,1); + xlims = cell(N,1); + for i = 1:N + xlims{i} = {x(i), x(i+1)}; + end + + % Interface couplings + conn = cell(N,N); + for i = 1:N + conn{i,i+1} = {'r','l'}; + end + + % Block names (id number as default) + if isempty(blockNames) + obj.blockNames = cell(1, N); + for i = 1:N + obj.blockNames{i} = sprintf('%d', i); + end + else + assert(length(blockNames) == N); + obj.blockNames = blockNames; + end + nBlocks = N; + + % Boundary groups + boundaryGroups = struct(); + L = { {1, 'l'} }; + R = { {N, 'r'} }; + boundaryGroups.L = multiblock.BoundaryGroup(L); + boundaryGroups.R = multiblock.BoundaryGroup(R); + boundaryGroups.all = multiblock.BoundaryGroup([L,R]); + + obj.connections = conn; + obj.nBlocks = nBlocks; + obj.boundaryGroups = boundaryGroups; + obj.xlims = xlims; + + end + + + % Returns a multiblock.Grid given some parameters + % ms: cell array of m values + % For same m in every block, just input one scalar. + function g = getGrid(obj, ms, varargin) + + default_arg('ms',21) + + % Extend ms if input is a single scalar + if (numel(ms) == 1) && ~iscell(ms) + m = ms; + ms = cell(1,obj.nBlocks); + for i = 1:obj.nBlocks + ms{i} = m; + end + end + + grids = cell(1, obj.nBlocks); + for i = 1:obj.nBlocks + grids{i} = grid.equidistant(ms{i}, obj.xlims{i}, obj.ylims{i}); + end + + g = multiblock.Grid(grids, obj.connections, obj.boundaryGroups); + end + + % Returns a multiblock.Grid given some parameters + % ms: cell array of m values + % For same m in every block, just input one scalar. + function g = getStaggeredGrid(obj, ms, varargin) + + default_arg('ms',21) + + % Extend ms if input is a single scalar + if (numel(ms) == 1) && ~iscell(ms) + m = ms; + ms = cell(1,obj.nBlocks); + for i = 1:obj.nBlocks + ms{i} = m; + end + end + + grids = cell(1, obj.nBlocks); + for i = 1:obj.nBlocks + [g_primal, g_dual] = grid.primalDual1D(ms{i}, obj.xlims{i}); + grids{i} = grid.Staggered1d(g_primal, g_dual); + end + + g = multiblock.Grid(grids, obj.connections, obj.boundaryGroups); + end + + % label is the type of label used for plotting, + % default is block name, 'id' show the index for each block. + function show(obj, label) + default_arg('label', 'name') + + m = 10; + figure + for i = 1:obj.nBlocks + x = linspace(obj.xlims{i}{1}, obj.xlims{i}{2}, m); + y = 0*x + 0.05* ( (-1)^i + 1 ) ; + plot(x,y,'+'); + hold on + end + hold off + + switch label + case 'name' + labels = obj.blockNames; + case 'id' + labels = {}; + for i = 1:obj.nBlocks + labels{i} = num2str(i); + end + otherwise + axis equal + return + end + + legend(labels) + axis equal + end + + % Returns the grid size of each block in a cell array + % The input parameters are determined by the subclass + function ms = getGridSizes(obj, varargin) + end + end +end
--- a/+multiblock/DiffOp.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+multiblock/DiffOp.m Tue Feb 12 17:12:42 2019 +0100 @@ -10,7 +10,7 @@ end methods - function obj = DiffOp(doHand, g, order, doParam) + function obj = DiffOp(doHand, g, order, doParam, intfTypes) % doHand -- may either be a function handle or a cell array of % function handles for each grid. The function handle(s) % should be on the form do = doHand(grid, order, ...) @@ -24,14 +24,17 @@ % corresponding function handle as extra parameters: % doHand(..., doParam{i}{:}) Otherwise doParam is sent as % extra parameters to all doHand: doHand(..., doParam{:}) + % + % intfTypes (optional) -- nBlocks x nBlocks cell array of types for + % every interface. default_arg('doParam', []) + default_arg('intfTypes', cell(g.nBlocks(), g.nBlocks()) ); [getHand, getParam] = parseInput(doHand, g, doParam); + obj.order = order; nBlocks = g.nBlocks(); - obj.order = order; - % Create the diffOps for each block obj.diffOps = cell(1, nBlocks); for i = 1:nBlocks @@ -70,12 +73,11 @@ continue end - - [ii, ij] = obj.diffOps{i}.interface(intf{1}, obj.diffOps{j}, intf{2}); + [ii, ij] = obj.diffOps{i}.interface(intf{1}, obj.diffOps{j}, intf{2}, intfTypes{i,j}); D{i,i} = D{i,i} + ii; D{i,j} = D{i,j} + ij; - [jj, ji] = obj.diffOps{j}.interface(intf{2}, obj.diffOps{i}, intf{1}); + [jj, ji] = obj.diffOps{j}.interface(intf{2}, obj.diffOps{i}, intf{1}, intfTypes{i,j}); D{j,j} = D{j,j} + jj; D{j,i} = D{j,i} + ji; end @@ -127,11 +129,11 @@ % Get a boundary operator specified by opName for the given boundary/BoundaryGroup function op = getBoundaryOperator(obj, opName, boundary) + switch class(boundary) case 'cell' - localOpName = [opName '_' boundary{2}]; blockId = boundary{1}; - localOp = obj.diffOps{blockId}.(localOpName); + localOp = obj.diffOps{blockId}.getBoundaryOperator(opName, boundary{2}); div = {obj.blockmatrixDiv{1}, size(localOp,2)}; blockOp = blockmatrix.zero(div); @@ -149,13 +151,10 @@ end function op = getBoundaryQuadrature(obj, boundary) - opName = 'H'; switch class(boundary) case 'cell' - localOpName = [opName '_' boundary{2}]; blockId = boundary{1}; - op = obj.diffOps{blockId}.(localOpName); - + op = obj.diffOps{blockId}.getBoundaryQuadrature(boundary{2}); return case 'multiblock.BoundaryGroup' N = length(boundary); @@ -201,33 +200,8 @@ [blockClosure, blockPenalty] = obj.diffOps{I}.boundary_condition(name, type); % Expand to matrix for full domain. - div = obj.blockmatrixDiv; - if ~iscell(blockClosure) - temp = blockmatrix.zero(div); - temp{I,I} = blockClosure; - closure = blockmatrix.toMatrix(temp); - else - for i = 1:length(blockClosure) - temp = blockmatrix.zero(div); - temp{I,I} = blockClosure{i}; - closure{i} = blockmatrix.toMatrix(temp); - end - end - - if ~iscell(blockPenalty) - div{2} = size(blockPenalty, 2); % Penalty is a column vector - p = blockmatrix.zero(div); - p{I} = blockPenalty; - penalty = blockmatrix.toMatrix(p); - else - % TODO: used by beam equation, should be eliminated. SHould only set one BC per call - for i = 1:length(blockPenalty) - div{2} = size(blockPenalty{i}, 2); % Penalty is a column vector - p = blockmatrix.zero(div); - p{I} = blockPenalty{i}; - penalty{i} = blockmatrix.toMatrix(p); - end - end + closure = multiblock.local2globalClosure(blockClosure, obj.blockmatrixDiv, I); + penalty = multiblock.local2globalPenalty(blockPenalty, obj.blockmatrixDiv, I); end function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+multiblock/local2globalClosure.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,10 @@ +% Takes the block-local closures and turns it into a global closure +% local -- The local closure +% div -- block matrix division for the diffOp +% I -- Index of blockmatrix block +function closure = local2globalClosure(local, div, I) + closure_bm = blockmatrix.zero(div); + closure_bm{I,I} = local; + + closure = blockmatrix.toMatrix(closure_bm); +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+multiblock/local2globalPenalty.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,11 @@ +% Takes the block-local penalty and turns it into a global penalty +% local -- The local penalty +% div -- block matrix division for the diffOp +% I -- Index of blockmatrix block +function penalty = local2globalPenalty(local, div, I) + penaltyDiv = {div{1}, size(local,2)}; + penalty_bm = blockmatrix.zero(penaltyDiv); + penalty_bm{I,1} = local; + + penalty = blockmatrix.toMatrix(penalty_bm); +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+multiblock/setAllInterfaceTypes.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,13 @@ +% Create interface configuration with a single type for all interfaces +% g -- multiblock grid +% type -- type for all interfaces +function intfTypes = setAllInterfaceTypes(g, type) + intfTypes = cell(g.nBlocks(), g.nBlocks()); + for i = 1:g.nBlocks() + for j = 1:g.nBlocks() + if ~isempty(g.connections{i,j}) + intfTypes{i,j} = type; + end + end + end +end
--- a/+sbp/+implementations/intOpAWW_orders_2to2_ratio2to1.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,47 +0,0 @@ -function [IC2F,IF2C,Hc,Hf] = IntOp_orders_2to2_ratio2to1(mc,hc,ACC) - -% ACC is a string. -% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. -% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. -ratio = 2; -mf = ratio*mc-1; -hf = hc/ratio; - -switch ACC - case 'F2C' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_2to2_ratio_2to1_accC2F1_accF2C2; - case 'C2F' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_2to2_ratio_2to1_accC2F2_accF2C1; -end - -stencil_width = length(stencil_F2C); -stencil_hw = (stencil_width-1)/2; -[BC_rows,BC_cols] = size(BC_F2C); - -%%% Norm matrices %%% -Hc = speye(mc,mc); -HcUm = length(HcU); -Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); -Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); -Hc = Hc*hc; - -Hf = speye(mf,mf); -HfUm = length(HfU); -Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); -Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); -Hf = Hf*hf; -%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IF2C from stencil and BC -IF2C = sparse(mc,mf); -for i = BC_rows+1 : mc-BC_rows - IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> -end -IF2C(1:BC_rows,1:BC_cols) = BC_F2C; -IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IC2F using symmetry condition %%%% -IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- a/+sbp/+implementations/intOpAWW_orders_2to2_ratio_2to1_accC2F1_accF2C2.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_2to2_ratio_2to1_accC2F1_accF2C2 -%INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F1_ACCF2C2_STENCIL_5_BC_2_5 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F1_ACCF2C2_STENCIL_5_BC_2_5 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:36:07 - -stencil_F2C = [-1.0./8.0,1.0./4.0,3.0./4.0,1.0./4.0,-1.0./8.0]; -if nargout > 1 - BC_F2C = reshape([6.288191560529559e-1,-6.440957802647795e-2,6.855471317807184e-1,1.572264341096408e-1,-2.438028498638558e-1,7.469014249319279e-1,-8.431231982626708e-2,2.921561599131335e-1,1.374888185644862e-2,-1.318744409282243e-1],[2,5]); -end -if nargout > 2 - HcU = 1.0./2.0; -end -if nargout > 3 - HfU = 1.0./2.0; -end
--- a/+sbp/+implementations/intOpAWW_orders_2to2_ratio_2to1_accC2F2_accF2C1.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_2to2_ratio_2to1_accC2F2_accF2C1 -%INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F2_ACCF2C1_STENCIL_5_BC_1_3 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F2_ACCF2C1_STENCIL_5_BC_1_3 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:36:08 - -stencil_F2C = [1.0./4.0,1.0./2.0,1.0./4.0]; -if nargout > 1 - BC_F2C = [1.0./2.0,1.0./2.0]; -end -if nargout > 2 - HcU = 1.0./2.0; -end -if nargout > 3 - HfU = 1.0./2.0; -end
--- a/+sbp/+implementations/intOpAWW_orders_4to4_ratio2to1.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,47 +0,0 @@ -function [IC2F,IF2C,Hc,Hf] = IntOp_orders_4to4_ratio2to1(mc,hc,ACC) - -% ACC is a string. -% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. -% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. -ratio = 2; -mf = ratio*mc-1; -hf = hc/ratio; - -switch ACC - case 'F2C' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_4to4_ratio_2to1_accC2F2_accF2C3; - case 'C2F' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_4to4_ratio_2to1_accC2F3_accF2C2; -end - -stencil_width = length(stencil_F2C); -stencil_hw = (stencil_width-1)/2; -[BC_rows,BC_cols] = size(BC_F2C); - -%%% Norm matrices %%% -Hc = speye(mc,mc); -HcUm = length(HcU); -Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); -Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); -Hc = Hc*hc; - -Hf = speye(mf,mf); -HfUm = length(HfU); -Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); -Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); -Hf = Hf*hf; -%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IF2C from stencil and BC -IF2C = sparse(mc,mf); -for i = BC_rows+1 : mc-BC_rows - IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> -end -IF2C(1:BC_rows,1:BC_cols) = BC_F2C; -IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IC2F using symmetry condition %%%% -IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- a/+sbp/+implementations/intOpAWW_orders_4to4_ratio_2to1_accC2F2_accF2C3.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_4to4_ratio_2to1_accC2F2_accF2C3 -%INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F2_ACCF2C3_STENCIL_9_BC_3_11 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F2_ACCF2C3_STENCIL_9_BC_3_11 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:36:01 - -stencil_F2C = [7.0./2.56e2,-1.0./3.2e1,-7.0./6.4e1,9.0./3.2e1,8.5e1./1.28e2,9.0./3.2e1,-7.0./6.4e1,-1.0./3.2e1,7.0./2.56e2]; -if nargout > 1 - BC_F2C = reshape([7.523257802630956e-2,2.447812262221267e-1,-1.679313063616916e-1,1.290510950666589,6.315723344677289e-3,1.67178747937954e-1,1.982667903557025,-7.554383893379468e-1,7.215271362899867e-1,-2.820478831383137,1.807034411305536,-7.589683751979843e-1,-7.685973268458095e-1,3.965751544535173e-1,4.119789638051451e-1,1.574000556785898e-1,-1.113618964927466e-1,3.631000220124657e-1,1.639694219982991,-9.114074742274862e-1,4.952715520862987e-1,-4.524162151353456e-1,2.65481378213589e-1,-2.268273408674622e-1,3.455365956773523e-1,-2.009765975089827e-1,1.722179564305811e-1,-5.52933488235368e-1,3.18109976271229e-1,-2.171481232558432e-1,1.033835580108027e-1,-5.911351224351343e-2,3.960076712054991e-2],[3,11]); -end -if nargout > 2 - t2 = [1.7e1./4.8e1,5.9e1./4.8e1,4.3e1./4.8e1,4.9e1./4.8e1]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- a/+sbp/+implementations/intOpAWW_orders_4to4_ratio_2to1_accC2F3_accF2C2.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_4to4_ratio_2to1_accC2F3_accF2C2 -%INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F3_ACCF2C2_STENCIL_9_BC_3_11 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F3_ACCF2C2_STENCIL_9_BC_3_11 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:36:05 - -stencil_F2C = [-1.0./2.56e2,-1.0./3.2e1,1.0./6.4e1,9.0./3.2e1,6.1e1./1.28e2,9.0./3.2e1,1.0./6.4e1,-1.0./3.2e1,-1.0./2.56e2]; -if nargout > 1 - BC_F2C = reshape([1.0./2.0,0.0,0.0,1.77e2./2.72e2,3.0./8.0,-5.9e1./6.88e2,1.125919117647059e-2,3.546742584745763e-1,1.335392441860465e-2,-4.9e1./5.44e2,2.335805084745763e-1,3.204941860465116e-1,-1.194852941176471e-2,1.350635593220339e-2,5.308866279069767e-1,-9.0./5.44e2,-1.11228813559322e-2,2.943313953488372e-1,-2.803308823529412e-2,2.105402542372881e-2,-1.580668604651163e-2,-9.0./5.44e2,1.430084745762712e-2,-5.450581395348837e-2,-9.191176470588235e-4,7.944915254237288e-4,-5.450581395348837e-3,1.0./5.44e2,-1.588983050847458e-3,2.180232558139535e-3,2.297794117647059e-4,-1.986228813559322e-4,2.725290697674419e-4],[3,11]); -end -if nargout > 2 - t2 = [1.7e1./4.8e1,5.9e1./4.8e1,4.3e1./4.8e1,4.9e1./4.8e1]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- a/+sbp/+implementations/intOpAWW_orders_6to6_ratio2to1.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,47 +0,0 @@ -function [IC2F,IF2C,Hc,Hf] = IntOp_orders_6to6_ratio2to1(mc,hc,ACC) - -% ACC is a string. -% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. -% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. -ratio = 2; -mf = ratio*mc-1; -hf = hc/ratio; - -switch ACC - case 'F2C' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_6to6_ratio_2to1_accC2F3_accF2C4; - case 'C2F' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_6to6_ratio_2to1_accC2F4_accF2C3; -end - -stencil_width = length(stencil_F2C); -stencil_hw = (stencil_width-1)/2; -[BC_rows,BC_cols] = size(BC_F2C); - -%%% Norm matrices %%% -Hc = speye(mc,mc); -HcUm = length(HcU); -Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); -Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); -Hc = Hc*hc; - -Hf = speye(mf,mf); -HfUm = length(HfU); -Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); -Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); -Hf = Hf*hf; -%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IF2C from stencil and BC -IF2C = sparse(mc,mf); -for i = BC_rows+1 : mc-BC_rows - IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> -end -IF2C(1:BC_rows,1:BC_cols) = BC_F2C; -IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IC2F using symmetry condition %%%% -IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- a/+sbp/+implementations/intOpAWW_orders_6to6_ratio_2to1_accC2F3_accF2C4.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_6to6_ratio_2to1_accC2F3_accF2C4 -%INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F3_ACCF2C4_STENCIL_13_BC_3_17 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F3_ACCF2C4_STENCIL_13_BC_3_17 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:35:47 - -stencil_F2C = [-5.95703125e-3,3.0./5.12e2,3.57421875e-2,-2.5e1./5.12e2,-8.935546875e-2,7.5e1./2.56e2,3.17e2./5.12e2,7.5e1./2.56e2,-8.935546875e-2,-2.5e1./5.12e2,3.57421875e-2,3.0./5.12e2,-5.95703125e-3]; -if nargout > 1 - BC_F2C = reshape([5.233890618131365e-1,-1.594459192645467e-2,3.532688727637403e-2,8.021234957689208e-1,3.90683205173562e-1,-1.73222951632239e-1,-8.87662686483442e-2,2.90091235796637e-1,-1.600356115709148e-1,-1.044025375027475e-1,2.346179009198368e-1,6.091329306528956e-1,1.561275522703128e-1,-1.168382445709856e-1,1.040987887887311,-2.387061036980731e-1,1.363504965974361e-1,1.082611928255256e-1,-5.745310654054326e-1,3.977694249198785e-1,-9.376217911402619e-1,3.554518646054656e-2,5.609157787396987e-5,-1.564625311232018e-1,6.107907974027401e-1,-3.786608696698368e-1,7.02265869951125e-1,2.054294270642538e-1,-1.302300112378257e-1,2.478941407690889e-1,-2.657085326191479e-1,1.568761445933572e-1,-2.632906518005349e-1,-1.228047556139644e-1,7.182193248980271e-2,-1.1291238242346e-1,5.811258780405158e-2,-3.466364400805378e-2,5.683680203338252e-2,1.781337575097077e-2,-1.030572999042704e-2,1.577197067502767e-2,-1.443802115768554e-2,8.391316308374261e-3,-1.29534117369052e-2,-1.548018627738296e-3,8.794183904936319e-4,-1.298961407229805e-3,1.573818938200601e-3,-8.940753636685258e-4,1.320610764016968e-3],[3,17]); -end -if nargout > 2 - t2 = [3.159490740740741e-1,1.390393518518519,6.275462962962963e-1,1.240509259259259,9.116898148148148e-1,1.013912037037037]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- a/+sbp/+implementations/intOpAWW_orders_6to6_ratio_2to1_accC2F4_accF2C3.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_6to6_ratio_2to1_accC2F4_accF2C3 -%INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F4_ACCF2C3_STENCIL_13_BC_4_17 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F4_ACCF2C3_STENCIL_13_BC_4_17 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:35:56 - -stencil_F2C = [1.07421875e-3,3.0./5.12e2,-6.4453125e-3,-2.5e1./5.12e2,1.611328125e-2,7.5e1./2.56e2,2.45e2./5.12e2,7.5e1./2.56e2,1.611328125e-2,-2.5e1./5.12e2,-6.4453125e-3,3.0./5.12e2,1.07421875e-3]; -if nargout > 1 - BC_F2C = reshape([1.0./2.0,0.0,0.0,0.0,6.876076086160158e-1,1.5e1./3.2e1,-3.461879841386942e-1,3.502577439820862e-2,3.099721991995751e-3,2.228547003766753e-1,9.363652999354482e-3,-3.15791046603844e-3,-1.05789143206462e-1,2.35563165945226e-1,6.070385985337514e-1,-4.847496617839149e-2,-4.809232246867902e-3,5.154694068405061e-3,7.049223649022501e-1,1.016749349808733e-2,3.460117842882262e-2,-4.996621498584866e-2,5.210650763094799e-1,2.233592875303228e-1,-2.239024779745769e-3,4.254668119953384e-4,9.213872590833641e-3,3.910524351558127e-1,-9.048711215107334e-2,8.597375629526346e-2,-3.468219752858724e-1,3.250682992395969e-1,-1.309107466664224e-1,1.199249722306043e-1,-4.071552384959425e-1,1.474417123938701e-1,-3.02863877390285e-2,3.046016554982103e-2,-1.081315128181483e-1,1.120705238850532e-2,7.977722870036266e-2,-6.772545887788229e-2,2.00270418837606e-1,-5.427183680490763e-2,6.524845570188292e-2,-5.637610037043203e-2,1.711235764016968e-1,-4.203646902407166e-2,4.639548341453586e-3,-4.055884445496545e-3,1.258630924935448e-2,-2.776451559292779e-3,-1.023784366070774e-2,8.817108288936985e-3,-2.659664906860937e-2,7.14445034054861e-3,-1.435466025441424e-3,1.240274208149505e-3,-3.764718680837329e-3,1.028716295017727e-3,1.032012418492197e-3,-8.794183904936319e-4,2.597922814459609e-3,-6.571159498040679e-4,1.892022767235695e-4,-1.612267049238325e-4,4.76285849317595e-4,-1.204712574640791e-4],[4,17]); -end -if nargout > 2 - t2 = [3.159490740740741e-1,1.390393518518519,6.275462962962963e-1,1.240509259259259,9.116898148148148e-1,1.013912037037037]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- a/+sbp/+implementations/intOpAWW_orders_8to8_ratio2to1.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,47 +0,0 @@ -function [IC2F,IF2C,Hc,Hf] = IntOp_orders_8to8_ratio2to1(mc,hc,ACC) - -% ACC is a string. -% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. -% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. -ratio = 2; -mf = ratio*mc-1; -hf = hc/ratio; - -switch ACC - case 'F2C' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_8to8_ratio_2to1_accC2F4_accF2C5; - case 'C2F' - [stencil_F2C,BC_F2C,HcU,HfU] = ... - sbp.implementations.intOpAWW_orders_8to8_ratio_2to1_accC2F5_accF2C4; -end - -stencil_width = length(stencil_F2C); -stencil_hw = (stencil_width-1)/2; -[BC_rows,BC_cols] = size(BC_F2C); - -%%% Norm matrices %%% -Hc = speye(mc,mc); -HcUm = length(HcU); -Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); -Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); -Hc = Hc*hc; - -Hf = speye(mf,mf); -HfUm = length(HfU); -Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); -Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); -Hf = Hf*hf; -%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IF2C from stencil and BC -IF2C = sparse(mc,mf); -for i = BC_rows+1 : mc-BC_rows - IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> -end -IF2C(1:BC_rows,1:BC_cols) = BC_F2C; -IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% Create IC2F using symmetry condition %%%% -IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- a/+sbp/+implementations/intOpAWW_orders_8to8_ratio_2to1_accC2F4_accF2C5.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_8to8_ratio_2to1_accC2F4_accF2C5 -%INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F4_ACCF2C5_STENCIL_17_BC_5_24 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F4_ACCF2C5_STENCIL_17_BC_5_24 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:35:02 - -stencil_F2C = [1.324608212425595e-3,-1.220703125e-3,-1.059686569940476e-2,1.1962890625e-2,3.708902994791667e-2,-5.9814453125e-2,-7.417805989583333e-2,2.99072265625e-1,5.927225748697917e-1,2.99072265625e-1,-7.417805989583333e-2,-5.9814453125e-2,3.708902994791667e-2,1.1962890625e-2,-1.059686569940476e-2,-1.220703125e-3,1.324608212425595e-3]; -if nargout > 1 - BC_F2C = reshape([2.087365925359584,-1.227221822236823,1.090916714284468e1,-1.041312149906314,1.134214373258162,-1.269686811479259,2.075368250436277,-1.520771409696474e1,1.389750473974189,-1.48485748783569,-1.040579640776707,8.899721508624742e-1,-7.177691661032869,6.882712043721976e-1,-7.599347599660409e-1,-1.26440526850463,1.160658043364166,-5.391509178445742,6.679923135342851e-1,-7.521725463922262e-1,3.752349810676949,-2.906684049793639,2.672876913566556e1,-2.493145660873,2.782825829667436,1.443588084644871e-1,-1.307230271348211e-1,2.216804748506809,1.437719804483573e-1,-1.145830952112369e-1,3.2149320801083e-1,-2.34361439272989e-1,1.855837403850803,1.286992417665136e-1,-5.758238484341108e-2,-1.301103772185027,9.973408313121463e-1,-8.837520107531879,9.534930382604288e-1,-1.429199518808459e-2,-2.384453600787036,1.818345997558567,-1.577342441239303e1,1.422846302346762,3.154159322410927e-3,3.589377915408905e-1,-2.109524979864723e-1,9.363227187483732e-1,6.301238593470628e-2,5.732390257964316e-2,2.793582225299658,-2.033528056927806,1.621324028555783e1,-1.189222718426265,6.189671387692164e-2,5.342131492864642e-1,-4.222231296997605e-1,3.787253511209165,-3.350064226195165e-1,1.245325350855226e-2,-2.184146687275183,1.551331905163865,-1.19387312118926e1,8.349589004472998e-1,-1.35383591594438e-1,-8.014367493869704e-1,5.668415377001197e-1,-4.302842643863972,2.84183319528176e-1,3.83514596570461e-2,9.45794880458861e-1,-6.732638898386457e-1,5.234390273661413,-3.83498639699941e-1,1.440453495443018e-1,5.645065377027613e-1,-4.039220855868618e-1,3.170156487564899,-2.383074337879712e-1,1.216617375214008e-1,-1.937863224145611e-1,1.358891032584724e-1,-1.023378722711107,6.830621267493578e-2,-4.169135139842575e-3,2.270306426219975e-2,-2.38399209865252e-2,2.928388757260058e-1,-4.02060181933195e-2,6.880595419697505e-2,9.638828970166005e-2,-6.98778025332229e-2,5.609317796857676e-1,-4.429526993510467e-2,2.882554468024363e-2,3.582431391759518e-2,-2.671910644265286e-2,2.251335440088556e-1,-1.966486325944329e-2,1.791756577091828e-2,-3.350790201878844e-1,2.581411034605136e-1,-2.283079071439122,2.162064132948073e-1,-2.321676317817421e-1,6.356644993195555e-2,-4.921907141164279e-2,4.384534411523264e-1,-4.198474091936761e-2,4.597203884996652e-2,2.261662512481835e-2,-1.740429407604355e-2,1.537038474929879e-1,-1.452709057733876e-2,1.556101844926456e-2,3.097679325854209e-2,-2.394872918869654e-2,2.128879105995857e-1,-2.032077838507769e-2,2.213372706946953e-2],[5,24]); -end -if nargout > 2 - t2 = [2.948906761778786e-1,1.525720623897707,2.57452876984127e-1,1.798113701499118,4.127080577601411e-1,1.278484623015873,9.232955798059965e-1,1.009333860859158]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- a/+sbp/+implementations/intOpAWW_orders_8to8_ratio_2to1_accC2F5_accF2C4.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -function [stencil_F2C,BC_F2C,HcU,HfU] = intOpAWW_orders_8to8_ratio_2to1_accC2F5_accF2C4 -%INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F5_ACCF2C4_STENCIL_17_BC_6_24 -% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F5_ACCF2C4_STENCIL_17_BC_6_24 - -% This function was generated by the Symbolic Math Toolbox version 8.0. -% 21-May-2018 15:35:39 - -stencil_F2C = [-2.564929780505952e-4,-1.220703125e-3,2.051943824404762e-3,1.1962890625e-2,-7.181803385416667e-3,-5.9814453125e-2,1.436360677083333e-2,2.99072265625e-1,4.820454915364583e-1,2.99072265625e-1,1.436360677083333e-2,-5.9814453125e-2,-7.181803385416667e-3,1.1962890625e-2,2.051943824404762e-3,-1.220703125e-3,-2.564929780505952e-4]; -if nargout > 1 - BC_F2C = reshape([-1.673327822994457e1,1.665420585653232e1,-1.973927473454954e2,2.826257908914756e1,-6.156813484052936e1,3.974966126696054,2.880639373222355e1,-2.660797294399895e1,3.202303847857831e2,-4.598960974033412e1,1.003152507870138e2,-6.481221721577338,8.061874893005659,-7.706608975219419,9.234201483040626e1,-1.322147613066874e1,2.880209985918895e1,-1.859523138300886,-2.19528557898034e1,2.13763239391502e1,-2.476320412310993e2,3.572924955195535e1,-7.795290920161567e1,5.036097395109802,-1.287197329845376,1.244100160910233,-1.394684346537857e1,2.112320869857597,-4.60441856527933,2.978264879234002e-1,1.935199269380359,-1.88580031845933,2.330807783420723e1,-2.91749306966336,6.644427567385864,-4.302395355488564e-1,-1.148984264037686,1.109982778464842,-1.314799057941425e1,2.137017065505111,-4.084082382904703,2.606486561845403e-1,1.565462612018858,-1.508309105065004,1.772442871757061e1,-2.40060893717649,6.31422909250156,-4.052444871368164e-1,3.179380137695096e-1,-3.071741522636364e-1,3.636264382483117,-5.183996466001354e-1,2.322192602480252,-6.467931586900172e-2,6.277081831671831e-1,-6.107890751034906e-1,7.335850436798604,-1.091016872160133,3.089218691662174,6.988892111841499e-2,1.639756762532723,-1.583883992641009,1.876236237708381e1,-2.685390559486947,5.859855615166555,3.919312696253764e-3,1.611803934956753,-1.540778869185931,1.795955382224485e1,-2.495154500270907,5.003492494640851,-4.157919873785453e-2,-6.213413520816026e-1,6.242581523412814e-1,-7.823535324240331,1.222418137438074,-3.120142966701915,2.975831327541895e-1,2.12230710100161,-2.0451058741188,2.412395225004063e1,-3.423544496956294,7.325914828631551,-4.793445914188063e-1,-4.31809447483846,4.158975059021769,-4.906211424150023e1,6.975058620124194,-1.501259943091044e1,9.418983630154896e-1,-6.138797742037704e-1,5.810969368378602e-1,-6.6821474226667,9.113864351863538e-1,-1.814400062103318,1.002574935832871e-1,-9.860044240994036e-2,9.448685284232805e-2,-1.106188847377502,1.552858946803229e-1,-3.265426230113952e-1,2.062042480203908e-2,-2.745034502159738,2.655226942873441,-3.151193386341271e1,4.520932327069998,-9.883338555855938,6.423439846307804e-1,2.139968493382333,-2.067738462547628,2.450223844197562e1,-3.50699574523559,7.635005983192545,-4.923960464980415e-1,1.036406872394752,-1.002008838408551,1.188339891704641e1,-1.70302259679446,3.715789696036691,-2.407301455417931e-1,1.606428513214277,-1.552524985439685,1.840245870449254e1,-2.635131753653705,5.741508438443495,-3.708346905830083e-1,5.659562678739624e-2,-5.465656201303744e-2,6.471932864664631e-1,-9.253169145609999e-2,2.010909570941804e-1,-1.292046400706276e-2,5.435391241988039e-1,-5.252672844681129e-1,6.225561585258754,-8.91344337215917e-1,1.941632399616401,-1.253426955105431e-1,-1.552116972709218,1.499962759958308,-1.777819805127299e1,2.545472086708348,-5.545140384142844,3.580057322157566e-1],[6,24]); -end -if nargout > 2 - t2 = [2.948906761778786e-1,1.525720623897707,2.57452876984127e-1,1.798113701499118,4.127080577601411e-1,1.278484623015873,9.232955798059965e-1,1.009333860859158]; - HcU = t2; -end -if nargout > 3 - HfU = t2; -end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_2to2_ratio2to1.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,47 @@ +function [IC2F,IF2C,Hc,Hf] = IntOpOP_orders_2to2_ratio2to1(mc,hc,ACC) + +% ACC is a string. +% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. +% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. +ratio = 2; +mf = ratio*mc-1; +hf = hc/ratio; + +switch ACC + case 'F2C' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_2to2_ratio_2to1_accC2F1_accF2C2; + case 'C2F' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_2to2_ratio_2to1_accC2F2_accF2C1; +end + +stencil_width = length(stencil_F2C); +stencil_hw = (stencil_width-1)/2; +[BC_rows,BC_cols] = size(BC_F2C); + +%%% Norm matrices %%% +Hc = speye(mc,mc); +HcUm = length(HcU); +Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); +Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); +Hc = Hc*hc; + +Hf = speye(mf,mf); +HfUm = length(HfU); +Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); +Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); +Hf = Hf*hf; +%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IF2C from stencil and BC +IF2C = sparse(mc,mf); +for i = BC_rows+1 : mc-BC_rows + IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> +end +IF2C(1:BC_rows,1:BC_cols) = BC_F2C; +IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IC2F using symmetry condition %%%% +IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_2to2_ratio_2to1_accC2F1_accF2C2.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,17 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_2to2_ratio_2to1_accC2F1_accF2C2 +%INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F1_ACCF2C2_STENCIL_5_BC_2_5 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F1_ACCF2C2_STENCIL_5_BC_2_5 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:36:07 + +stencil_F2C = [-1.0./8.0,1.0./4.0,3.0./4.0,1.0./4.0,-1.0./8.0]; +if nargout > 1 + BC_F2C = reshape([6.288191560529559e-1,-6.440957802647795e-2,6.855471317807184e-1,1.572264341096408e-1,-2.438028498638558e-1,7.469014249319279e-1,-8.431231982626708e-2,2.921561599131335e-1,1.374888185644862e-2,-1.318744409282243e-1],[2,5]); +end +if nargout > 2 + HcU = 1.0./2.0; +end +if nargout > 3 + HfU = 1.0./2.0; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_2to2_ratio_2to1_accC2F2_accF2C1.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,17 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_2to2_ratio_2to1_accC2F2_accF2C1 +%INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F2_ACCF2C1_STENCIL_5_BC_1_3 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_2TO2_RATIO_2TO1_ACCC2F2_ACCF2C1_STENCIL_5_BC_1_3 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:36:08 + +stencil_F2C = [1.0./4.0,1.0./2.0,1.0./4.0]; +if nargout > 1 + BC_F2C = [1.0./2.0,1.0./2.0]; +end +if nargout > 2 + HcU = 1.0./2.0; +end +if nargout > 3 + HfU = 1.0./2.0; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_4to4_ratio2to1.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,47 @@ +function [IC2F,IF2C,Hc,Hf] = IntOpOP_orders_4to4_ratio2to1(mc,hc,ACC) + +% ACC is a string. +% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. +% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. +ratio = 2; +mf = ratio*mc-1; +hf = hc/ratio; + +switch ACC + case 'F2C' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_4to4_ratio_2to1_accC2F2_accF2C3; + case 'C2F' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_4to4_ratio_2to1_accC2F3_accF2C2; +end + +stencil_width = length(stencil_F2C); +stencil_hw = (stencil_width-1)/2; +[BC_rows,BC_cols] = size(BC_F2C); + +%%% Norm matrices %%% +Hc = speye(mc,mc); +HcUm = length(HcU); +Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); +Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); +Hc = Hc*hc; + +Hf = speye(mf,mf); +HfUm = length(HfU); +Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); +Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); +Hf = Hf*hf; +%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IF2C from stencil and BC +IF2C = sparse(mc,mf); +for i = BC_rows+1 : mc-BC_rows + IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> +end +IF2C(1:BC_rows,1:BC_cols) = BC_F2C; +IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IC2F using symmetry condition %%%% +IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_4to4_ratio_2to1_accC2F2_accF2C3.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_4to4_ratio_2to1_accC2F2_accF2C3 +%INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F2_ACCF2C3_STENCIL_9_BC_3_11 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F2_ACCF2C3_STENCIL_9_BC_3_11 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:36:01 + +stencil_F2C = [7.0./2.56e2,-1.0./3.2e1,-7.0./6.4e1,9.0./3.2e1,8.5e1./1.28e2,9.0./3.2e1,-7.0./6.4e1,-1.0./3.2e1,7.0./2.56e2]; +if nargout > 1 + BC_F2C = reshape([7.523257802630956e-2,2.447812262221267e-1,-1.679313063616916e-1,1.290510950666589,6.315723344677289e-3,1.67178747937954e-1,1.982667903557025,-7.554383893379468e-1,7.215271362899867e-1,-2.820478831383137,1.807034411305536,-7.589683751979843e-1,-7.685973268458095e-1,3.965751544535173e-1,4.119789638051451e-1,1.574000556785898e-1,-1.113618964927466e-1,3.631000220124657e-1,1.639694219982991,-9.114074742274862e-1,4.952715520862987e-1,-4.524162151353456e-1,2.65481378213589e-1,-2.268273408674622e-1,3.455365956773523e-1,-2.009765975089827e-1,1.722179564305811e-1,-5.52933488235368e-1,3.18109976271229e-1,-2.171481232558432e-1,1.033835580108027e-1,-5.911351224351343e-2,3.960076712054991e-2],[3,11]); +end +if nargout > 2 + t2 = [1.7e1./4.8e1,5.9e1./4.8e1,4.3e1./4.8e1,4.9e1./4.8e1]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_4to4_ratio_2to1_accC2F3_accF2C2.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_4to4_ratio_2to1_accC2F3_accF2C2 +%INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F3_ACCF2C2_STENCIL_9_BC_3_11 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_4TO4_RATIO_2TO1_ACCC2F3_ACCF2C2_STENCIL_9_BC_3_11 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:36:05 + +stencil_F2C = [-1.0./2.56e2,-1.0./3.2e1,1.0./6.4e1,9.0./3.2e1,6.1e1./1.28e2,9.0./3.2e1,1.0./6.4e1,-1.0./3.2e1,-1.0./2.56e2]; +if nargout > 1 + BC_F2C = reshape([1.0./2.0,0.0,0.0,1.77e2./2.72e2,3.0./8.0,-5.9e1./6.88e2,1.125919117647059e-2,3.546742584745763e-1,1.335392441860465e-2,-4.9e1./5.44e2,2.335805084745763e-1,3.204941860465116e-1,-1.194852941176471e-2,1.350635593220339e-2,5.308866279069767e-1,-9.0./5.44e2,-1.11228813559322e-2,2.943313953488372e-1,-2.803308823529412e-2,2.105402542372881e-2,-1.580668604651163e-2,-9.0./5.44e2,1.430084745762712e-2,-5.450581395348837e-2,-9.191176470588235e-4,7.944915254237288e-4,-5.450581395348837e-3,1.0./5.44e2,-1.588983050847458e-3,2.180232558139535e-3,2.297794117647059e-4,-1.986228813559322e-4,2.725290697674419e-4],[3,11]); +end +if nargout > 2 + t2 = [1.7e1./4.8e1,5.9e1./4.8e1,4.3e1./4.8e1,4.9e1./4.8e1]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_6to6_ratio2to1.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,47 @@ +function [IC2F,IF2C,Hc,Hf] = IntOpOP_orders_6to6_ratio2to1(mc,hc,ACC) + +% ACC is a string. +% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. +% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. +ratio = 2; +mf = ratio*mc-1; +hf = hc/ratio; + +switch ACC + case 'F2C' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_6to6_ratio_2to1_accC2F3_accF2C4; + case 'C2F' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_6to6_ratio_2to1_accC2F4_accF2C3; +end + +stencil_width = length(stencil_F2C); +stencil_hw = (stencil_width-1)/2; +[BC_rows,BC_cols] = size(BC_F2C); + +%%% Norm matrices %%% +Hc = speye(mc,mc); +HcUm = length(HcU); +Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); +Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); +Hc = Hc*hc; + +Hf = speye(mf,mf); +HfUm = length(HfU); +Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); +Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); +Hf = Hf*hf; +%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IF2C from stencil and BC +IF2C = sparse(mc,mf); +for i = BC_rows+1 : mc-BC_rows + IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> +end +IF2C(1:BC_rows,1:BC_cols) = BC_F2C; +IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IC2F using symmetry condition %%%% +IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_6to6_ratio_2to1_accC2F3_accF2C4.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_6to6_ratio_2to1_accC2F3_accF2C4 +%INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F3_ACCF2C4_STENCIL_13_BC_3_17 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F3_ACCF2C4_STENCIL_13_BC_3_17 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:35:47 + +stencil_F2C = [-5.95703125e-3,3.0./5.12e2,3.57421875e-2,-2.5e1./5.12e2,-8.935546875e-2,7.5e1./2.56e2,3.17e2./5.12e2,7.5e1./2.56e2,-8.935546875e-2,-2.5e1./5.12e2,3.57421875e-2,3.0./5.12e2,-5.95703125e-3]; +if nargout > 1 + BC_F2C = reshape([5.233890618131365e-1,-1.594459192645467e-2,3.532688727637403e-2,8.021234957689208e-1,3.90683205173562e-1,-1.73222951632239e-1,-8.87662686483442e-2,2.90091235796637e-1,-1.600356115709148e-1,-1.044025375027475e-1,2.346179009198368e-1,6.091329306528956e-1,1.561275522703128e-1,-1.168382445709856e-1,1.040987887887311,-2.387061036980731e-1,1.363504965974361e-1,1.082611928255256e-1,-5.745310654054326e-1,3.977694249198785e-1,-9.376217911402619e-1,3.554518646054656e-2,5.609157787396987e-5,-1.564625311232018e-1,6.107907974027401e-1,-3.786608696698368e-1,7.02265869951125e-1,2.054294270642538e-1,-1.302300112378257e-1,2.478941407690889e-1,-2.657085326191479e-1,1.568761445933572e-1,-2.632906518005349e-1,-1.228047556139644e-1,7.182193248980271e-2,-1.1291238242346e-1,5.811258780405158e-2,-3.466364400805378e-2,5.683680203338252e-2,1.781337575097077e-2,-1.030572999042704e-2,1.577197067502767e-2,-1.443802115768554e-2,8.391316308374261e-3,-1.29534117369052e-2,-1.548018627738296e-3,8.794183904936319e-4,-1.298961407229805e-3,1.573818938200601e-3,-8.940753636685258e-4,1.320610764016968e-3],[3,17]); +end +if nargout > 2 + t2 = [3.159490740740741e-1,1.390393518518519,6.275462962962963e-1,1.240509259259259,9.116898148148148e-1,1.013912037037037]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_6to6_ratio_2to1_accC2F4_accF2C3.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_6to6_ratio_2to1_accC2F4_accF2C3 +%INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F4_ACCF2C3_STENCIL_13_BC_4_17 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_6TO6_RATIO_2TO1_ACCC2F4_ACCF2C3_STENCIL_13_BC_4_17 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:35:56 + +stencil_F2C = [1.07421875e-3,3.0./5.12e2,-6.4453125e-3,-2.5e1./5.12e2,1.611328125e-2,7.5e1./2.56e2,2.45e2./5.12e2,7.5e1./2.56e2,1.611328125e-2,-2.5e1./5.12e2,-6.4453125e-3,3.0./5.12e2,1.07421875e-3]; +if nargout > 1 + BC_F2C = reshape([1.0./2.0,0.0,0.0,0.0,6.876076086160158e-1,1.5e1./3.2e1,-3.461879841386942e-1,3.502577439820862e-2,3.099721991995751e-3,2.228547003766753e-1,9.363652999354482e-3,-3.15791046603844e-3,-1.05789143206462e-1,2.35563165945226e-1,6.070385985337514e-1,-4.847496617839149e-2,-4.809232246867902e-3,5.154694068405061e-3,7.049223649022501e-1,1.016749349808733e-2,3.460117842882262e-2,-4.996621498584866e-2,5.210650763094799e-1,2.233592875303228e-1,-2.239024779745769e-3,4.254668119953384e-4,9.213872590833641e-3,3.910524351558127e-1,-9.048711215107334e-2,8.597375629526346e-2,-3.468219752858724e-1,3.250682992395969e-1,-1.309107466664224e-1,1.199249722306043e-1,-4.071552384959425e-1,1.474417123938701e-1,-3.02863877390285e-2,3.046016554982103e-2,-1.081315128181483e-1,1.120705238850532e-2,7.977722870036266e-2,-6.772545887788229e-2,2.00270418837606e-1,-5.427183680490763e-2,6.524845570188292e-2,-5.637610037043203e-2,1.711235764016968e-1,-4.203646902407166e-2,4.639548341453586e-3,-4.055884445496545e-3,1.258630924935448e-2,-2.776451559292779e-3,-1.023784366070774e-2,8.817108288936985e-3,-2.659664906860937e-2,7.14445034054861e-3,-1.435466025441424e-3,1.240274208149505e-3,-3.764718680837329e-3,1.028716295017727e-3,1.032012418492197e-3,-8.794183904936319e-4,2.597922814459609e-3,-6.571159498040679e-4,1.892022767235695e-4,-1.612267049238325e-4,4.76285849317595e-4,-1.204712574640791e-4],[4,17]); +end +if nargout > 2 + t2 = [3.159490740740741e-1,1.390393518518519,6.275462962962963e-1,1.240509259259259,9.116898148148148e-1,1.013912037037037]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_8to8_ratio2to1.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,47 @@ +function [IC2F,IF2C,Hc,Hf] = IntOpOP_orders_8to8_ratio2to1(mc,hc,ACC) + +% ACC is a string. +% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C. +% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F. +ratio = 2; +mf = ratio*mc-1; +hf = hc/ratio; + +switch ACC + case 'F2C' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_8to8_ratio_2to1_accC2F4_accF2C5; + case 'C2F' + [stencil_F2C,BC_F2C,HcU,HfU] = ... + sbp.implementations.intOpOP_orders_8to8_ratio_2to1_accC2F5_accF2C4; +end + +stencil_width = length(stencil_F2C); +stencil_hw = (stencil_width-1)/2; +[BC_rows,BC_cols] = size(BC_F2C); + +%%% Norm matrices %%% +Hc = speye(mc,mc); +HcUm = length(HcU); +Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm); +Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm); +Hc = Hc*hc; + +Hf = speye(mf,mf); +HfUm = length(HfU); +Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm); +Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm); +Hf = Hf*hf; +%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IF2C from stencil and BC +IF2C = sparse(mc,mf); +for i = BC_rows+1 : mc-BC_rows + IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX> +end +IF2C(1:BC_rows,1:BC_cols) = BC_F2C; +IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2); +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%% Create IC2F using symmetry condition %%%% +IC2F = Hf\IF2C.'*Hc; \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_8to8_ratio_2to1_accC2F4_accF2C5.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_8to8_ratio_2to1_accC2F4_accF2C5 +%INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F4_ACCF2C5_STENCIL_17_BC_5_24 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F4_ACCF2C5_STENCIL_17_BC_5_24 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:35:02 + +stencil_F2C = [1.324608212425595e-3,-1.220703125e-3,-1.059686569940476e-2,1.1962890625e-2,3.708902994791667e-2,-5.9814453125e-2,-7.417805989583333e-2,2.99072265625e-1,5.927225748697917e-1,2.99072265625e-1,-7.417805989583333e-2,-5.9814453125e-2,3.708902994791667e-2,1.1962890625e-2,-1.059686569940476e-2,-1.220703125e-3,1.324608212425595e-3]; +if nargout > 1 + BC_F2C = reshape([2.087365925359584,-1.227221822236823,1.090916714284468e1,-1.041312149906314,1.134214373258162,-1.269686811479259,2.075368250436277,-1.520771409696474e1,1.389750473974189,-1.48485748783569,-1.040579640776707,8.899721508624742e-1,-7.177691661032869,6.882712043721976e-1,-7.599347599660409e-1,-1.26440526850463,1.160658043364166,-5.391509178445742,6.679923135342851e-1,-7.521725463922262e-1,3.752349810676949,-2.906684049793639,2.672876913566556e1,-2.493145660873,2.782825829667436,1.443588084644871e-1,-1.307230271348211e-1,2.216804748506809,1.437719804483573e-1,-1.145830952112369e-1,3.2149320801083e-1,-2.34361439272989e-1,1.855837403850803,1.286992417665136e-1,-5.758238484341108e-2,-1.301103772185027,9.973408313121463e-1,-8.837520107531879,9.534930382604288e-1,-1.429199518808459e-2,-2.384453600787036,1.818345997558567,-1.577342441239303e1,1.422846302346762,3.154159322410927e-3,3.589377915408905e-1,-2.109524979864723e-1,9.363227187483732e-1,6.301238593470628e-2,5.732390257964316e-2,2.793582225299658,-2.033528056927806,1.621324028555783e1,-1.189222718426265,6.189671387692164e-2,5.342131492864642e-1,-4.222231296997605e-1,3.787253511209165,-3.350064226195165e-1,1.245325350855226e-2,-2.184146687275183,1.551331905163865,-1.19387312118926e1,8.349589004472998e-1,-1.35383591594438e-1,-8.014367493869704e-1,5.668415377001197e-1,-4.302842643863972,2.84183319528176e-1,3.83514596570461e-2,9.45794880458861e-1,-6.732638898386457e-1,5.234390273661413,-3.83498639699941e-1,1.440453495443018e-1,5.645065377027613e-1,-4.039220855868618e-1,3.170156487564899,-2.383074337879712e-1,1.216617375214008e-1,-1.937863224145611e-1,1.358891032584724e-1,-1.023378722711107,6.830621267493578e-2,-4.169135139842575e-3,2.270306426219975e-2,-2.38399209865252e-2,2.928388757260058e-1,-4.02060181933195e-2,6.880595419697505e-2,9.638828970166005e-2,-6.98778025332229e-2,5.609317796857676e-1,-4.429526993510467e-2,2.882554468024363e-2,3.582431391759518e-2,-2.671910644265286e-2,2.251335440088556e-1,-1.966486325944329e-2,1.791756577091828e-2,-3.350790201878844e-1,2.581411034605136e-1,-2.283079071439122,2.162064132948073e-1,-2.321676317817421e-1,6.356644993195555e-2,-4.921907141164279e-2,4.384534411523264e-1,-4.198474091936761e-2,4.597203884996652e-2,2.261662512481835e-2,-1.740429407604355e-2,1.537038474929879e-1,-1.452709057733876e-2,1.556101844926456e-2,3.097679325854209e-2,-2.394872918869654e-2,2.128879105995857e-1,-2.032077838507769e-2,2.213372706946953e-2],[5,24]); +end +if nargout > 2 + t2 = [2.948906761778786e-1,1.525720623897707,2.57452876984127e-1,1.798113701499118,4.127080577601411e-1,1.278484623015873,9.232955798059965e-1,1.009333860859158]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/intOpOP_orders_8to8_ratio_2to1_accC2F5_accF2C4.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function [stencil_F2C,BC_F2C,HcU,HfU] = intOpOP_orders_8to8_ratio_2to1_accC2F5_accF2C4 +%INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F5_ACCF2C4_STENCIL_17_BC_6_24 +% [STENCIL_F2C,BC_F2C,HCU,HFU] = INT_ORDERS_8TO8_RATIO_2TO1_ACCC2F5_ACCF2C4_STENCIL_17_BC_6_24 + +% This function was generated by the Symbolic Math Toolbox version 8.0. +% 21-May-2018 15:35:39 + +stencil_F2C = [-2.564929780505952e-4,-1.220703125e-3,2.051943824404762e-3,1.1962890625e-2,-7.181803385416667e-3,-5.9814453125e-2,1.436360677083333e-2,2.99072265625e-1,4.820454915364583e-1,2.99072265625e-1,1.436360677083333e-2,-5.9814453125e-2,-7.181803385416667e-3,1.1962890625e-2,2.051943824404762e-3,-1.220703125e-3,-2.564929780505952e-4]; +if nargout > 1 + BC_F2C = reshape([-1.673327822994457e1,1.665420585653232e1,-1.973927473454954e2,2.826257908914756e1,-6.156813484052936e1,3.974966126696054,2.880639373222355e1,-2.660797294399895e1,3.202303847857831e2,-4.598960974033412e1,1.003152507870138e2,-6.481221721577338,8.061874893005659,-7.706608975219419,9.234201483040626e1,-1.322147613066874e1,2.880209985918895e1,-1.859523138300886,-2.19528557898034e1,2.13763239391502e1,-2.476320412310993e2,3.572924955195535e1,-7.795290920161567e1,5.036097395109802,-1.287197329845376,1.244100160910233,-1.394684346537857e1,2.112320869857597,-4.60441856527933,2.978264879234002e-1,1.935199269380359,-1.88580031845933,2.330807783420723e1,-2.91749306966336,6.644427567385864,-4.302395355488564e-1,-1.148984264037686,1.109982778464842,-1.314799057941425e1,2.137017065505111,-4.084082382904703,2.606486561845403e-1,1.565462612018858,-1.508309105065004,1.772442871757061e1,-2.40060893717649,6.31422909250156,-4.052444871368164e-1,3.179380137695096e-1,-3.071741522636364e-1,3.636264382483117,-5.183996466001354e-1,2.322192602480252,-6.467931586900172e-2,6.277081831671831e-1,-6.107890751034906e-1,7.335850436798604,-1.091016872160133,3.089218691662174,6.988892111841499e-2,1.639756762532723,-1.583883992641009,1.876236237708381e1,-2.685390559486947,5.859855615166555,3.919312696253764e-3,1.611803934956753,-1.540778869185931,1.795955382224485e1,-2.495154500270907,5.003492494640851,-4.157919873785453e-2,-6.213413520816026e-1,6.242581523412814e-1,-7.823535324240331,1.222418137438074,-3.120142966701915,2.975831327541895e-1,2.12230710100161,-2.0451058741188,2.412395225004063e1,-3.423544496956294,7.325914828631551,-4.793445914188063e-1,-4.31809447483846,4.158975059021769,-4.906211424150023e1,6.975058620124194,-1.501259943091044e1,9.418983630154896e-1,-6.138797742037704e-1,5.810969368378602e-1,-6.6821474226667,9.113864351863538e-1,-1.814400062103318,1.002574935832871e-1,-9.860044240994036e-2,9.448685284232805e-2,-1.106188847377502,1.552858946803229e-1,-3.265426230113952e-1,2.062042480203908e-2,-2.745034502159738,2.655226942873441,-3.151193386341271e1,4.520932327069998,-9.883338555855938,6.423439846307804e-1,2.139968493382333,-2.067738462547628,2.450223844197562e1,-3.50699574523559,7.635005983192545,-4.923960464980415e-1,1.036406872394752,-1.002008838408551,1.188339891704641e1,-1.70302259679446,3.715789696036691,-2.407301455417931e-1,1.606428513214277,-1.552524985439685,1.840245870449254e1,-2.635131753653705,5.741508438443495,-3.708346905830083e-1,5.659562678739624e-2,-5.465656201303744e-2,6.471932864664631e-1,-9.253169145609999e-2,2.010909570941804e-1,-1.292046400706276e-2,5.435391241988039e-1,-5.252672844681129e-1,6.225561585258754,-8.91344337215917e-1,1.941632399616401,-1.253426955105431e-1,-1.552116972709218,1.499962759958308,-1.777819805127299e1,2.545472086708348,-5.545140384142844,3.580057322157566e-1],[6,24]); +end +if nargout > 2 + t2 = [2.948906761778786e-1,1.525720623897707,2.57452876984127e-1,1.798113701499118,4.127080577601411e-1,1.278484623015873,9.232955798059965e-1,1.009333860859158]; + HcU = t2; +end +if nargout > 3 + HfU = t2; +end
--- a/+sbp/InterpAWW.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -classdef InterpAWW < sbp.InterpOps - properties - - % Interpolation operators - IC2F - IF2C - - % Orders used on coarse and fine sides - order_C - order_F - - % Grid points, refinement ratio. - ratio - m_C - m_F - - % Boundary accuracy of IC2F and IF2C. - acc_C2F - acc_F2C - end - - methods - % accOp : String, 'C2F' or 'F2C'. Specifies which of the operators - % should have higher accuracy. - function obj = InterpAWW(m_C,m_F,order_C,order_F,accOp) - assertIsMember(accOp, {'C2F','F2C'}); - - ratio = (m_F-1)/(m_C-1); - h_C = 1; - - assert(order_C == order_F,... - 'Error: Different orders of accuracy not available'); - - switch ratio - case 2 - switch order_C - case 2 - [IC2F,IF2C] = sbp.implementations.intOpAWW_orders_2to2_ratio2to1(m_C, h_C, accOp); - case 4 - [IC2F,IF2C] = sbp.implementations.intOpAWW_orders_4to4_ratio2to1(m_C, h_C, accOp); - case 6 - [IC2F,IF2C] = sbp.implementations.intOpAWW_orders_6to6_ratio2to1(m_C, h_C, accOp); - case 8 - [IC2F,IF2C] = sbp.implementations.intOpAWW_orders_8to8_ratio2to1(m_C, h_C, accOp); - otherwise - error(['Order ' num2str(order_C) ' not available.']); - end - otherwise - error(['Grid ratio ' num2str(ratio) ' not available']); - end - - obj.IC2F = IC2F; - obj.IF2C = IF2C; - obj.order_C = order_C; - obj.order_F = order_F; - obj.ratio = ratio; - obj.m_C = m_C; - obj.m_F = m_F; - - end - - function str = string(obj) - str = [class(obj) '_orders' num2str(obj.order_F) 'to'... - num2str(obj.order_C) '_ratio' num2str(obj.ratio) 'to1']; - end - - end -end
--- a/+sbp/InterpMC.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,61 +0,0 @@ -classdef InterpMC < sbp.InterpOps - properties - - % Interpolation operators - IC2F - IF2C - - % Orders used on coarse and fine sides - order_C - order_F - - % Grid points, refinement ratio. - ratio - m_C - m_F - end - - methods - function obj = InterpMC(m_C,m_F,order_C,order_F) - - ratio = (m_F-1)/(m_C-1); - - assert(order_C == order_F,... - 'Error: Different orders of accuracy not available'); - - switch ratio - case 2 - switch order_C - case 2 - [IC2F,IF2C] = sbp.implementations.intOpMC_orders_2to2_ratio2to1(m_C); - case 4 - [IC2F,IF2C] = sbp.implementations.intOpMC_orders_4to4_ratio2to1(m_C); - case 6 - [IC2F,IF2C] = sbp.implementations.intOpMC_orders_6to6_ratio2to1(m_C); - case 8 - [IC2F,IF2C] = sbp.implementations.intOpMC_orders_8to8_ratio2to1(m_C); - otherwise - error(['Order ' num2str(order_C) ' not available.']); - end - otherwise - error(['Grid ratio ' num2str(ratio) ' not available']); - end - - obj.IC2F = IC2F; - obj.IF2C = IF2C; - obj.order_C = order_C; - obj.order_F = order_F; - obj.ratio = ratio; - obj.m_C = m_C; - obj.m_F = m_F; - - - end - - function str = string(obj) - str = [class(obj) '_orders' num2str(obj.order_F) 'to'... - num2str(obj.order_C) '_ratio' num2str(obj.ratio) 'to1']; - end - - end -end
--- a/+sbp/InterpOps.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+sbp/InterpOps.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,9 +1,7 @@ classdef (Abstract) InterpOps properties (Abstract) - % C and F may refer to coarse and fine, but it's not a must. - IC2F % Interpolation operator from "C" to "F" - IF2C % Interpolation operator from "F" to "C" - + Iu2v % Interpolation operator(s) from "u" to "v" + Iv2u % Interpolation operator(s) from "v" to "u" end methods (Abstract)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/InterpOpsMC.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,78 @@ +% Interpolation operators by Mattsson and Carpenter (MC), see +% Mattsson and Carpenter, +% "Stable and Accurate Interpolatino Operators for High-Order Multiblock Finite DIfference Methods", +% https://epubs.siam.org/doi/pdf/10.1137/090750068 +% +% Let ^* denote the adjoint. These operators satsify +% +% Iuv2 = Iv2u^* +% +% Both Iu2v and Iv2u have p:th order accuracy, if the interior stencil is +% of order 2p. +% +% This approach leads to a reduction of the convergence rate by one order for +% PDEs with 2nd derivatives in space, as compared to conforming interfaces. +% To obtain full convergence rate, use the order-preserving (OP) operators in +% InterpOpsOP.m +classdef InterpOpsMC < sbp.InterpOps + properties + + % Structs of interpolation operators, fields .good and .bad + % Here .good and .bad are the same, but this makes them fit in the + % OP (order-preserving) framework. + Iu2v + Iv2u + end + + methods + % m_u, m_v -- number of grid points along the interface + % order_u, order_v -- order of accuracy in the different blocks + function obj = InterpOpsMC(m_u, m_v, order_u, order_v) + + assert(order_u == order_v,... + 'InterpOpsMC: Different orders of accuracy not available'); + + switch order_u + case 2 + intOpSet = @sbp.implementations.intOpMC_orders_2to2_ratio2to1; + case 4 + intOpSet = @sbp.implementations.intOpMC_orders_4to4_ratio2to1; + case 6 + intOpSet = @sbp.implementations.intOpMC_orders_6to6_ratio2to1; + case 8 + intOpSet = @sbp.implementations.intOpMC_orders_8to8_ratio2to1; + otherwise + error('InterpOpsMC: Order of accuracy %d not available.', order_u); + end + + Iu2v = struct; + Iv2u = struct; + + if (m_u-1)/(m_v-1) == 2 + % Block u is fine, v is coarse + m_C = m_v; + [Iv2u.good, Iu2v.bad] = intOpSet(m_C); + Iv2u.bad = Iv2u.good; + Iu2v.good = Iu2v.bad; + + elseif (m_v-1)/(m_u-1) == 2 + % Block v is fine, u is coarse + m_C = m_u; + [Iu2v.good, Iv2u.bad] = intOpSet(m_C); + Iu2v.bad = Iu2v.good; + Iv2u.good = Iv2u.bad; + else + error('InterpOpsMC: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1)); + end + + obj.Iu2v = Iu2v; + obj.Iv2u = Iv2u; + + end + + function str = string(obj) + str = [class(obj)]; + end + + end +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/InterpOpsOP.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,76 @@ +% Order-preserving (OP) interpolation operators, see +% Almquist, Wang, Werpers, +% "Order-Preserving Interpolation for Summation-by-Parts Operators +% at Non-Conforming Interfaces", https://arxiv.org/abs/1806.01931 +% +% Let ^* denote the adjoint. These operators satsify +% +% Iuv2.good = Iv2u.bad^* +% Iv2u.good = Iu2v.bad^* +% +% The .bad operators have the same order of accuracy as the operators +% by Mattsson and Carpenter (MC) in InterpOpsMC, i.e. order p, +% if the interior stencil is order 2p. The .good operators are +% one order more accurate, i.e. order p+1. +% +% For PDEs of second order in space, the OP operators allow for the same +% convergence rate as with conforming interfaces, which is an improvement +% by one order compared what is possible with the MC operators. +classdef InterpOpsOP < sbp.InterpOps + properties + + % Structs of interpolation operators, fields .good and .bad + Iu2v + Iv2u + end + + methods + % m_u, m_v -- number of grid points along the interface + % order_u, order_v -- order of accuracy in the different blocks + function obj = InterpOpsOP(m_u, m_v, order_u, order_v) + + assert(order_u == order_v,... + 'InterpOpsOP: Different orders of accuracy not available'); + + switch order_u + case 2 + intOpSet = @sbp.implementations.intOpOP_orders_2to2_ratio2to1; + case 4 + intOpSet = @sbp.implementations.intOpOP_orders_4to4_ratio2to1; + case 6 + intOpSet = @sbp.implementations.intOpOP_orders_6to6_ratio2to1; + case 8 + intOpSet = @sbp.implementations.intOpOP_orders_8to8_ratio2to1; + otherwise + error('InterpOpsOP: Order of accuracy %d not available.', order_u); + end + + Iu2v = struct; + Iv2u = struct; + + if (m_u-1)/(m_v-1) == 2 + % Block u is fine, v is coarse + m_C = m_v; + [Iv2u.good, Iu2v.bad] = intOpSet(m_C, 1, 'C2F'); + [Iv2u.bad, Iu2v.good] = intOpSet(m_C, 1, 'F2C'); + + elseif (m_v-1)/(m_u-1) == 2 + % Block v is fine, u is coarse + m_C = m_u; + [Iu2v.good, Iv2u.bad] = intOpSet(m_C, 1, 'C2F'); + [Iu2v.bad, Iv2u.good] = intOpSet(m_C, 1, 'F2C'); + else + error('InterpOpsOP: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1)); + end + + obj.Iu2v = Iu2v; + obj.Iv2u = Iv2u; + + end + + function str = string(obj) + str = [class(obj)]; + end + + end +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/+bc/closureSetup.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,25 @@ +% Setup closure and penalty matrices for several boundary conditions at once. +% Each bc is a struct with the fields +% * type -- Type of boundary condition +% * boundary -- Boundary identifier +% * data -- A function_handle for a function which provides boundary data.(see below) +% Also takes S_sign which modifies the sign of the penalty function, [-1,1] +% Returns a closure matrix and a penalty matrices for each boundary condition. +% +% The boundary data function can either be a function of time or a function of time and space coordinates. +% In the case where it only depends on time it should return the data as grid function for the boundary. +% In the case where it also takes space coordinates the number of space coordinates should match the number of dimensions of the problem domain. +% For example in the 2D case: f(t,x,y). +function [closure, penalties] = closureSetup(diffOp, bcs) + scheme.bc.verifyFormat(bcs, diffOp); + + % Setup storage arrays + closure = spzeros(size(diffOp)); + penalties = cell(1, length(bcs)); + + % Collect closures and penalties + for i = 1:length(bcs) + [localClosure, penalties{i}] = diffOp.boundary_condition(bcs{i}.boundary, bcs{i}.type); + closure = closure + localClosure; + end +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/+bc/forcingSetup.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,86 @@ +% Setup the forcing function for the given boundary conditions and data. +% Each bc is a struct with the fields +% * type -- Type of boundary condition +% * boundary -- Boundary identifier +% * data -- A function_handle for a function which provides boundary data.(see below) +% S_sign allows changing the sign of the function to put on different sides in the system of ODEs. +% default is 1, which the same side as the diffOp. +% Returns a forcing function S. +% +% The boundary data function can either be a function of time or a function of time and space coordinates. +% In the case where it only depends on time it should return the data as grid function for the boundary. +% In the case where it also takes space coordinates the number of space coordinates should match the number of dimensions of the problem domain. +% For example in the 2D case: f(t,x,y). + +function S = forcingSetup(diffOp, penalties, bcs, S_sign) + default_arg('S_sign', 1); + + assertType(bcs, 'cell'); + assertIsMember(S_sign, [1, -1]); + + scheme.bc.verifyFormat(bcs, diffOp); + + [gridData, symbolicData] = parseAndSortData(bcs, penalties, diffOp); + + % Setup penalty function + O = spzeros(size(diffOp),1); + function v = S_fun(t) + v = O; + for i = 1:length(gridData) + v = v + gridData{i}.penalty*gridData{i}.func(t); + end + + for i = 1:length(symbolicData) + v = v + symbolicData{i}.penalty*symbolicData{i}.func(t, symbolicData{i}.coords{:}); + end + + v = S_sign * v; + end + S = @S_fun; +end + +% Go through a cell array of boundary condition specifications and return cell arrays +% of structs for grid and symbolic data. +function [gridData, symbolicData] = parseAndSortData(bcs, penalties, diffOp) + gridData = {}; + symbolicData = {}; + for i = 1:length(bcs) + [ok, isSymbolic, data] = parseData(bcs{i}, penalties{i}, diffOp.grid); + + if ~ok + continue % There was no data + end + + if isSymbolic + symbolicData{end+1} = data; + else + gridData{end+1} = data; + end + end +end + +function [ok, isSymbolic, dataStruct] = parseData(bc, penalty, grid) + if ~isfield(bc,'data') || isempty(bc.data) + isSymbolic = []; + dataStruct = struct(); + ok = false; + return + end + ok = true; + + nArg = nargin(bc.data); + + if nArg > 1 + % Symbolic data + isSymbolic = true; + coord = grid.getBoundary(bc.boundary); + dataStruct.penalty = penalty; + dataStruct.func = bc.data; + dataStruct.coords = num2cell(coord, 1); + else + % Grid data + isSymbolic = false; + dataStruct.penalty = penalty; + dataStruct.func = bc.data; + end +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/+bc/verifyFormat.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,31 @@ +% Errors with a more or less detailed error message if there is a problem with the bc specification +function verifyBcFormat(bcs, diffOp) + assertType(bcs, 'cell'); + for i = 1:length(bcs) + assertType(bcs{i}, 'struct'); + assertStructFields(bcs{i}, {'type', 'boundary'}); + + if ~isfield(bcs{i}, 'data') || isempty(bcs{i}.data) + continue + end + + if ~isa(bcs{i}.data, 'function_handle') + error('bcs{%d}.data should be a function of time or a function of time and space',i); + end + + % Find dimension of boundary + b = diffOp.grid.getBoundary(bcs{i}.boundary); + dim = size(b,2); + + % Assert that the data function has a valid number of input arguments + if ~(nargin(bcs{i}.data) == 1 || nargin(bcs{i}.data) == 1 + dim) + error('sbplib:scheme:bcSetup:DataWrongNumberOfArguments', 'bcs{%d}.data has the wrong number of input arguments. Must be either only time or time and space.', i); + end + + if nargin(bcs{i}.data) == 1 + % Grid data (only function of time) + % Assert that the data has the correct dimension + assertSize(bcs{i}.data(0), 1, size(b,1)); + end + end +end
--- a/+scheme/Beam.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Beam.m Tue Feb 12 17:12:42 2019 +0100 @@ -19,7 +19,7 @@ alphaII alphaIII - opt + opt % TODO: Get rid of this and use the interface type instead end methods @@ -86,7 +86,11 @@ function [closure, penalty] = boundary_condition(obj,boundary,type) default_arg('type','dn'); - [e, d1, d2, d3, s] = obj.get_boundary_ops(boundary); + e = obj.getBoundaryOperator('e', boundary); + d1 = obj.getBoundaryOperator('d1', boundary); + d2 = obj.getBoundaryOperator('d2', boundary); + d3 = obj.getBoundaryOperator('d3', boundary); + s = obj.getBoundarySign(boundary); gamm = obj.gamm; delt = obj.delt; @@ -124,7 +128,7 @@ closure = obj.Hi*(tau*d2' + sig*d3'); penalty{1} = -obj.Hi*tau; - penalty{1} = -obj.Hi*sig; + penalty{2} = -obj.Hi*sig; case 'e' alpha = obj.alpha; @@ -170,17 +174,24 @@ end end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary, type) % u denotes the solution in the own domain % v denotes the solution in the neighbour domain - [e_u,d1_u,d2_u,d3_u,s_u] = obj.get_boundary_ops(boundary); - [e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); + e_u = obj.getBoundaryOperator('e', boundary); + d1_u = obj.getBoundaryOperator('d1', boundary); + d2_u = obj.getBoundaryOperator('d2', boundary); + d3_u = obj.getBoundaryOperator('d3', boundary); + s_u = obj.getBoundarySign(boundary); + e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + d1_v = neighbour_scheme.getBoundaryOperator('d1', neighbour_boundary); + d2_v = neighbour_scheme.getBoundaryOperator('d2', neighbour_boundary); + d3_v = neighbour_scheme.getBoundaryOperator('d3', neighbour_boundary); + s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); alpha_u = obj.alpha; alpha_v = neighbour_scheme.alpha; - switch boundary case 'l' interface_opt = obj.opt.interface_l; @@ -234,24 +245,37 @@ penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v'); end - % Returns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e, d1, d2, d3, s] = get_boundary_ops(obj,boundary) + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string + % boundary -- string + function o = getBoundaryOperator(obj, op, boundary) + assertIsMember(op, {'e', 'd1', 'd2', 'd3'}) + assertIsMember(boundary, {'l', 'r'}) + + o = obj.([op, '_', boundary]); + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + % Note: for 1d diffOps, the boundary quadrature is the scalar 1. + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + H_b = 1; + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + switch boundary - case 'l' - e = obj.e_l; - d1 = obj.d1_l; - d2 = obj.d2_l; - d3 = obj.d3_l; + case {'r'} + s = 1; + case {'l'} s = -1; - case 'r' - e = obj.e_r; - d1 = obj.d1_r; - d2 = obj.d2_r; - d3 = obj.d3_r; - s = 1; - otherwise - error('No such boundary: boundary = %s',boundary); end end
--- a/+scheme/Beam2d.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,245 +0,0 @@ -classdef Beam2d < scheme.Scheme - properties - grid - order % Order accuracy for the approximation - - D % non-stabalized scheme operator - M % Derivative norm - alpha - - H % Discrete norm - Hi - H_x, H_y % Norms in the x and y directions - Hx,Hy % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. - Hi_x, Hi_y - Hix, Hiy - e_w, e_e, e_s, e_n - d1_w, d1_e, d1_s, d1_n - d2_w, d2_e, d2_s, d2_n - d3_w, d3_e, d3_s, d3_n - gamm_x, gamm_y - delt_x, delt_y - end - - methods - function obj = Beam2d(m,lim,order,alpha,opsGen) - default_arg('alpha',1); - default_arg('opsGen',@sbp.Higher); - - if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 2 - error('Grid must be 2d cartesian'); - end - - obj.grid = grid; - obj.alpha = alpha; - obj.order = order; - - m_x = grid.m(1); - m_y = grid.m(2); - - h = grid.scaling(); - h_x = h(1); - h_y = h(2); - - ops_x = opsGen(m_x,h_x,order); - ops_y = opsGen(m_y,h_y,order); - - I_x = speye(m_x); - I_y = speye(m_y); - - D4_x = sparse(ops_x.derivatives.D4); - H_x = sparse(ops_x.norms.H); - Hi_x = sparse(ops_x.norms.HI); - e_l_x = sparse(ops_x.boundary.e_1); - e_r_x = sparse(ops_x.boundary.e_m); - d1_l_x = sparse(ops_x.boundary.S_1); - d1_r_x = sparse(ops_x.boundary.S_m); - d2_l_x = sparse(ops_x.boundary.S2_1); - d2_r_x = sparse(ops_x.boundary.S2_m); - d3_l_x = sparse(ops_x.boundary.S3_1); - d3_r_x = sparse(ops_x.boundary.S3_m); - - D4_y = sparse(ops_y.derivatives.D4); - H_y = sparse(ops_y.norms.H); - Hi_y = sparse(ops_y.norms.HI); - e_l_y = sparse(ops_y.boundary.e_1); - e_r_y = sparse(ops_y.boundary.e_m); - d1_l_y = sparse(ops_y.boundary.S_1); - d1_r_y = sparse(ops_y.boundary.S_m); - d2_l_y = sparse(ops_y.boundary.S2_1); - d2_r_y = sparse(ops_y.boundary.S2_m); - d3_l_y = sparse(ops_y.boundary.S3_1); - d3_r_y = sparse(ops_y.boundary.S3_m); - - - D4 = kr(D4_x, I_y) + kr(I_x, D4_y); - - % Norms - obj.H = kr(H_x,H_y); - obj.Hx = kr(H_x,I_x); - obj.Hy = kr(I_x,H_y); - obj.Hix = kr(Hi_x,I_y); - obj.Hiy = kr(I_x,Hi_y); - obj.Hi = kr(Hi_x,Hi_y); - - % Boundary operators - obj.e_w = kr(e_l_x,I_y); - obj.e_e = kr(e_r_x,I_y); - obj.e_s = kr(I_x,e_l_y); - obj.e_n = kr(I_x,e_r_y); - obj.d1_w = kr(d1_l_x,I_y); - obj.d1_e = kr(d1_r_x,I_y); - obj.d1_s = kr(I_x,d1_l_y); - obj.d1_n = kr(I_x,d1_r_y); - obj.d2_w = kr(d2_l_x,I_y); - obj.d2_e = kr(d2_r_x,I_y); - obj.d2_s = kr(I_x,d2_l_y); - obj.d2_n = kr(I_x,d2_r_y); - obj.d3_w = kr(d3_l_x,I_y); - obj.d3_e = kr(d3_r_x,I_y); - obj.d3_s = kr(I_x,d3_l_y); - obj.d3_n = kr(I_x,d3_r_y); - - obj.D = alpha*D4; - - obj.gamm_x = h_x*ops_x.borrowing.N.S2/2; - obj.delt_x = h_x^3*ops_x.borrowing.N.S3/2; - - obj.gamm_y = h_y*ops_y.borrowing.N.S2/2; - obj.delt_y = h_y^3*ops_y.borrowing.N.S3/2; - end - - - % Closure functions return the opertors applied to the own doamin to close the boundary - % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. - % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. - % type is a string specifying the type of boundary condition if there are several. - % data is a function returning the data that should be applied at the boundary. - % neighbour_scheme is an instance of Scheme that should be interfaced to. - % neighbour_boundary is a string specifying which boundary to interface to. - function [closure, penalty_e,penalty_d] = boundary_condition(obj,boundary,type,data) - default_arg('type','dn'); - default_arg('data',0); - - [e,d1,d2,d3,s,gamm,delt,halfnorm_inv] = obj.get_boundary_ops(boundary); - - switch type - % Dirichlet-neumann boundary condition - case {'dn'} - alpha = obj.alpha; - - % tau1 < -alpha^2/gamma - tuning = 1.1; - - tau1 = tuning * alpha/delt; - tau4 = s*alpha; - - sig2 = tuning * alpha/gamm; - sig3 = -s*alpha; - - tau = tau1*e+tau4*d3; - sig = sig2*d1+sig3*d2; - - closure = halfnorm_inv*(tau*e' + sig*d1'); - - pp_e = halfnorm_inv*tau; - pp_d = halfnorm_inv*sig; - switch class(data) - case 'double' - penalty_e = pp_e*data; - penalty_d = pp_d*data; - case 'function_handle' - penalty_e = @(t)pp_e*data(t); - penalty_d = @(t)pp_d*data(t); - otherwise - error('Wierd data argument!') - end - - % Unknown, boundary condition - otherwise - error('No such boundary condition: type = %s',type); - end - end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - % u denotes the solution in the own domain - % v denotes the solution in the neighbour domain - [e_u,d1_u,d2_u,d3_u,s_u,gamm_u,delt_u, halfnorm_inv] = obj.get_boundary_ops(boundary); - [e_v,d1_v,d2_v,d3_v,s_v,gamm_v,delt_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); - - tuning = 2; - - alpha_u = obj.alpha; - alpha_v = neighbour_scheme.alpha; - - tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning; - % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning; - tau4 = s_u*alpha_u/2; - - sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning; - sig3 = -s_u*alpha_u/2; - - phi2 = s_u*1/2; - - psi1 = -s_u*1/2; - - tau = tau1*e_u + tau4*d3_u; - sig = sig2*d1_u + sig3*d2_u ; - phi = phi2*d1_u ; - psi = psi1*e_u ; - - closure = halfnorm_inv*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u'); - penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v'); - end - - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e,d1,d2,d3,s,gamm, delt, halfnorm_inv] = get_boundary_ops(obj,boundary) - switch boundary - case 'w' - e = obj.e_w; - d1 = obj.d1_w; - d2 = obj.d2_w; - d3 = obj.d3_w; - s = -1; - gamm = obj.gamm_x; - delt = obj.delt_x; - halfnorm_inv = obj.Hix; - case 'e' - e = obj.e_e; - d1 = obj.d1_e; - d2 = obj.d2_e; - d3 = obj.d3_e; - s = 1; - gamm = obj.gamm_x; - delt = obj.delt_x; - halfnorm_inv = obj.Hix; - case 's' - e = obj.e_s; - d1 = obj.d1_s; - d2 = obj.d2_s; - d3 = obj.d3_s; - s = -1; - gamm = obj.gamm_y; - delt = obj.delt_y; - halfnorm_inv = obj.Hiy; - case 'n' - e = obj.e_n; - d1 = obj.d1_n; - d2 = obj.d2_n; - d3 = obj.d3_n; - s = 1; - gamm = obj.gamm_y; - delt = obj.delt_y; - halfnorm_inv = obj.Hiy; - otherwise - error('No such boundary: boundary = %s',boundary); - end - end - - function N = size(obj) - N = prod(obj.m); - end - - end -end
--- a/+scheme/Elastic2dCurvilinear.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Elastic2dCurvilinear.m Tue Feb 12 17:12:42 2019 +0100 @@ -3,12 +3,12 @@ % Discretizes the elastic wave equation in curvilinear coordinates. % % Untransformed equation: -% rho u_{i,tt} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i +% rho u_{i,tt} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i % % Transformed equation: -% J*rho u_{i,tt} = dk J b_ik lambda b_jl dl u_j -% + dk J b_jk mu b_il dl u_j -% + dk J b_jk mu b_jl dl u_i +% J*rho u_{i,tt} = dk J b_ik lambda b_jl dl u_j +% + dk J b_jk mu b_il dl u_j +% + dk J b_jk mu b_jl dl u_i % opSet should be cell array of opSets, one per dimension. This % is useful if we have periodic BC in one direction. @@ -49,7 +49,7 @@ e_l, e_r d1_l, d1_r % Normal derivatives at the boundary E % E{i}^T picks out component i - + H_boundary_l, H_boundary_r % Boundary inner products % Kroneckered norms and coefficients @@ -145,7 +145,7 @@ opSetMetric{1} = sbp.D2Variable(m(1), {0, xmax}, order); opSetMetric{2} = sbp.D2Variable(m(2), {0, ymax}, order); D1Metric{1} = kron(opSetMetric{1}.D1, I{2}); - D1Metric{2} = kron(I{1}, opSetMetric{2}.D1); + D1Metric{2} = kron(I{1}, opSetMetric{2}.D1); x_xi = D1Metric{1}*x; x_eta = D1Metric{2}*x; @@ -327,12 +327,12 @@ for m = 1:dim for l = 1:dim - T_l{j}{i,k} = T_l{j}{i,k} + ... + T_l{j}{i,k} = T_l{j}{i,k} + ... -d(k,l)* J*b{i,j}*b{k,m}*LAMBDA*(d(m,j)*e_l{m}*d1_l{m}' + db(m,j)*D1{m}) ... -d(k,l)* J*b{k,j}*b{i,m}*MU*(d(m,j)*e_l{m}*d1_l{m}' + db(m,j)*D1{m}) ... -d(i,k)* J*b{l,j}*b{l,m}*MU*(d(m,j)*e_l{m}*d1_l{m}' + db(m,j)*D1{m}); - T_r{j}{i,k} = T_r{j}{i,k} + ... + T_r{j}{i,k} = T_r{j}{i,k} + ... d(k,l)* J*b{i,j}*b{k,m}*LAMBDA*(d(m,j)*e_r{m}*d1_r{m}' + db(m,j)*D1{m}) + ... d(k,l)* J*b{k,j}*b{i,m}*MU*(d(m,j)*e_r{m}*d1_r{m}' + db(m,j)*D1{m}) + ... d(i,k)* J*b{l,j}*b{l,m}*MU*(d(m,j)*e_r{m}*d1_r{m}' + db(m,j)*D1{m}); @@ -340,7 +340,7 @@ end T_l{j}{i,k} = inv(beta{j})*T_l{j}{i,k}; - T_r{j}{i,k} = inv(beta{j})*T_r{j}{i,k}; + T_r{j}{i,k} = inv(beta{j})*T_r{j}{i,k}; tau_l{j}{i} = tau_l{j}{i} + T_l{j}{i,k}*E{k}'; tau_r{j}{i} = tau_r{j}{i} + T_r{j}{i,k}*E{k}'; @@ -387,7 +387,7 @@ % j is the coordinate direction of the boundary j = obj.get_boundary_number(boundary); - [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary); + [e, T, tau, H_gamma] = obj.getBoundaryOperator({'e','T','tau','H'}, boundary); E = obj.E; Hi = obj.Hi; @@ -423,20 +423,20 @@ db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta alpha = @(i,j) tuning*( d(i,j)* a_lambda*LAMBDA ... + d(i,j)* a_mu_i*MU ... - + db(i,j)*a_mu_ij*MU ); + + db(i,j)*a_mu_ij*MU ); % Loop over components that Dirichlet penalties end up on for i = 1:dim C = T{k,i}; A = -d(i,k)*alpha(i,j); B = A + C; - closure = closure + E{i}*RHOi*Hi*Ji*B'*e*H_gamma*(e'*E{k}' ); + closure = closure + E{i}*RHOi*Hi*Ji*B'*e*H_gamma*(e'*E{k}' ); penalty = penalty - E{i}*RHOi*Hi*Ji*B'*e*H_gamma; - end + end % Free boundary condition case {'F','f','Free','free','traction','Traction','t','T'} - closure = closure - E{k}*RHOi*Ji*Hi*e*H_gamma* (e'*tau{k} ); + closure = closure - E{k}*RHOi*Ji*Hi*e*H_gamma* (e'*tau{k} ); penalty = penalty + E{k}*RHOi*Ji*Hi*e*H_gamma; % Unknown boundary condition @@ -457,14 +457,14 @@ j_v = neighbour_scheme.get_boundary_number(neighbour_boundary); % Get boundary operators - [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary); - [e_v, tau_v] = neighbour_scheme.get_boundary_operator({'e','tau'}, neighbour_boundary); + [e, T, tau, H_gamma] = obj.getBoundaryOperator({'e','T','tau','H'}, boundary); + [e_v, tau_v] = neighbour_scheme.getBoundaryOperator({'e','tau'}, neighbour_boundary); % Operators and quantities that correspond to the own domain only Hi = obj.Hi; RHOi = obj.RHOi; dim = obj.dim; - + %--- Other operators ---- m_tot_u = obj.grid.N(); E = obj.E; @@ -480,7 +480,7 @@ lambda_v = e_v'*LAMBDA_v*e_v; mu_v = e_v'*MU_v*e_v; %------------------------- - + % Borrowing constants phi_u = obj.phi{j}; h_u = obj.h(j); @@ -493,7 +493,7 @@ gamma_v = neighbour_scheme.gamma{j_v}; % E > sum_i 1/(2*alpha_ij)*(tau_i)^2 - function [alpha_ii, alpha_ij] = computeAlpha(phi,h,h11,gamma,lambda,mu) + function [alpha_ii, alpha_ij] = computeAlpha(phi,h,h11,gamma,lambda,mu) th1 = h11/(2*dim); th2 = h11*phi/2; th3 = h*gamma; @@ -505,7 +505,7 @@ end [alpha_ii_u, alpha_ij_u] = computeAlpha(phi_u,h_u,h11_u,gamma_u,lambda_u,mu_u); - [alpha_ii_v, alpha_ij_v] = computeAlpha(phi_v,h_v,h11_v,gamma_v,lambda_v,mu_v); + [alpha_ii_v, alpha_ij_v] = computeAlpha(phi_v,h_v,h11_v,gamma_v,lambda_v,mu_v); sigma_ii = tuning*(alpha_ii_u + alpha_ii_v)/4; sigma_ij = tuning*(alpha_ij_u + alpha_ij_v)/4; @@ -527,9 +527,9 @@ % Loop over components that we have interface conditions on for k = 1:dim - closure = closure + 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e'*E{k}'; - penalty = penalty - 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e_v'*E_v{k}'; - end + closure = closure + 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e'*E{k}'; + penalty = penalty - 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e_v'*E_v{k}'; + end end end @@ -555,7 +555,7 @@ % Returns the boundary operator op for the boundary specified by the string boundary. % op: may be a cell array of strings - function [varargout] = get_boundary_operator(obj, op, boundary) + function [varargout] = getBoundaryOperator(obj, op, boundary) switch boundary case {'w','W','west','West', 'e', 'E', 'east', 'East'} @@ -587,7 +587,7 @@ varargout{i} = obj.d1_r{j}; end case 'H' - switch boundary + switch boundary case {'w','W','west','West','s','S','south','South'} varargout{i} = obj.H_boundary_l{j}; case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} @@ -606,7 +606,7 @@ varargout{i} = obj.tau_l{j}; case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} varargout{i} = obj.tau_r{j}; - end + end otherwise error(['No such operator: operator = ' op{i}]); end @@ -614,6 +614,27 @@ end + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'w'} + H = H_boundary_l{1}; + case 'e' + H = H_boundary_r{1}; + case 's' + H = H_boundary_l{2}; + case 'n' + H = H_boundary_r{2}; + end + I_dim = speye(obj.dim, obj.dim); + H = kron(H, I_dim); + end + function N = size(obj) N = obj.dim*prod(obj.m); end
--- a/+scheme/Elastic2dVariable.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Elastic2dVariable.m Tue Feb 12 17:12:42 2019 +0100 @@ -30,18 +30,10 @@ T_l, T_r tau_l, tau_r - H, Hi % Inner products - - phi % Borrowing constant for (d1 - e^T*D1) from R - gamma % Borrowing constant for d1 from M - H11 % First element of H + H, Hi, H_1D % Inner products + e_l, e_r - % Borrowing from H, M, and R - thH - thM - thR - e_l, e_r d1_l, d1_r % Normal derivatives at the boundary E % E{i}^T picks out component i @@ -50,22 +42,38 @@ % Kroneckered norms and coefficients RHOi_kron Hi_kron + + % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant. + theta_R % Borrowing (d1- D1)^2 from R + theta_H % First entry in norm matrix + theta_M % Borrowing d1^2 from M. + + % Structures used for adjoint optimization + B end methods - function obj = Elastic2dVariable(g ,order, lambda_fun, mu_fun, rho_fun, opSet) + % The coefficients can either be function handles or grid functions + function obj = Elastic2dVariable(g ,order, lambda, mu, rho, opSet) default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable}); - default_arg('lambda_fun', @(x,y) 0*x+1); - default_arg('mu_fun', @(x,y) 0*x+1); - default_arg('rho_fun', @(x,y) 0*x+1); + default_arg('lambda', @(x,y) 0*x+1); + default_arg('mu', @(x,y) 0*x+1); + default_arg('rho', @(x,y) 0*x+1); dim = 2; assert(isa(g, 'grid.Cartesian')) - lambda = grid.evalOn(g, lambda_fun); - mu = grid.evalOn(g, mu_fun); - rho = grid.evalOn(g, rho_fun); + if isa(lambda, 'function_handle') + lambda = grid.evalOn(g, lambda); + end + if isa(mu, 'function_handle') + mu = grid.evalOn(g, mu); + end + if isa(rho, 'function_handle') + rho = grid.evalOn(g, rho); + end + m = g.size(); m_tot = g.N(); @@ -87,15 +95,9 @@ % Borrowing constants for i = 1:dim - beta = ops{i}.borrowing.R.delta_D; - obj.H11{i} = ops{i}.borrowing.H11; - obj.phi{i} = beta/obj.H11{i}; - obj.gamma{i} = ops{i}.borrowing.M.d1; - - % Better names - obj.thR{i} = ops{i}.borrowing.R.delta_D; - obj.thM{i} = ops{i}.borrowing.M.d1; - obj.thH{i} = ops{i}.borrowing.H11; + obj.theta_R{i} = h(i)*ops{i}.borrowing.R.delta_D; + obj.theta_H{i} = h(i)*ops{i}.borrowing.H11; + obj.theta_M{i} = h(i)*ops{i}.borrowing.M.d1; end I = cell(dim,1); @@ -183,6 +185,7 @@ obj.H_boundary = cell(dim,1); obj.H_boundary{1} = H{2}; obj.H_boundary{2} = H{1}; + obj.H_1D = {H{1}, H{2}}; % E{i}^T picks out component i. E = cell(dim,1); @@ -213,7 +216,7 @@ end end obj.D = D; - %=========================================% + %=========================================%' % Numerical traction operators for BC. % Because d1 =/= e0^T*D1, the numerical tractions are different @@ -237,20 +240,28 @@ tau_l{j} = cell(dim,1); tau_r{j} = cell(dim,1); + LAMBDA_l = e_l{j}'*LAMBDA*e_l{j}; + LAMBDA_r = e_r{j}'*LAMBDA*e_r{j}; + MU_l = e_l{j}'*MU*e_l{j}; + MU_r = e_r{j}'*MU*e_r{j}; + + [~, n_l] = size(e_l{j}); + [~, n_r] = size(e_r{j}); + % Loop over components for i = 1:dim - tau_l{j}{i} = sparse(m_tot,dim*m_tot); - tau_r{j}{i} = sparse(m_tot,dim*m_tot); + tau_l{j}{i} = sparse(n_l, dim*m_tot); + tau_r{j}{i} = sparse(n_r, dim*m_tot); for k = 1:dim T_l{j}{i,k} = ... - -d(i,j)*LAMBDA*(d(i,k)*e_l{k}*d1_l{k}' + db(i,k)*D1{k})... - -d(j,k)*MU*(d(i,j)*e_l{i}*d1_l{i}' + db(i,j)*D1{i})... - -d(i,k)*MU*e_l{j}*d1_l{j}'; + -d(i,j)*LAMBDA_l*(d(i,k)*d1_l{j}' + db(i,k)*e_l{j}'*D1{k})... + -d(j,k)*MU_l*(d(i,j)*d1_l{j}' + db(i,j)*e_l{j}'*D1{i})... + -d(i,k)*MU_l*d1_l{j}'; T_r{j}{i,k} = ... - d(i,j)*LAMBDA*(d(i,k)*e_r{k}*d1_r{k}' + db(i,k)*D1{k})... - +d(j,k)*MU*(d(i,j)*e_r{i}*d1_r{i}' + db(i,j)*D1{i})... - +d(i,k)*MU*e_r{j}*d1_r{j}'; + d(i,j)*LAMBDA_r*(d(i,k)*d1_r{j}' + db(i,k)*e_r{j}'*D1{k})... + +d(j,k)*MU_r*(d(i,j)*d1_r{j}' + db(i,j)*e_r{j}'*D1{i})... + +d(i,k)*MU_r*d1_r{j}'; tau_l{j}{i} = tau_l{j}{i} + T_l{j}{i,k}*E{k}'; tau_r{j}{i} = tau_r{j}{i} + T_r{j}{i,k}*E{k}'; @@ -258,6 +269,19 @@ end end + + % Transpose T and tau to match boundary operator convention + for i = 1:dim + for j = 1:dim + tau_l{i}{j} = transpose(tau_l{i}{j}); + tau_r{i}{j} = transpose(tau_r{i}{j}); + for k = 1:dim + T_l{i}{j,k} = transpose(T_l{i}{j,k}); + T_r{i}{j,k} = transpose(T_r{i}{j,k}); + end + end + end + obj.T_l = T_l; obj.T_r = T_r; obj.tau_l = tau_l; @@ -275,6 +299,44 @@ obj.grid = g; obj.dim = dim; + % B, used for adjoint optimization + B = cell(dim, 1); + for i = 1:dim + B{i} = cell(m_tot, 1); + end + + for i = 1:dim + for j = 1:m_tot + B{i}{j} = sparse(m_tot, m_tot); + end + end + + ind = grid.funcToMatrix(g, 1:m_tot); + + % Direction 1 + for k = 1:m(1) + c = sparse(m(1),1); + c(k) = 1; + [~, B_1D] = ops{1}.D2(c); + for l = 1:m(2) + p = ind(:,l); + B{1}{(k-1)*m(2) + l}(p, p) = B_1D; + end + end + + % Direction 2 + for k = 1:m(2) + c = sparse(m(2),1); + c(k) = 1; + [~, B_1D] = ops{2}.D2(c); + for l = 1:m(1) + p = ind(l,:); + B{2}{(l-1)*m(2) + k}(p, p) = B_1D; + end + end + + obj.B = B; + end @@ -295,7 +357,8 @@ % j is the coordinate direction of the boundary j = obj.get_boundary_number(boundary); - [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary); + [e, T, tau, H_gamma] = obj.getBoundaryOperator({'e','T','tau','H'}, boundary); + E = obj.E; Hi = obj.Hi; @@ -316,33 +379,20 @@ % Dirichlet boundary condition case {'D','d','dirichlet','Dirichlet'} - phi = obj.phi{j}; - h = obj.h(j); - h11 = obj.H11{j}*h; - gamma = obj.gamma{j}; - - a_lambda = dim/h11 + 1/(h11*phi); - a_mu_i = 2/(gamma*h); - a_mu_ij = 2/h11 + 1/(h11*phi); - - d = @kroneckerDelta; % Kronecker delta - db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta - alpha = @(i,j) tuning*( d(i,j)* a_lambda*LAMBDA ... - + d(i,j)* a_mu_i*MU ... - + db(i,j)*a_mu_ij*MU ); + alpha = obj.getBoundaryOperator('alpha', boundary); % Loop over components that Dirichlet penalties end up on for i = 1:dim - C = T{k,i}; - A = -d(i,k)*alpha(i,j); - B = A + C; + C = transpose(T{k,i}); + A = -tuning*e*transpose(alpha{i,k}); + B = A + e*C; closure = closure + E{i}*RHOi*Hi*B'*e*H_gamma*(e'*E{k}' ); penalty = penalty - E{i}*RHOi*Hi*B'*e*H_gamma; end % Free boundary condition case {'F','f','Free','free','traction','Traction','t','T'} - closure = closure - E{k}*RHOi*Hi*e*H_gamma* (e'*tau{k} ); + closure = closure - E{k}*RHOi*Hi*e*H_gamma*tau{k}'; penalty = penalty + E{k}*RHOi*Hi*e*H_gamma; % Unknown boundary condition @@ -351,160 +401,216 @@ end end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + % type Struct that specifies the interface coupling. + % Fields: + % -- tuning: penalty strength, defaults to 1.2 + % -- interpolation: type of interpolation, default 'none' + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + defaultType.tuning = 1.2; + defaultType.interpolation = 'none'; + default_struct('type', defaultType); + + switch type.interpolation + case {'none', ''} + [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type); + case {'op','OP'} + [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type); + otherwise + error('Unknown type of interpolation: %s ', type.interpolation); + end + end + + function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type) + tuning = type.tuning; + % u denotes the solution in the own domain % v denotes the solution in the neighbour domain % Operators without subscripts are from the own domain. - tuning = 1.2; - - % j is the coordinate direction of the boundary - j = obj.get_boundary_number(boundary); - j_v = neighbour_scheme.get_boundary_number(neighbour_boundary); % Get boundary operators - [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary); - [e_v, tau_v] = neighbour_scheme.get_boundary_operator({'e','tau'}, neighbour_boundary); + e = obj.getBoundaryOperator('e_tot', boundary); + tau = obj.getBoundaryOperator('tau_tot', boundary); + + e_v = neighbour_scheme.getBoundaryOperator('e_tot', neighbour_boundary); + tau_v = neighbour_scheme.getBoundaryOperator('tau_tot', neighbour_boundary); + + H_gamma = obj.getBoundaryQuadrature(boundary); % Operators and quantities that correspond to the own domain only - Hi = obj.Hi; - RHOi = obj.RHOi; - dim = obj.dim; - - %--- Other operators ---- - m_tot_u = obj.grid.N(); - E = obj.E; - LAMBDA_u = obj.LAMBDA; - MU_u = obj.MU; - lambda_u = e'*LAMBDA_u*e; - mu_u = e'*MU_u*e; + Hi = obj.Hi_kron; + RHOi = obj.RHOi_kron; - m_tot_v = neighbour_scheme.grid.N(); - E_v = neighbour_scheme.E; - LAMBDA_v = neighbour_scheme.LAMBDA; - MU_v = neighbour_scheme.MU; - lambda_v = e_v'*LAMBDA_v*e_v; - mu_v = e_v'*MU_v*e_v; - %------------------------- + % Penalty strength operators + alpha_u = 1/4*tuning*obj.getBoundaryOperator('alpha_tot', boundary); + alpha_v = 1/4*tuning*neighbour_scheme.getBoundaryOperator('alpha_tot', neighbour_boundary); - % Borrowing constants - h_u = obj.h(j); - thR_u = obj.thR{j}*h_u; - thM_u = obj.thM{j}*h_u; - thH_u = obj.thH{j}*h_u; - - h_v = neighbour_scheme.h(j_v); - thR_v = neighbour_scheme.thR{j_v}*h_v; - thH_v = neighbour_scheme.thH{j_v}*h_v; - thM_v = neighbour_scheme.thM{j_v}*h_v; + closure = -RHOi*Hi*e*H_gamma*(alpha_u' + alpha_v'*e_v*e'); + penalty = RHOi*Hi*e*H_gamma*(alpha_u'*e*e_v' + alpha_v'); - % alpha = penalty strength for normal component, beta for tangential - alpha_u = dim*lambda_u/(4*thH_u) + lambda_u/(4*thR_u) + mu_u/(2*thM_u); - alpha_v = dim*lambda_v/(4*thH_v) + lambda_v/(4*thR_v) + mu_v/(2*thM_v); - beta_u = mu_u/(2*thH_u) + mu_u/(4*thR_u); - beta_v = mu_v/(2*thH_v) + mu_v/(4*thR_v); - alpha = alpha_u + alpha_v; - beta = beta_u + beta_v; - - d = @kroneckerDelta; % Kronecker delta - db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta - strength = @(i,j) tuning*(d(i,j)*alpha + db(i,j)*beta); + closure = closure - 1/2*RHOi*Hi*e*H_gamma*tau'; + penalty = penalty - 1/2*RHOi*Hi*e*H_gamma*tau_v'; - % Preallocate - closure = sparse(dim*m_tot_u, dim*m_tot_u); - penalty = sparse(dim*m_tot_u, dim*m_tot_v); - - % Loop over components that penalties end up on - for i = 1:dim - closure = closure - E{i}*RHOi*Hi*e*strength(i,j)*H_gamma*e'*E{i}'; - penalty = penalty + E{i}*RHOi*Hi*e*strength(i,j)*H_gamma*e_v'*E_v{i}'; + closure = closure + 1/2*RHOi*Hi*tau*H_gamma*e'; + penalty = penalty - 1/2*RHOi*Hi*tau*H_gamma*e_v'; - closure = closure - 1/2*E{i}*RHOi*Hi*e*H_gamma*e'*tau{i}; - penalty = penalty - 1/2*E{i}*RHOi*Hi*e*H_gamma*e_v'*tau_v{i}; + end - % Loop over components that we have interface conditions on - for k = 1:dim - closure = closure + 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e'*E{k}'; - penalty = penalty - 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e_v'*E_v{k}'; - end - end + function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type) + error('Non-conforming interfaces not implemented yet.'); end % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. function [j, nj] = get_boundary_number(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} + case {'w', 'e'} j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} + case {'s', 'n'} j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); end switch boundary - case {'w','W','west','West','s','S','south','South'} + case {'w', 's'} nj = -1; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} + case {'e', 'n'} nj = 1; end end % Returns the boundary operator op for the boundary specified by the string boundary. - % op: may be a cell array of strings - function [varargout] = get_boundary_operator(obj, op, boundary) + % op -- string + % Only operators with name *_tot can be used with multiblock.DiffOp.getBoundaryOperator() + function [varargout] = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + assertIsMember(op, {'e', 'e_tot', 'd', 'T', 'tau', 'tau_tot', 'H', 'alpha', 'alpha_tot'}) switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} + case {'w', 'e'} j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} + case {'s', 'n'} j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); - end - - if ~iscell(op) - op = {op}; end - for i = 1:length(op) - switch op{i} - case 'e' - switch boundary - case {'w','W','west','West','s','S','south','South'} - varargout{i} = obj.e_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - varargout{i} = obj.e_r{j}; - end - case 'd' - switch boundary - case {'w','W','west','West','s','S','south','South'} - varargout{i} = obj.d1_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - varargout{i} = obj.d1_r{j}; + switch op + case 'e' + switch boundary + case {'w', 's'} + o = obj.e_l{j}; + case {'e', 'n'} + o = obj.e_r{j}; + end + + case 'e_tot' + e = obj.getBoundaryOperator('e', boundary); + I_dim = speye(obj.dim, obj.dim); + o = kron(e, I_dim); + + case 'd' + switch boundary + case {'w', 's'} + o = obj.d1_l{j}; + case {'e', 'n'} + o = obj.d1_r{j}; + end + + case 'T' + switch boundary + case {'w', 's'} + o = obj.T_l{j}; + case {'e', 'n'} + o = obj.T_r{j}; + end + + case 'tau' + switch boundary + case {'w', 's'} + o = obj.tau_l{j}; + case {'e', 'n'} + o = obj.tau_r{j}; + end + + case 'tau_tot' + [e, tau] = obj.getBoundaryOperator({'e', 'tau'}, boundary); + + I_dim = speye(obj.dim, obj.dim); + e_tot = kron(e, I_dim); + E = obj.E; + tau_tot = (e_tot'*E{1}*e*tau{1}')'; + for i = 2:obj.dim + tau_tot = tau_tot + (e_tot'*E{i}*e*tau{i}')'; + end + o = tau_tot; + + case 'H' + o = obj.H_boundary{j}; + + case 'alpha' + % alpha = alpha(i,j) is the penalty strength for displacement BC. + e = obj.getBoundaryOperator('e', boundary); + + LAMBDA = obj.LAMBDA; + MU = obj.MU; + + dim = obj.dim; + theta_R = obj.theta_R{j}; + theta_H = obj.theta_H{j}; + theta_M = obj.theta_M{j}; + + a_lambda = dim/theta_H + 1/theta_R; + a_mu_i = 2/theta_M; + a_mu_ij = 2/theta_H + 1/theta_R; + + d = @kroneckerDelta; % Kronecker delta + db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta + alpha = cell(obj.dim, obj.dim); + + alpha_func = @(i,j) d(i,j)* a_lambda*LAMBDA ... + + d(i,j)* a_mu_i*MU ... + + db(i,j)*a_mu_ij*MU; + for i = 1:obj.dim + for l = 1:obj.dim + alpha{i,l} = d(i,l)*alpha_func(i,j)*e; end - case 'H' - varargout{i} = obj.H_boundary{j}; - case 'T' - switch boundary - case {'w','W','west','West','s','S','south','South'} - varargout{i} = obj.T_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - varargout{i} = obj.T_r{j}; + end + + o = alpha; + + case 'alpha_tot' + % alpha = alpha(i,j) is the penalty strength for displacement BC. + [e, e_tot, alpha] = obj.getBoundaryOperator({'e', 'e_tot', 'alpha'}, boundary); + E = obj.E; + [m, n] = size(alpha{1,1}); + alpha_tot = sparse(m*obj.dim, n*obj.dim); + for i = 1:obj.dim + for l = 1:obj.dim + alpha_tot = alpha_tot + (e_tot'*E{i}*e*alpha{i,l}'*E{l}')'; end - case 'tau' - switch boundary - case {'w','W','west','West','s','S','south','South'} - varargout{i} = obj.tau_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - varargout{i} = obj.tau_r{j}; - end - otherwise - error(['No such operator: operator = ' op{i}]); - end + end + o = alpha_tot; end end + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'w','e'} + j = 1; + case {'s','n'} + j = 2; + end + H = obj.H_boundary{j}; + I_dim = speye(obj.dim, obj.dim); + H = kron(H, I_dim); + end + function N = size(obj) N = obj.dim*prod(obj.m); end
--- a/+scheme/Euler1d.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Euler1d.m Tue Feb 12 17:12:42 2019 +0100 @@ -201,7 +201,8 @@ % Enforces the boundary conditions % w+ = R*w- + g(t) function closure = boundary_condition(obj,boundary, type, varargin) - [e_s,e_S,s] = obj.get_boundary_ops(boundary); + [e_s, e_S] = obj.getBoundaryOperator({'e', 'E'}, boundary); + s = obj.getBoundarySign(boundary); % Boundary condition on form % w_in = R*w_out + g, where g is data @@ -232,7 +233,8 @@ % % Returns closure(q,g) function closure = boundary_condition_L(obj, boundary, L_fun, p_in) - [e_s,e_S,s] = obj.get_boundary_ops(boundary); + [e_s, e_S] = obj.getBoundaryOperator({'e', 'E'}, boundary); + s = obj.getBoundarySign(boundary); p_ot = 1:3; p_ot(p_in) = []; @@ -273,7 +275,8 @@ % Return closure(q,g) function closure = boundary_condition_char(obj,boundary) - [e_s,e_S,s] = obj.get_boundary_ops(boundary); + [e_s, e_S] = obj.getBoundaryOperator({'e', 'E'}, boundary); + s = obj.getBoundarySign(boundary); function o = closure_fun(q, w_data) q_s = e_S'*q; @@ -314,7 +317,7 @@ % Return closure(q,[v; p]) function closure = boundary_condition_inflow(obj, boundary) - [~,~,s] = obj.get_boundary_ops(boundary); + s = obj.getBoundarySign(boundary); switch s case -1 @@ -335,7 +338,7 @@ % Return closure(q, p) function closure = boundary_condition_outflow(obj, boundary) - [~,~,s] = obj.get_boundary_ops(boundary); + s = obj.getBoundarySign(boundary); switch s case -1 @@ -352,7 +355,7 @@ % Return closure(q,[v; rho]) function closure = boundary_condition_inflow_rho(obj, boundary) - [~,~,s] = obj.get_boundary_ops(boundary); + s = obj.getBoundarySign(boundary); switch s case -1 @@ -372,7 +375,7 @@ % Return closure(q,rho) function closure = boundary_condition_outflow_rho(obj, boundary) - [~,~,s] = obj.get_boundary_ops(boundary); + s = obj.getBoundarySign(boundary); switch s case -1 @@ -388,7 +391,8 @@ % Set wall boundary condition v = 0. function closure = boundary_condition_wall(obj,boundary) - [e_s,e_S,s] = obj.get_boundary_ops(boundary); + [e_s, e_S] = obj.getBoundaryOperator({'e', 'E'}, boundary); + s = obj.getBoundarySign(boundary); % Vill vi sätta penalty på karateristikan som är nära noll också eller vill % vi låta den vara fri? @@ -446,7 +450,7 @@ closure = @closure_fun; end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) error('NOT DONE') % u denotes the solution in the own domain % v denotes the solution in the neighbour domain @@ -478,18 +482,61 @@ penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v'); end - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e,E,s] = get_boundary_ops(obj,boundary) + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'l' + e = obj.e_l; + case 'r' + e = obj.e_r; + otherwise + error('No such boundary: boundary = %s',boundary); + end + varargout{i} = e; + + case 'E' + switch boundary + case 'l' + E = obj.e_L; + case 'r' + E = obj.e_R; + otherwise + error('No such boundary: boundary = %s',boundary); + end + varargout{i} = E; + end + end + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + % Note: for 1d diffOps, the boundary quadrature is the scalar 1. + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + H_b = 1; + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) switch boundary - case 'l' - e = obj.e_l; - E = obj.e_L; + case {'r'} + s = 1; + case {'l'} s = -1; - case 'r' - e = obj.e_r; - E = obj.e_R; - s = 1; otherwise error('No such boundary: boundary = %s',boundary); end
--- a/+scheme/Heat2dCurvilinear.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Heat2dCurvilinear.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,9 +1,9 @@ classdef Heat2dCurvilinear < scheme.Scheme % Discretizes the Laplacian with variable coefficent, curvilinear, -% in the Heat equation way (i.e., the discretization matrix is not necessarily +% in the Heat equation way (i.e., the discretization matrix is not necessarily % symmetric) -% u_t = div * (kappa * grad u ) +% u_t = div * (kappa * grad u ) % opSet should be cell array of opSets, one per dimension. This % is useful if we have periodic BC in one direction. @@ -29,9 +29,9 @@ e_l, e_r d1_l, d1_r % Normal derivatives at the boundary alpha % Vector of borrowing constants - + % Boundary inner products - H_boundary_l, H_boundary_r + H_boundary_l, H_boundary_r % Metric coefficients b % Cell matrix of size dim x dim @@ -109,7 +109,7 @@ opSetMetric{1} = sbp.D2Variable(m(1), {0, xmax}, order); opSetMetric{2} = sbp.D2Variable(m(2), {0, ymax}, order); D1Metric{1} = kron(opSetMetric{1}.D1, I{2}); - D1Metric{2} = kron(I{1}, opSetMetric{2}.D1); + D1Metric{2} = kron(I{1}, opSetMetric{2}.D1); x_xi = D1Metric{1}*x; x_eta = D1Metric{2}*x; @@ -157,7 +157,7 @@ % D2 coefficients kappa_coeff = cell(dim,dim); for j = 1:dim - obj.D2_kappa{j} = sparse(m_tot,m_tot); + obj.D2_kappa{j} = sparse(m_tot,m_tot); kappa_coeff{j} = sparse(m_tot,1); for i = 1:dim kappa_coeff{j} = kappa_coeff{j} + b{i,j}*J*b{i,j}*kappa; @@ -270,28 +270,20 @@ default_arg('symmetric', false); default_arg('tuning',1.2); - % j is the coordinate direction of the boundary - % nj: outward unit normal component. + % nj: outward unit normal component. % nj = -1 for west, south, bottom boundaries % nj = 1 for east, north, top boundaries - [j, nj] = obj.get_boundary_number(boundary); - switch nj - case 1 - e = obj.e_r{j}; - flux = obj.flux_r{j}; - H_gamma = obj.H_boundary_r{j}; - case -1 - e = obj.e_l{j}; - flux = obj.flux_l{j}; - H_gamma = obj.H_boundary_l{j}; - end + nj = obj.getBoundarySign(boundary); + + Hi = obj.Hi; + [e, flux] = obj.getBoundaryOperator({'e', 'flux'}, boundary); + H_gamma = obj.getBoundaryQuadrature(boundary); + alpha = obj.getBoundaryBorrowing(boundary); Hi = obj.Hi; Ji = obj.Ji; KAPPA = obj.KAPPA; - kappa_gamma = e'*KAPPA*e; - h = obj.h(j); - alpha = h*obj.alpha(j); + kappa_gamma = e'*KAPPA*e; switch type @@ -299,19 +291,19 @@ case {'D','d','dirichlet','Dirichlet'} if ~symmetric - closure = -Ji*Hi*flux'*e*H_gamma*(e' ); + closure = -Ji*Hi*flux'*e*H_gamma*(e' ); penalty = Ji*Hi*flux'*e*H_gamma; else closure = Ji*Hi*flux'*e*H_gamma*(e' )... - -tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma*(e' ) ; + -tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma*(e' ) ; penalty = -Ji*Hi*flux'*e*H_gamma ... +tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma; end % Normal flux boundary condition case {'N','n','neumann','Neumann'} - closure = -Ji*Hi*e*H_gamma*(e'*flux ); - penalty = Ji*Hi*e*H_gamma; + closure = -Ji*Hi*e*H_gamma*(e'*flux ); + penalty = Ji*Hi*e*H_gamma; % Unknown boundary condition otherwise @@ -325,57 +317,103 @@ error('Interface not implemented'); end - % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. - function [j, nj] = get_boundary_number(obj, boundary) + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) - switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} - j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} - j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); + if ~iscell(op) + op = {op}; end - switch boundary - case {'w','W','west','West','s','S','south','South'} - nj = -1; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - nj = 1; + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_l{1}; + case 'e' + e = obj.e_r{1}; + case 's' + e = obj.e_l{2}; + case 'n' + e = obj.e_r{2}; + end + varargout{i} = e; + + case 'd' + switch boundary + case 'w' + d = obj.d1_l{1}; + case 'e' + d = obj.d1_r{1}; + case 's' + d = obj.d1_l{2}; + case 'n' + d = obj.d1_r{2}; + end + varargout{i} = d; + + case 'flux' + switch boundary + case 'w' + flux = obj.flux_l{1}; + case 'e' + flux = obj.flux_r{1}; + case 's' + flux = obj.flux_l{2}; + case 'n' + flux = obj.flux_r{2}; + end + varargout{i} = flux; + end end end - % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. - function [return_op] = get_boundary_operator(obj, op, boundary) + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} - j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} - j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); - end - - switch op + case 'w' + H_b = obj.H_boundary_l{1}; case 'e' - switch boundary - case {'w','W','west','West','s','S','south','South'} - return_op = obj.e_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - return_op = obj.e_r{j}; - end - case 'd' - switch boundary - case {'w','W','west','West','s','S','south','South'} - return_op = obj.d1_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - return_op = obj.d1_r{j}; - end - otherwise - error(['No such operator: operatr = ' op]); + H_b = obj.H_boundary_r{1}; + case 's' + H_b = obj.H_boundary_l{2}; + case 'n' + H_b = obj.H_boundary_r{2}; end + end + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'e','n'} + s = 1; + case {'w','s'} + s = -1; + end + end + + % Returns borrowing constant gamma*h + % boundary -- string + function gamm = getBoundaryBorrowing(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'w','e'} + gamm = obj.h(1)*obj.alpha(1); + case {'s','n'} + gamm = obj.h(2)*obj.alpha(2); + end end function N = size(obj)
--- a/+scheme/Heat2dVariable.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Heat2dVariable.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,9 +1,9 @@ classdef Heat2dVariable < scheme.Scheme % Discretizes the Laplacian with variable coefficent, -% In the Heat equation way (i.e., the discretization matrix is not necessarily +% In the Heat equation way (i.e., the discretization matrix is not necessarily % symmetric) -% u_t = div * (kappa * grad u ) +% u_t = div * (kappa * grad u ) % opSet should be cell array of opSets, one per dimension. This % is useful if we have periodic BC in one direction. @@ -29,7 +29,7 @@ e_l, e_r d1_l, d1_r % Normal derivatives at the boundary alpha % Vector of borrowing constants - + H_boundary % Boundary inner products end @@ -162,26 +162,18 @@ default_arg('symmetric', false); default_arg('tuning',1.2); - % j is the coordinate direction of the boundary - % nj: outward unit normal component. + % nj: outward unit normal component. % nj = -1 for west, south, bottom boundaries % nj = 1 for east, north, top boundaries - [j, nj] = obj.get_boundary_number(boundary); - switch nj - case 1 - e = obj.e_r; - d = obj.d1_r; - case -1 - e = obj.e_l; - d = obj.d1_l; - end + nj = obj.getBoundarySign(boundary); Hi = obj.Hi; - H_gamma = obj.H_boundary{j}; + [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary); + H_gamma = obj.getBoundaryQuadrature(boundary); + alpha = obj.getBoundaryBorrowing(boundary); + KAPPA = obj.KAPPA; - kappa_gamma = e{j}'*KAPPA*e{j}; - h = obj.h(j); - alpha = h*obj.alpha(j); + kappa_gamma = e'*KAPPA*e; switch type @@ -189,19 +181,19 @@ case {'D','d','dirichlet','Dirichlet'} if ~symmetric - closure = -nj*Hi*d{j}*kappa_gamma*H_gamma*(e{j}' ); - penalty = nj*Hi*d{j}*kappa_gamma*H_gamma; + closure = -nj*Hi*d*kappa_gamma*H_gamma*(e' ); + penalty = nj*Hi*d*kappa_gamma*H_gamma; else - closure = nj*Hi*d{j}*kappa_gamma*H_gamma*(e{j}' )... - -tuning*2/alpha*Hi*e{j}*kappa_gamma*H_gamma*(e{j}' ) ; - penalty = -nj*Hi*d{j}*kappa_gamma*H_gamma ... - +tuning*2/alpha*Hi*e{j}*kappa_gamma*H_gamma; + closure = nj*Hi*d*kappa_gamma*H_gamma*(e' )... + -tuning*2/alpha*Hi*e*kappa_gamma*H_gamma*(e' ) ; + penalty = -nj*Hi*d*kappa_gamma*H_gamma ... + +tuning*2/alpha*Hi*e*kappa_gamma*H_gamma; end % Free boundary condition case {'N','n','neumann','Neumann'} - closure = -nj*Hi*e{j}*kappa_gamma*H_gamma*(d{j}' ); - penalty = Hi*e{j}*kappa_gamma*H_gamma; + closure = -nj*Hi*e*kappa_gamma*H_gamma*(d' ); + penalty = Hi*e*kappa_gamma*H_gamma; % penalty is for normal derivative and not for derivative, hence the sign. % Unknown boundary condition @@ -216,57 +208,90 @@ error('Interface not implemented'); end - % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. - function [j, nj] = get_boundary_number(obj, boundary) + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) - switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} - j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} - j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); + if ~iscell(op) + op = {op}; end - switch boundary - case {'w','W','west','West','s','S','south','South'} - nj = -1; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - nj = 1; + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_l{1}; + case 'e' + e = obj.e_r{1}; + case 's' + e = obj.e_l{2}; + case 'n' + e = obj.e_r{2}; + end + varargout{i} = e; + + case 'd' + switch boundary + case 'w' + d = obj.d1_l{1}; + case 'e' + d = obj.d1_r{1}; + case 's' + d = obj.d1_l{2}; + case 'n' + d = obj.d1_r{2}; + end + varargout{i} = d; + end end end - % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. - function [return_op] = get_boundary_operator(obj, op, boundary) + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) switch boundary - case {'w','W','west','West', 'e', 'E', 'east', 'East'} - j = 1; - case {'s','S','south','South', 'n', 'N', 'north', 'North'} - j = 2; - otherwise - error('No such boundary: boundary = %s',boundary); - end - - switch op + case 'w' + H_b = obj.H_boundary{1}; case 'e' - switch boundary - case {'w','W','west','West','s','S','south','South'} - return_op = obj.e_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - return_op = obj.e_r{j}; - end - case 'd' - switch boundary - case {'w','W','west','West','s','S','south','South'} - return_op = obj.d1_l{j}; - case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} - return_op = obj.d1_r{j}; - end - otherwise - error(['No such operator: operatr = ' op]); + H_b = obj.H_boundary{1}; + case 's' + H_b = obj.H_boundary{2}; + case 'n' + H_b = obj.H_boundary{2}; end + end + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'e','n'} + s = 1; + case {'w','s'} + s = -1; + end + end + + % Returns borrowing constant gamma*h + % boundary -- string + function gamm = getBoundaryBorrowing(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'w','e'} + gamm = obj.h(1)*obj.alpha(1); + case {'s','n'} + gamm = obj.h(2)*obj.alpha(2); + end end function N = size(obj)
--- a/+scheme/Hypsyst2d.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Hypsyst2d.m Tue Feb 12 17:12:42 2019 +0100 @@ -6,10 +6,10 @@ x,y % Grid X,Y % Values of x and y for each grid point order % Order accuracy for the approximation - + D % non-stabalized scheme operator A, B, E %Coefficient matrices - + H % Discrete norm % Norms in the x and y directions Hxi,Hyi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. @@ -17,65 +17,65 @@ e_w, e_e, e_s, e_n params %parameters for the coeficient matrice end - + methods %Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Eu function obj = Hypsyst2d(m, lim, order, A, B, E, params) default_arg('E', []) xlim = lim{1}; ylim = lim{2}; - + if length(m) == 1 m = [m m]; end - + obj.A=A; obj.B=B; obj.E=E; - + m_x = m(1); m_y = m(2); obj.params = params; - + ops_x = sbp.D2Standard(m_x,xlim,order); ops_y = sbp.D2Standard(m_y,ylim,order); - + obj.x = ops_x.x; obj.y = ops_y.x; - + obj.X = kr(obj.x,ones(m_y,1)); obj.Y = kr(ones(m_x,1),obj.y); - + Aevaluated = obj.evaluateCoefficientMatrix(A, obj.X, obj.Y); Bevaluated = obj.evaluateCoefficientMatrix(B, obj.X, obj.Y); Eevaluated = obj.evaluateCoefficientMatrix(E, obj.X, obj.Y); - + obj.n = length(A(obj.params,0,0)); - + I_n = eye(obj.n);I_x = speye(m_x); obj.I_x = I_x; I_y = speye(m_y); obj.I_y = I_y; - - + + D1_x = kr(I_n, ops_x.D1, I_y); obj.Hxi = kr(I_n, ops_x.HI, I_y); D1_y = kr(I_n, I_x, ops_y.D1); obj.Hyi = kr(I_n, I_x, ops_y.HI); - + obj.e_w = kr(I_n, ops_x.e_l, I_y); obj.e_e = kr(I_n, ops_x.e_r, I_y); obj.e_s = kr(I_n, I_x, ops_y.e_l); obj.e_n = kr(I_n, I_x, ops_y.e_r); - + obj.m = m; obj.h = [ops_x.h ops_y.h]; obj.order = order; - + obj.D = -Aevaluated*D1_x-Bevaluated*D1_y-Eevaluated; - + end - + % Closure functions return the opertors applied to the own doamin to close the boundary % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. @@ -92,18 +92,18 @@ error('No such boundary condition') end end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - error('An interface function does not exist yet'); + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + error('Not implemented'); end - + function N = size(obj) N = obj.m; end - + function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y) params = obj.params; - + if isa(mat,'function_handle') [rows,cols] = size(mat(params,0,0)); matVec = mat(params,X',Y'); @@ -116,7 +116,7 @@ cols = cols/side; end ret = cell(rows,cols); - + for ii = 1:rows for jj=1:cols ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side)); @@ -124,13 +124,13 @@ end ret = cell2mat(ret); end - + %Characteristic boundary conditions function [closure, penalty] = boundary_condition_char(obj,boundary) params = obj.params; x = obj.x; y = obj.y; - + switch boundary case {'w','W','west'} e_ = obj.e_w; @@ -164,7 +164,7 @@ pos = signVec(1); zeroval = signVec(2); neg = signVec(3); - + switch boundPos case {'l'} tau = sparse(obj.n*side,pos); @@ -180,16 +180,16 @@ penalty = -Hi*e_*V*tau*Vi_minus; end end - + % General boundary condition in the form Lu=g(x) function [closure,penalty] = boundary_condition_general(obj,boundary,L) params = obj.params; x = obj.x; y = obj.y; - + e_ = obj.getBoundaryOperator('e', boundary); + switch boundary case {'w','W','west'} - e_ = obj.e_w; mat = obj.A; boundPos = 'l'; Hi = obj.Hxi; @@ -197,7 +197,6 @@ L = obj.evaluateCoefficientMatrix(L,x(1),y); side = max(length(y)); case {'e','E','east'} - e_ = obj.e_e; mat = obj.A; boundPos = 'r'; Hi = obj.Hxi; @@ -205,7 +204,6 @@ L = obj.evaluateCoefficientMatrix(L,x(end),y); side = max(length(y)); case {'s','S','south'} - e_ = obj.e_s; mat = obj.B; boundPos = 'l'; Hi = obj.Hyi; @@ -213,19 +211,18 @@ L = obj.evaluateCoefficientMatrix(L,x,y(1)); side = max(length(x)); case {'n','N','north'} - e_ = obj.e_n; mat = obj.B; boundPos = 'r'; Hi = obj.Hyi; [V,Vi,D,signVec] = obj.matrixDiag(mat,x,y(end)); - L = obj.evaluateCoefficientMatrix(L,x,y(end)); + L = obj.evaluateCoefficientMatrix(L,x,y(end)); side = max(length(x)); end - + pos = signVec(1); zeroval = signVec(2); neg = signVec(3); - + switch boundPos case {'l'} tau = sparse(obj.n*side,pos); @@ -233,7 +230,7 @@ Vi_minus = Vi(pos+zeroval+1:obj.n*side,:); V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); - + tau(1:pos,:) = -abs(D(1:pos,1:pos)); R = -inv(L*V_plus)*(L*V_minus); closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; @@ -243,7 +240,7 @@ tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side)); Vi_plus = Vi(1:pos,:); Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:); - + V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); R = -inv(L*V_minus)*(L*V_plus); @@ -251,13 +248,13 @@ penalty = -Hi*e_*V*tau*inv(L*V_minus)*L; end end - + % Function that diagonalizes a symbolic matrix A as A=V*D*Vi % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign % [d+ ] % D = [ d0 ] % [ d-] - % signVec is a vector specifying the number of possitive, zero and negative eigenvalues of D + % signVec is a vector specifying the number of possitive, zero and negative eigenvalues of D function [V,Vi, D,signVec] = matrixDiag(obj,mat,x,y) params = obj.params; syms xs ys @@ -265,12 +262,12 @@ Vi = inv(V); xs = x; ys = y; - + side = max(length(x),length(y)); Dret = zeros(obj.n,side*obj.n); Vret = zeros(obj.n,side*obj.n); Viret = zeros(obj.n,side*obj.n); - + for ii = 1:obj.n for jj = 1:obj.n Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii)); @@ -278,7 +275,7 @@ Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii)); end end - + D = sparse(Dret); V = sparse(Vret); Vi = sparse(Viret); @@ -286,16 +283,65 @@ Vi = obj.evaluateCoefficientMatrix(Vi,x,y); D = obj.evaluateCoefficientMatrix(D,x,y); DD = diag(D); - + poseig = (DD>0); zeroeig = (DD==0); negeig = (DD<0); - + D = diag([DD(poseig); DD(zeroeig); DD(negeig)]); V = [V(:,poseig) V(:,zeroeig) V(:,negeig)]; Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)]; signVec = [sum(poseig),sum(zeroeig),sum(negeig)]; end - + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_w; + case 'e' + e = obj.e_e; + case 's' + e = obj.e_s; + case 'n' + e = obj.e_n; + end + varargout{i} = e; + end + end + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + e = obj.getBoundaryOperator('e', boundary); + + switch boundary + case 'w' + H_b = inv(e'*obj.Hyi*e); + case 'e' + H_b = inv(e'*obj.Hyi*e); + case 's' + H_b = inv(e'*obj.Hxi*e); + case 'n' + H_b = inv(e'*obj.Hxi*e); + end + end + end end \ No newline at end of file
--- a/+scheme/Hypsyst2dCurve.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Hypsyst2dCurve.m Tue Feb 12 17:12:42 2019 +0100 @@ -4,19 +4,19 @@ n % size of system h % Grid spacing X,Y % Values of x and y for each grid point - + J, Ji % Jacobaian and inverse Jacobian xi,eta Xi,Eta - + A,B X_eta, Y_eta X_xi,Y_xi order % Order accuracy for the approximation - + D % non-stabalized scheme operator Ahat, Bhat, E - + H % Discrete norm Hxii,Hetai % Kroneckerd norms in xi and eta. I_xi,I_eta, I_N, onesN @@ -24,93 +24,93 @@ index_w, index_e,index_s,index_n params % Parameters for the coeficient matrice end - - + + methods % Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Eu function obj = Hypsyst2dCurve(m, order, A, B, E, params, ti) default_arg('E', []) xilim = {0 1}; etalim = {0 1}; - + if length(m) == 1 m = [m m]; end obj.params = params; obj.A=A; obj.B=B; - + obj.Ahat=@(params,x,y,x_eta,y_eta)(A(params,x,y).*y_eta-B(params,x,y).*x_eta); obj.Bhat=@(params,x,y,x_xi,y_xi)(B(params,x,y).*x_xi-A(params,x,y).*y_xi); obj.E=@(params,x,y,~,~)E(params,x,y); - + m_xi = m(1); m_eta = m(2); m_tot=m_xi*m_eta; - + ops_xi = sbp.D2Standard(m_xi,xilim,order); ops_eta = sbp.D2Standard(m_eta,etalim,order); - + obj.xi = ops_xi.x; obj.eta = ops_eta.x; - + obj.Xi = kr(obj.xi,ones(m_eta,1)); obj.Eta = kr(ones(m_xi,1),obj.eta); - + obj.n = length(A(obj.params,0,0)); obj.onesN=ones(obj.n); - + obj.index_w=1:m_eta; - obj.index_e=(m_tot-m_e - + obj.index_e=(m_tot-m_e + metric_termsta+1):m_tot; obj.index_s=1:m_eta:(m_tot-m_eta+1); obj.index_n=(m_eta):m_eta:m_tot; - + I_n = eye(obj.n); I_xi = speye(m_xi); obj.I_xi = I_xi; I_eta = speye(m_eta); obj.I_eta = I_eta; - + D1_xi = kr(I_n, ops_xi.D1, I_eta); obj.Hxii = kr(I_n, ops_xi.HI, I_eta); D1_eta = kr(I_n, I_xi, ops_eta.D1); obj.Hetai = kr(I_n, I_xi, ops_eta.HI); - + obj.e_w = kr(I_n, ops_xi.e_l, I_eta); obj.e_e = kr(I_n, ops_xi.e_r, I_eta); obj.e_s = kr(I_n, I_xi, ops_eta.e_l); - obj.e_n = kr(I_n, I_xi, - + obj.e_n = kr(I_n, I_xi, + metric_termsops_eta.e_r); - + [X,Y] = ti.map(obj.xi,obj.eta); - + [x_xi,x_eta] = gridDerivatives(X,ops_xi.D1,ops_eta.D1); [y_xi,y_eta] = gridDerivatives(Y,ops_xi.D1, ops_eta.D1); - + obj.X = reshape(X,m_tot,1); obj.Y = reshape(Y,m_tot,1); obj.X_xi = reshape(x_xi,m_tot,1); obj.Y_xi = reshape(y_xi,m_tot,1); obj.X_eta = reshape(x_eta,m_tot,1); obj.Y_eta = reshape(y_eta,m_tot,1); - + Ahat_evaluated = obj.evaluateCoefficientMatrix(obj.Ahat, obj.X, obj.Y,obj.X_eta,obj.Y_eta); Bhat_evaluated = obj.evaluateCoefficientMatrix(obj.Bhat, obj.X, obj.Y,obj.X_xi,obj.Y_xi); E_evaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,[],[]); - + obj.m = m; obj.h = [ops_xi.h ops_eta.h]; obj.order = order; obj.J = obj.X_xi.*obj.Y_eta - obj.X_eta.*obj.Y_xi; obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot)); - + obj.D = obj.Ji*(-Ahat_evaluated*D1_xi-Bhat_evaluated*D1_eta)-E_evaluated; - + end - + % Closure functions return the opertors applied to the own doamin to close the boundary % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w',General boundary conditions'n','s'. @@ -127,18 +127,18 @@ error('No such boundary condition') end end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundaryGeneral boundary conditions) - error('An interface function does not exist yet'); + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + error('Not implemented'); end - + function N = size(obj) N = obj.m; end - + function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y,x_,y_) params = obj.params; - + if isa(mat,'function_handle') [rows,cols] = size(mat(params,0,0,0,0)); x_ = kr(obj.onesN,x_); @@ -152,7 +152,7 @@ side = max(length(X),length(Y)); cols = cols/side; end - + ret = cell(rows,cols); for ii = 1:rows for jj = 1:cols @@ -161,7 +161,7 @@ end ret = cell2mat(ret); end - + %Characteristic boundary conditions function [closure, penalty] = boundary_condition_char(obj,boundary) params = obj.params; @@ -169,42 +169,39 @@ Y = obj.Y; xi = obj.xi; eta = obj.eta; - + e_ = obj.getBoundaryOperator('e', boundary); + switch boundary case {'w','W','west'} - e_ = obj.e_w; mat = obj.Ahat; boundPos = 'l'; Hi = obj.Hxii; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_w),Y(obj.index_w),obj.X_eta(obj.index_w),obj.Y_eta(obj.index_w)); side = max(length(eta)); case {'e','E','east'} - e_ = obj.e_e; mat = obj.Ahat; boundPos = 'r'; Hi = obj.Hxii; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_e),Y(obj.index_e),obj.X_eta(obj.index_e),obj.Y_eta(obj.index_e)); side = max(length(eta)); case {'s','S','south'} - e_ = obj.e_s; mat = obj.Bhat; boundPos = 'l'; Hi = obj.Hetai; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_s),Y(obj.index_s),obj.X_xi(obj.index_s),obj.Y_xi(obj.index_s)); side = max(length(xi)); case {'n','N','north'} - e_ = obj.e_n; mat = obj.Bhat; boundPos = 'r'; Hi = obj.Hetai; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_n),Y(obj.index_n),obj.X_xi(obj.index_n),obj.Y_xi(obj.index_n)); side = max(length(xi)); end - + pos = signVec(1); zeroval = signVec(2); neg = signVec(3); - + switch boundPos case {'l'} tau = sparse(obj.n*side,pos); @@ -218,10 +215,10 @@ Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:); closure = Hi*e_*V*tau*Vi_minus*e_'; penalty = -Hi*e_*V*tau*Vi_minus; - end + end end - - + + % General boundary condition in the form Lu=g(x) function [closure,penalty] = boundary_condition_general(obj,boundary,L) params = obj.params; @@ -229,7 +226,7 @@ Y = obj.Y; xi = obj.xi; eta = obj.eta; - + switch boundary case {'w','W','west'} e_ = obj.e_w; @@ -237,7 +234,7 @@ boundPos = 'l'; Hi = obj.Hxii; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_w),Y(obj.index_w),obj.X_eta(obj.index_w),obj.Y_eta(obj.index_w)); - + Ji_vec = diag(obj.Ji); Ji = diag(Ji_vec(obj.index_w)); xi_x = Ji*obj.Y_eta(obj.index_w); @@ -250,7 +247,7 @@ boundPos = 'r'; Hi = obj.Hxii; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_e),Y(obj.index_e),obj.X_eta(obj.index_e),obj.Y_eta(obj.index_e)); - + Ji_vec = diag(obj.Ji); Ji = diag(Ji_vec(obj.index_e)); xi_x = Ji*obj.Y_eta(obj.index_e); @@ -263,7 +260,7 @@ boundPos = 'l'; Hi = obj.Hetai; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_s),Y(obj.index_s),obj.X_xi(obj.index_s),obj.Y_xi(obj.index_s)); - + Ji_vec = diag(obj.Ji); Ji = diag(Ji_vec(obj.index_s)); eta_x = Ji*obj.Y_xi(obj.index_s); @@ -276,7 +273,7 @@ boundPos = 'r'; Hi = obj.Hetai; [V,Vi,D,signVec] = obj.matrixDiag(mat,X(obj.index_n),Y(obj.index_n),obj.X_xi(obj.index_n),obj.Y_xi(obj.index_n)); - + Ji_vec = diag(obj.Ji); Ji = diag(Ji_vec(obj.index_n)); eta_x = Ji*obj.Y_xi(obj.index_n); @@ -284,11 +281,11 @@ L = obj.evaluateCoefficientMatrix(L,-eta_x,-eta_y,[],[]); side = max(length(xi)); end - + pos = signVec(1); zeroval = signVec(2); neg = signVec(3); - + switch boundPos case {'l'} tau = sparse(obj.n*side,pos); @@ -296,7 +293,7 @@ Vi_minus = Vi(pos+1:obj.n*side,:); V_plus = V(:,1:pos); V_minus = V(:,(pos)+1:obj.n*side); - + tau(1:pos,:) = -abs(D(1:pos,1:pos)); R = -inv(L*V_plus)*(L*V_minus); closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; @@ -306,7 +303,7 @@ tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side)); Vi_plus = Vi(1:pos,:); Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:); - + V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); R = -inv(L*V_minus)*(L*V_plus); @@ -314,7 +311,7 @@ penalty = -Hi*e_*V*tau*inv(L*V_minus)*L; end end - + % Function that diagonalizes a symbolic matrix A as A=V*D*Vi % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign % [d+ ] @@ -329,22 +326,22 @@ else xs_ = 0; end - + if(sum(abs(y_))~= 0) syms ys_; else ys_ = 0; end - + [V, D] = eig(mat(params,xs,ys,xs_,ys_)); Vi = inv(V); syms xs ys xs_ ys_ - + xs = x; ys = y; xs_ = x_; ys_ = y_; - + side = max(length(x),length(y)); Dret = zeros(obj.n,side*obj.n); Vret = zeros(obj.n,side*obj.n); @@ -356,7 +353,7 @@ Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii)); end end - + D = sparse(Dret); V = sparse(Vret); Vi = sparse(Viret); @@ -364,15 +361,66 @@ D = obj.evaluateCoefficientMatrix(D,x,y,x_,y_); Vi = obj.evaluateCoefficientMatrix(Vi,x,y,x_,y_); DD = diag(D); - + poseig = (DD>0); zeroeig = (DD==0); negeig = (DD<0); - + D = diag([DD(poseig); DD(zeroeig); DD(negeig)]); V = [V(:,poseig) V(:,zeroeig) V(:,negeig)]; Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)]; signVec = [sum(poseig),sum(zeroeig),sum(negeig)]; end + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_w; + case 'e' + e = obj.e_e; + case 's' + e = obj.e_s; + case 'n' + e = obj.e_n; + end + varargout{i} = e; + end + end + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + e = obj.getBoundaryOperator('e', boundary); + + switch boundary + case 'w' + H_b = inv(e'*obj.Hetai*e); + case 'e' + H_b = inv(e'*obj.Hetai*e); + case 's' + H_b = inv(e'*obj.Hxii*e); + case 'n' + H_b = inv(e'*obj.Hxii*e); + end + end + + end end \ No newline at end of file
--- a/+scheme/Hypsyst3d.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Hypsyst3d.m Tue Feb 12 17:12:42 2019 +0100 @@ -7,11 +7,11 @@ X, Y, Z% Values of x and y for each grid point Yx, Zx, Xy, Zy, Xz, Yz %Grid values for boundary surfaces order % Order accuracy for the approximation - + D % non-stabalized scheme operator A, B, C, E % Symbolic coefficient matrices Aevaluated,Bevaluated,Cevaluated, Eevaluated - + H % Discrete norm Hx, Hy, Hz % Norms in the x, y and z directions Hxi,Hyi, Hzi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. @@ -19,8 +19,8 @@ e_w, e_e, e_s, e_n, e_b, e_t params % Parameters for the coeficient matrice end - - + + methods % Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Cu_z-Eu function obj = Hypsyst3d(m, lim, order, A, B,C, E, params,operator) @@ -28,11 +28,11 @@ xlim = lim{1}; ylim = lim{2}; zlim = lim{3}; - + if length(m) == 1 m = [m m m]; end - + obj.A = A; obj.B = B; obj.C = C; @@ -41,7 +41,7 @@ m_y = m(2); m_z = m(3); obj.params = params; - + switch operator case 'upwind' ops_x = sbp.D1Upwind(m_x,xlim,order); @@ -52,29 +52,29 @@ ops_y = sbp.D2Standard(m_y,ylim,order); ops_z = sbp.D2Standard(m_z,zlim,order); end - + obj.x = ops_x.x; obj.y = ops_y.x; obj.z = ops_z.x; - + obj.X = kr(obj.x,ones(m_y,1),ones(m_z,1)); obj.Y = kr(ones(m_x,1),obj.y,ones(m_z,1)); obj.Z = kr(ones(m_x,1),ones(m_y,1),obj.z); - + obj.Yx = kr(obj.y,ones(m_z,1)); obj.Zx = kr(ones(m_y,1),obj.z); obj.Xy = kr(obj.x,ones(m_z,1)); obj.Zy = kr(ones(m_x,1),obj.z); obj.Xz = kr(obj.x,ones(m_y,1)); obj.Yz = kr(ones(m_z,1),obj.y); - + obj.Aevaluated = obj.evaluateCoefficientMatrix(A, obj.X, obj.Y,obj.Z); obj.Bevaluated = obj.evaluateCoefficientMatrix(B, obj.X, obj.Y,obj.Z); obj.Cevaluated = obj.evaluateCoefficientMatrix(C, obj.X, obj.Y,obj.Z); obj.Eevaluated = obj.evaluateCoefficientMatrix(E, obj.X, obj.Y,obj.Z); - + obj.n = length(A(obj.params,0,0,0)); - + I_n = speye(obj.n); I_x = speye(m_x); obj.I_x = I_x; @@ -83,31 +83,31 @@ I_z = speye(m_z); obj.I_z = I_z; I_N = kr(I_n,I_x,I_y,I_z); - + obj.Hxi = kr(I_n, ops_x.HI, I_y,I_z); obj.Hx = ops_x.H; obj.Hyi = kr(I_n, I_x, ops_y.HI,I_z); obj.Hy = ops_y.H; obj.Hzi = kr(I_n, I_x,I_y, ops_z.HI); obj.Hz = ops_z.H; - + obj.e_w = kr(I_n, ops_x.e_l, I_y,I_z); obj.e_e = kr(I_n, ops_x.e_r, I_y,I_z); obj.e_s = kr(I_n, I_x, ops_y.e_l,I_z); obj.e_n = kr(I_n, I_x, ops_y.e_r,I_z); obj.e_b = kr(I_n, I_x, I_y, ops_z.e_l); obj.e_t = kr(I_n, I_x, I_y, ops_z.e_r); - + obj.m = m; obj.h = [ops_x.h ops_y.h ops_x.h]; obj.order = order; - + switch operator case 'upwind' alphaA = max(abs(eig(A(params,obj.x(end),obj.y(end),obj.z(end))))); alphaB = max(abs(eig(B(params,obj.x(end),obj.y(end),obj.z(end))))); alphaC = max(abs(eig(C(params,obj.x(end),obj.y(end),obj.z(end))))); - + Ap = (obj.Aevaluated+alphaA*I_N)/2; Am = (obj.Aevaluated-alphaA*I_N)/2; Dpx = kr(I_n, ops_x.Dp, I_y,I_z); @@ -116,7 +116,7 @@ temp = Ap*Dmx; obj.D = obj.D-temp; clear Ap Am Dpx Dmx - + Bp = (obj.Bevaluated+alphaB*I_N)/2; Bm = (obj.Bevaluated-alphaB*I_N)/2; Dpy = kr(I_n, I_x, ops_y.Dp,I_z); @@ -126,20 +126,20 @@ temp = Bp*Dmy; obj.D = obj.D-temp; clear Bp Bm Dpy Dmy - - + + Cp = (obj.Cevaluated+alphaC*I_N)/2; Cm = (obj.Cevaluated-alphaC*I_N)/2; Dpz = kr(I_n, I_x, I_y,ops_z.Dp); Dmz = kr(I_n, I_x, I_y,ops_z.Dm); - + temp = Cm*Dpz; obj.D = obj.D-temp; temp = Cp*Dmz; obj.D = obj.D-temp; clear Cp Cm Dpz Dmz obj.D = obj.D-obj.Eevaluated; - + case 'standard' D1_x = kr(I_n, ops_x.D1, I_y,I_z); D1_y = kr(I_n, I_x, ops_y.D1,I_z); @@ -149,7 +149,7 @@ error('Opperator not supported'); end end - + % Closure functions return the opertors applied to the own doamin to close the boundary % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. @@ -167,15 +167,15 @@ error('No such boundary condition') end end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - error('An interface function does not exist yet'); + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + error('Not implemented'); end - + function N = size(obj) N = obj.m; end - + function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y, Z) params = obj.params; side = max(length(X),length(Y)); @@ -189,7 +189,7 @@ side = max(length(X),length(Y)); cols = cols/side; end - + ret = cell(rows,cols); for ii = 1:rows for jj = 1:cols @@ -198,10 +198,10 @@ end ret = cell2mat(ret); end - + function [BM] = boundary_matrices(obj,boundary) params = obj.params; - + switch boundary case {'w','W','west'} BM.e_ = obj.e_w; @@ -248,7 +248,7 @@ end BM.pos = signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3); end - + % Characteristic bouyndary consitions function [closure, penalty]=boundary_condition_char(obj,BM) side = BM.side; @@ -260,7 +260,7 @@ Hi = BM.Hi; D = BM.D; e_ = BM.e_; - + switch BM.boundpos case {'l'} tau = sparse(obj.n*side,pos); @@ -276,9 +276,9 @@ penalty = -Hi*e_*V*tau*Vi_minus; end end - + % General boundary condition in the form Lu=g(x) - function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L) + function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L) side = BM.side; pos = BM.pos; neg = BM.neg; @@ -288,7 +288,7 @@ Hi = BM.Hi; D = BM.D; e_ = BM.e_; - + switch boundary case {'w','W','west'} L = obj.evaluateCoefficientMatrix(L,obj.x(1),obj.Yx,obj.Zx); @@ -303,7 +303,7 @@ case {'t','T','top'} L = obj.evaluateCoefficientMatrix(L,obj.Xz,obj.Yz,obj.z(end)); end - + switch BM.boundpos case {'l'} tau = sparse(obj.n*side,pos); @@ -311,7 +311,7 @@ Vi_minus = Vi(pos+zeroval+1:obj.n*side,:); V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); - + tau(1:pos,:) = -abs(D(1:pos,1:pos)); R = -inv(L*V_plus)*(L*V_minus); closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; @@ -321,7 +321,7 @@ tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side)); Vi_plus = Vi(1:pos,:); Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:); - + V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); R = -inv(L*V_minus)*(L*V_plus); @@ -329,7 +329,7 @@ penalty = -Hi*e_*V*tau*inv(L*V_minus)*L; end end - + % Function that diagonalizes a symbolic matrix A as A=V*D*Vi % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign % [d+ ] @@ -344,13 +344,13 @@ xs = x; ys = y; zs = z; - - + + side = max(length(x),length(y)); Dret = zeros(obj.n,side*obj.n); Vret = zeros(obj.n,side*obj.n); Viret= zeros(obj.n,side*obj.n); - + for ii=1:obj.n for jj=1:obj.n Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii)); @@ -358,7 +358,7 @@ Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii)); end end - + D = sparse(Dret); V = sparse(Vret); Vi = sparse(Viret); @@ -366,11 +366,11 @@ Vi= obj.evaluateCoefficientMatrix(Vi,x,y,z); D = obj.evaluateCoefficientMatrix(D,x,y,z); DD = diag(D); - + poseig = (DD>0); zeroeig = (DD==0); negeig = (DD<0); - + D = diag([DD(poseig); DD(zeroeig); DD(negeig)]); V = [V(:,poseig) V(:,zeroeig) V(:,negeig)]; Vi= [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
--- a/+scheme/Hypsyst3dCurve.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Hypsyst3dCurve.m Tue Feb 12 17:12:42 2019 +0100 @@ -5,22 +5,22 @@ h % Grid spacing X, Y, Z% Values of x and y for each grid point Yx, Zx, Xy, Zy, Xz, Yz %Grid values for boundary surfaces - + xi,eta,zeta Xi, Eta, Zeta - + Eta_xi, Zeta_xi, Xi_eta, Zeta_eta, Xi_zeta, Eta_zeta % Metric terms X_xi, X_eta, X_zeta,Y_xi,Y_eta,Y_zeta,Z_xi,Z_eta,Z_zeta % Metric terms - + order % Order accuracy for the approximation - + D % non-stabalized scheme operator Aevaluated, Bevaluated, Cevaluated, Eevaluated % Numeric Coeffiecient matrices Ahat, Bhat, Chat % Symbolic Transformed Coefficient matrices A, B, C, E % Symbolic coeffiecient matrices - + J, Ji % JAcobian and inverse Jacobian - + H % Discrete norm % Norms in the x, y and z directions Hxii,Hetai,Hzetai, Hzi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. @@ -30,14 +30,14 @@ index_w, index_e,index_s,index_n, index_b, index_t params %parameters for the coeficient matrice end - - + + methods function obj = Hypsyst3dCurve(m, order, A, B,C, E, params,ti,operator) xilim ={0 1}; etalim = {0 1}; zetalim = {0 1}; - + if length(m) == 1 m = [m m m]; end @@ -47,11 +47,11 @@ m_tot = m_xi*m_eta*m_zeta; obj.params = params; obj.n = length(A(obj,0,0,0)); - + obj.m = m; obj.order = order; obj.onesN = ones(obj.n); - + switch operator case 'upwind' ops_xi = sbp.D1Upwind(m_xi,xilim,order); @@ -64,21 +64,21 @@ otherwise error('Operator not available') end - + obj.xi = ops_xi.x; obj.eta = ops_eta.x; obj.zeta = ops_zeta.x; - + obj.Xi = kr(obj.xi,ones(m_eta,1),ones(m_zeta,1)); obj.Eta = kr(ones(m_xi,1),obj.eta,ones(m_zeta,1)); obj.Zeta = kr(ones(m_xi,1),ones(m_eta,1),obj.zeta); - - + + [X,Y,Z] = ti.map(obj.Xi,obj.Eta,obj.Zeta); obj.X = X; obj.Y = Y; obj.Z = Z; - + I_n = eye(obj.n); I_xi = speye(m_xi); obj.I_xi = I_xi; @@ -86,19 +86,19 @@ obj.I_eta = I_eta; I_zeta = speye(m_zeta); obj.I_zeta = I_zeta; - + I_N=kr(I_n,I_xi,I_eta,I_zeta); - + O_xi = ones(m_xi,1); O_eta = ones(m_eta,1); O_zeta = ones(m_zeta,1); - - + + obj.Hxi = ops_xi.H; obj.Heta = ops_eta.H; obj.Hzeta = ops_zeta.H; obj.h = [ops_xi.h ops_eta.h ops_zeta.h]; - + switch operator case 'upwind' D1_xi = kr((ops_xi.Dp+ops_xi.Dm)/2, I_eta,I_zeta); @@ -109,11 +109,11 @@ D1_eta = kr(I_xi, ops_eta.D1,I_zeta); D1_zeta = kr(I_xi, I_eta,ops_zeta.D1); end - + obj.A = A; obj.B = B; obj.C = C; - + obj.X_xi = D1_xi*X; obj.X_eta = D1_eta*X; obj.X_zeta = D1_zeta*X; @@ -123,55 +123,55 @@ obj.Z_xi = D1_xi*Z; obj.Z_eta = D1_eta*Z; obj.Z_zeta = D1_zeta*Z; - + obj.Ahat = @transform_coefficient_matrix; obj.Bhat = @transform_coefficient_matrix; obj.Chat = @transform_coefficient_matrix; obj.E = @(obj,x,y,z,~,~,~,~,~,~)E(obj,x,y,z); - + obj.Aevaluated = obj.evaluateCoefficientMatrix(obj.Ahat,obj.X, obj.Y,obj.Z, obj.X_eta,obj.X_zeta,obj.Y_eta,obj.Y_zeta,obj.Z_eta,obj.Z_zeta); obj.Bevaluated = obj.evaluateCoefficientMatrix(obj.Bhat,obj.X, obj.Y,obj.Z, obj.X_zeta,obj.X_xi,obj.Y_zeta,obj.Y_xi,obj.Z_zeta,obj.Z_xi); obj.Cevaluated = obj.evaluateCoefficientMatrix(obj.Chat,obj.X,obj.Y,obj.Z, obj.X_xi,obj.X_eta,obj.Y_xi,obj.Y_eta,obj.Z_xi,obj.Z_eta); - + switch operator case 'upwind' clear D1_xi D1_eta D1_zeta alphaA = max(abs(eig(obj.Ahat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_eta(end),obj.X_zeta(end),obj.Y_eta(end),obj.Y_zeta(end),obj.Z_eta(end),obj.Z_zeta(end))))); alphaB = max(abs(eig(obj.Bhat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_zeta(end),obj.X_xi(end),obj.Y_zeta(end),obj.Y_xi(end),obj.Z_zeta(end),obj.Z_xi(end))))); alphaC = max(abs(eig(obj.Chat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_xi(end),obj.X_eta(end),obj.Y_xi(end),obj.Y_eta(end),obj.Z_xi(end),obj.Z_eta(end))))); - + Ap = (obj.Aevaluated+alphaA*I_N)/2; Dmxi = kr(I_n, ops_xi.Dm, I_eta,I_zeta); diffSum = -Ap*Dmxi; clear Ap Dmxi - + Am = (obj.Aevaluated-alphaA*I_N)/2; - + obj.Aevaluated = []; Dpxi = kr(I_n, ops_xi.Dp, I_eta,I_zeta); temp = Am*Dpxi; diffSum = diffSum-temp; clear Am Dpxi - + Bp = (obj.Bevaluated+alphaB*I_N)/2; Dmeta = kr(I_n, I_xi, ops_eta.Dm,I_zeta); temp = Bp*Dmeta; diffSum = diffSum-temp; clear Bp Dmeta - + Bm = (obj.Bevaluated-alphaB*I_N)/2; obj.Bevaluated = []; Dpeta = kr(I_n, I_xi, ops_eta.Dp,I_zeta); temp = Bm*Dpeta; diffSum = diffSum-temp; clear Bm Dpeta - + Cp = (obj.Cevaluated+alphaC*I_N)/2; Dmzeta = kr(I_n, I_xi, I_eta,ops_zeta.Dm); temp = Cp*Dmzeta; diffSum = diffSum-temp; clear Cp Dmzeta - + Cm = (obj.Cevaluated-alphaC*I_N)/2; clear I_N obj.Cevaluated = []; @@ -179,72 +179,72 @@ temp = Cm*Dpzeta; diffSum = diffSum-temp; clear Cm Dpzeta temp - + obj.J = obj.X_xi.*obj.Y_eta.*obj.Z_zeta... +obj.X_zeta.*obj.Y_xi.*obj.Z_eta... +obj.X_eta.*obj.Y_zeta.*obj.Z_xi... -obj.X_xi.*obj.Y_zeta.*obj.Z_eta... -obj.X_eta.*obj.Y_xi.*obj.Z_zeta... -obj.X_zeta.*obj.Y_eta.*obj.Z_xi; - + obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot)); obj.Eevaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,obj.Z,[],[],[],[],[],[]); - + obj.D = obj.Ji*diffSum-obj.Eevaluated; - + case 'standard' D1_xi = kr(I_n,D1_xi); D1_eta = kr(I_n,D1_eta); D1_zeta = kr(I_n,D1_zeta); - + obj.J = obj.X_xi.*obj.Y_eta.*obj.Z_zeta... +obj.X_zeta.*obj.Y_xi.*obj.Z_eta... +obj.X_eta.*obj.Y_zeta.*obj.Z_xi... -obj.X_xi.*obj.Y_zeta.*obj.Z_eta... -obj.X_eta.*obj.Y_xi.*obj.Z_zeta... -obj.X_zeta.*obj.Y_eta.*obj.Z_xi; - + obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot)); obj.Eevaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,obj.Z,[],[],[],[],[],[]); - + obj.D = obj.Ji*(-obj.Aevaluated*D1_xi-obj.Bevaluated*D1_eta -obj.Cevaluated*D1_zeta)-obj.Eevaluated; otherwise error('Operator not supported') end - + obj.Hxii = kr(I_n, ops_xi.HI, I_eta,I_zeta); obj.Hetai = kr(I_n, I_xi, ops_eta.HI,I_zeta); obj.Hzetai = kr(I_n, I_xi,I_eta, ops_zeta.HI); - + obj.index_w = (kr(ops_xi.e_l, O_eta,O_zeta)==1); obj.index_e = (kr(ops_xi.e_r, O_eta,O_zeta)==1); obj.index_s = (kr(O_xi, ops_eta.e_l,O_zeta)==1); obj.index_n = (kr(O_xi, ops_eta.e_r,O_zeta)==1); obj.index_b = (kr(O_xi, O_eta, ops_zeta.e_l)==1); obj.index_t = (kr(O_xi, O_eta, ops_zeta.e_r)==1); - + obj.e_w = kr(I_n, ops_xi.e_l, I_eta,I_zeta); obj.e_e = kr(I_n, ops_xi.e_r, I_eta,I_zeta); obj.e_s = kr(I_n, I_xi, ops_eta.e_l,I_zeta); obj.e_n = kr(I_n, I_xi, ops_eta.e_r,I_zeta); obj.e_b = kr(I_n, I_xi, I_eta, ops_zeta.e_l); obj.e_t = kr(I_n, I_xi, I_eta, ops_zeta.e_r); - + obj.Eta_xi = kr(obj.eta,ones(m_xi,1)); obj.Zeta_xi = kr(ones(m_eta,1),obj.zeta); obj.Xi_eta = kr(obj.xi,ones(m_zeta,1)); obj.Zeta_eta = kr(ones(m_xi,1),obj.zeta); obj.Xi_zeta = kr(obj.xi,ones(m_eta,1)); - obj.Eta_zeta = kr(ones(m_zeta,1),obj.eta); + obj.Eta_zeta = kr(ones(m_zeta,1),obj.eta); end - + function [ret] = transform_coefficient_matrix(obj,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2) ret = obj.A(obj,x,y,z).*(y_1.*z_2-z_1.*y_2); ret = ret+obj.B(obj,x,y,z).*(x_2.*z_1-x_1.*z_2); ret = ret+obj.C(obj,x,y,z).*(x_1.*y_2-x_2.*y_1); end - - + + % Closure functions return the opertors applied to the own doamin to close the boundary % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. @@ -253,7 +253,7 @@ function [closure, penalty] = boundary_condition(obj,boundary,type,L) default_arg('type','char'); BM = boundary_matrices(obj,boundary); - + switch type case{'c','char'} [closure,penalty] = boundary_condition_char(obj,BM); @@ -263,15 +263,15 @@ error('No such boundary condition') end end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - error('An interface function does not exist yet'); + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + error('Not implemented'); end - + function N = size(obj) N = obj.m; end - + % Evaluates the symbolic Coeffiecient matrix mat function [ret] = evaluateCoefficientMatrix(obj,mat, X, Y, Z , x_1 , x_2 , y_1 , y_2 , z_1 , z_2) params = obj.params; @@ -294,7 +294,7 @@ end matVec(abs(matVec)<10^(-10)) = 0; ret = cell(rows,cols); - + for ii = 1:rows for jj = 1:cols ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side)); @@ -302,7 +302,7 @@ end ret = cell2mat(ret); end - + function [BM] = boundary_matrices(obj,boundary) params = obj.params; BM.boundary = boundary; @@ -385,7 +385,7 @@ BM.side = sum(BM.index); BM.pos = signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3); end - + % Characteristic boundary condition function [closure, penalty] = boundary_condition_char(obj,BM) side = BM.side; @@ -397,7 +397,7 @@ Hi = BM.Hi; D = BM.D; e_ = BM.e_; - + switch BM.boundpos case {'l'} tau = sparse(obj.n*side,pos); @@ -413,7 +413,7 @@ penalty = -Hi*e_*V*tau*Vi_minus; end end - + % General boundary condition in the form Lu=g(x) function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L) side = BM.side; @@ -426,7 +426,7 @@ D = BM.D; e_ = BM.e_; index = BM.index; - + switch BM.boundary case{'b','B','bottom'} Ji_vec = diag(obj.Ji); @@ -434,10 +434,10 @@ Zeta_x = Ji*(obj.Y_xi(index).*obj.Z_eta(index)-obj.Z_xi(index).*obj.Y_eta(index)); Zeta_y = Ji*(obj.X_eta(index).*obj.Z_xi(index)-obj.X_xi(index).*obj.Z_eta(index)); Zeta_z = Ji*(obj.X_xi(index).*obj.Y_eta(index)-obj.Y_xi(index).*obj.X_eta(index)); - + L = obj.evaluateCoefficientMatrix(L,Zeta_x,Zeta_y,Zeta_z,[],[],[],[],[],[]); end - + switch BM.boundpos case {'l'} tau = sparse(obj.n*side,pos); @@ -445,7 +445,7 @@ Vi_minus = Vi(pos+zeroval+1:obj.n*side,:); V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); - + tau(1:pos,:) = -abs(D(1:pos,1:pos)); R = -inv(L*V_plus)*(L*V_minus); closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; @@ -455,7 +455,7 @@ tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side)); Vi_plus = Vi(1:pos,:); Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:); - + V_plus = V(:,1:pos); V_minus = V(:,(pos+zeroval)+1:obj.n*side); R = -inv(L*V_minus)*(L*V_plus); @@ -463,7 +463,7 @@ penalty = -Hi*e_*V*tau*inv(L*V_minus)*L; end end - + % Function that diagonalizes a symbolic matrix A as A=V*D*Vi % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign % [d+ ] @@ -478,38 +478,38 @@ else x_1s = 0; end - + if(sum(abs(x_2))>eps) syms x_2s; else x_2s = 0; end - - + + if(sum(abs(y_1))>eps) syms y_1s else y_1s = 0; end - + if(sum(abs(y_2))>eps) syms y_2s; else y_2s = 0; end - + if(sum(abs(z_1))>eps) syms z_1s else z_1s = 0; end - + if(sum(abs(z_2))>eps) syms z_2s; else z_2s = 0; end - + syms xs ys zs [V, D] = eig(mat(obj,xs,ys,zs,x_1s,x_2s,y_1s,y_2s,z_1s,z_2s)); Vi = inv(V); @@ -522,12 +522,12 @@ y_2s = y_2; z_1s = z_1; z_2s = z_2; - + side = max(length(x),length(y)); Dret = zeros(obj.n,side*obj.n); Vret = zeros(obj.n,side*obj.n); Viret = zeros(obj.n,side*obj.n); - + for ii=1:obj.n for jj=1:obj.n Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii)); @@ -535,7 +535,7 @@ Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii)); end end - + D = sparse(Dret); V = sparse(Vret); Vi = sparse(Viret); @@ -543,11 +543,11 @@ D = obj.evaluateCoefficientMatrix(D,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2); Vi = obj.evaluateCoefficientMatrix(Vi,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2); DD = diag(D); - + poseig = (DD>0); zeroeig = (DD==0); negeig = (DD<0); - + D = diag([DD(poseig); DD(zeroeig); DD(negeig)]); V = [V(:,poseig) V(:,zeroeig) V(:,negeig)]; Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Laplace1d.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,158 @@ +classdef Laplace1d < scheme.Scheme + properties + grid + order % Order accuracy for the approximation + + D % non-stabalized scheme operator + H % Discrete norm + M % Derivative norm + a + + D2 + Hi + e_l + e_r + d_l + d_r + gamm + end + + methods + function obj = Laplace1d(grid, order, a) + default_arg('a', 1); + + assertType(grid, 'grid.Cartesian'); + + ops = sbp.D2Standard(grid.size(), grid.lim{1}, order); + + obj.D2 = sparse(ops.D2); + obj.H = sparse(ops.H); + obj.Hi = sparse(ops.HI); + obj.M = sparse(ops.M); + obj.e_l = sparse(ops.e_l); + obj.e_r = sparse(ops.e_r); + obj.d_l = -sparse(ops.d1_l); + obj.d_r = sparse(ops.d1_r); + + + obj.grid = grid; + obj.order = order; + + obj.a = a; + obj.D = a*obj.D2; + + obj.gamm = grid.h*ops.borrowing.M.S; + end + + + % Closure functions return the opertors applied to the own doamin to close the boundary + % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. + % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. + % type is a string specifying the type of boundary condition if there are several. + % data is a function returning the data that should be applied at the boundary. + % neighbour_scheme is an instance of Scheme that should be interfaced to. + % neighbour_boundary is a string specifying which boundary to interface to. + function [closure, penalty] = boundary_condition(obj,boundary,type,data) + default_arg('type','neumann'); + default_arg('data',0); + + e = obj.getBoundaryOperator('e', boundary); + d = obj.getBoundaryOperator('d', boundary); + s = obj.getBoundarySign(boundary); + + switch type + % Dirichlet boundary condition + case {'D','dirichlet'} + tuning = 1.1; + tau1 = -tuning/obj.gamm; + tau2 = 1; + + tau = tau1*e + tau2*d; + + closure = obj.a*obj.Hi*tau*e'; + penalty = obj.a*obj.Hi*tau; + + % Neumann boundary condition + case {'N','neumann'} + tau = -e; + + closure = obj.a*obj.Hi*tau*d'; + penalty = -obj.a*obj.Hi*tau; + + % Unknown, boundary condition + otherwise + error('No such boundary condition: type = %s',type); + end + end + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + % u denotes the solution in the own domain + % v denotes the solution in the neighbour domain + e_u = obj.getBoundaryOperator('e', boundary); + d_u = obj.getBoundaryOperator('d', boundary); + s_u = obj.getBoundarySign(boundary); + + e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary); + s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); + + a_u = obj.a; + a_v = neighbour_scheme.a; + + gamm_u = obj.gamm; + gamm_v = neighbour_scheme.gamm; + + tuning = 1.1; + + tau1 = -(a_u/gamm_u + a_v/gamm_v) * tuning; + tau2 = 1/2*a_u; + sig1 = -1/2; + sig2 = 0; + + tau = tau1*e_u + tau2*d_u; + sig = sig1*e_u + sig2*d_u; + + closure = obj.Hi*( tau*e_u' + sig*a_u*d_u'); + penalty = obj.Hi*(-tau*e_v' + sig*a_v*d_v'); + end + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string + % boundary -- string + function o = getBoundaryOperator(obj, op, boundary) + assertIsMember(op, {'e', 'd'}) + assertIsMember(boundary, {'l', 'r'}) + + o = obj.([op, '_', boundary]) + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + % Note: for 1d diffOps, the boundary quadrature is the scalar 1. + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + H_b = 1; + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + switch boundary + case {'r'} + s = 1; + case {'l'} + s = -1; + end + end + + function N = size(obj) + N = obj.grid.size(); + end + + end +end
--- a/+scheme/LaplaceCurvilinear.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/LaplaceCurvilinear.m Tue Feb 12 17:12:42 2019 +0100 @@ -38,6 +38,7 @@ du_n, dv_n gamm_u, gamm_v lambda + end methods @@ -53,7 +54,11 @@ error('Not implemented yet') end - assert(isa(g, 'grid.Curvilinear')) + % assert(isa(g, 'grid.Curvilinear')) + if isa(a, 'function_handle') + a = grid.evalOn(g, a); + a = spdiag(a); + end m = g.size(); m_u = m(1); @@ -233,7 +238,10 @@ default_arg('type','neumann'); default_arg('parameter', []); - [e, d, gamm, H_b, ~] = obj.get_boundary_ops(boundary); + e = obj.getBoundaryOperator('e', boundary); + d = obj.getBoundaryOperator('d', boundary); + H_b = obj.getBoundaryQuadrature(boundary); + gamm = obj.getBoundaryBorrowing(boundary); switch type % Dirichlet boundary condition case {'D','d','dirichlet'} @@ -268,13 +276,42 @@ end end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + % type Struct that specifies the interface coupling. + % Fields: + % -- tuning: penalty strength, defaults to 1.2 + % -- interpolation: type of interpolation, default 'none' + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + defaultType.tuning = 1.2; + defaultType.interpolation = 'none'; + default_struct('type', defaultType); + + switch type.interpolation + case {'none', ''} + [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type); + case {'op','OP'} + [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type); + otherwise + error('Unknown type of interpolation: %s ', type.interpolation); + end + end + + function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type) + tuning = type.tuning; + % u denotes the solution in the own domain % v denotes the solution in the neighbour domain - tuning = 1.2; - % tuning = 20.2; - [e_u, d_u, gamm_u, H_b_u, I_u] = obj.get_boundary_ops(boundary); - [e_v, d_v, gamm_v, H_b_v, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); + e_u = obj.getBoundaryOperator('e', boundary); + d_u = obj.getBoundaryOperator('d', boundary); + H_b_u = obj.getBoundaryQuadrature(boundary); + I_u = obj.getBoundaryIndices(boundary); + gamm_u = obj.getBoundaryBorrowing(boundary); + + e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary); + H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary); + I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary); + gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary); u = obj; v = neighbour_scheme; @@ -298,41 +335,113 @@ penalty = obj.a*obj.Hi*(-tau*e_v' + sig*d_v'); end - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary + function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + % TODO: Make this work for curvilinear grids + warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.'); + + % User can request special interpolation operators by specifying type.interpOpSet + default_field(type, 'interpOpSet', @sbp.InterpOpsOP); + interpOpSet = type.interpOpSet; + tuning = type.tuning; + + + % u denotes the solution in the own domain + % v denotes the solution in the neighbour domain + e_u = obj.getBoundaryOperator('e', boundary); + d_u = obj.getBoundaryOperator('d', boundary); + H_b_u = obj.getBoundaryQuadrature(boundary); + I_u = obj.getBoundaryIndices(boundary); + gamm_u = obj.getBoundaryBorrowing(boundary); + + e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary); + H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary); + I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary); + gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary); + + + % Find the number of grid points along the interface + m_u = size(e_u, 2); + m_v = size(e_v, 2); + + Hi = obj.Hi; + a = obj.a; + + u = obj; + v = neighbour_scheme; + + b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; + b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; + b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; + b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; + + tau_u = -1./(4*b1_u) -1./(4*b2_u); + tau_v = -1./(4*b1_v) -1./(4*b2_v); + + tau_u = tuning * spdiag(tau_u); + tau_v = tuning * spdiag(tau_v); + beta_u = tau_v; + + % Build interpolation operators + intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order); + Iu2v = intOps.Iu2v; + Iv2u = intOps.Iv2u; + + closure = a*Hi*e_u*tau_u*H_b_u*e_u' + ... + a*Hi*e_u*H_b_u*Iv2u.bad*beta_u*Iu2v.good*e_u' + ... + a*1/2*Hi*d_u*H_b_u*e_u' + ... + -a*1/2*Hi*e_u*H_b_u*d_u'; + + penalty = -a*Hi*e_u*tau_u*H_b_u*Iv2u.good*e_v' + ... + -a*Hi*e_u*H_b_u*Iv2u.bad*beta_u*e_v' + ... + -a*1/2*Hi*d_u*H_b_u*Iv2u.good*e_v' + ... + -a*1/2*Hi*e_u*H_b_u*Iv2u.bad*d_v'; + + end + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string + % boundary -- string + function o = getBoundaryOperator(obj, op, boundary) + assertIsMember(op, {'e', 'd'}) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + o = obj.([op, '_', boundary]); + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points % - % I -- the indecies of the boundary points in the grid matrix - function [e, d, gamm, H_b, I] = get_boundary_ops(obj, boundary) + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) - % gridMatrix = zeros(obj.m(2),obj.m(1)); - % gridMatrix(:) = 1:numel(gridMatrix); + H_b = obj.(['H_', boundary]); + end + + % Returns the indices of the boundary points in the grid matrix + % boundary -- string + function I = getBoundaryIndices(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); - switch boundary case 'w' - e = obj.e_w; - d = obj.d_w; - H_b = obj.H_w; I = ind(1,:); case 'e' - e = obj.e_e; - d = obj.d_e; - H_b = obj.H_e; I = ind(end,:); case 's' - e = obj.e_s; - d = obj.d_s; - H_b = obj.H_s; I = ind(:,1)'; case 'n' - e = obj.e_n; - d = obj.d_n; - H_b = obj.H_n; I = ind(:,end)'; - otherwise - error('No such boundary: boundary = %s',boundary); end + end + + % Returns borrowing constant gamma + % boundary -- string + function gamm = getBoundaryBorrowing(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) switch boundary case {'w','e'}
--- a/+scheme/Scheme.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Scheme.m Tue Feb 12 17:12:42 2019 +0100 @@ -26,22 +26,15 @@ % interface to. % penalty may be a cell array if there are several penalties with different weights [closure, penalty] = boundary_condition(obj,boundary,type) % TODO: Change name to boundaryCondition - [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - % TODO: op = getBoundaryOperator()?? - % makes sense to have it available through a method instead of random properties + % type -- sets the type of interface, could be a string or a struct or something else + % depending on the particular scheme implementation + [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + op = getBoundaryOperator(obj, opName, boundary) + H_b= getBoundaryQuadrature(obj, boundary) % Returns the number of degrees of freedom. N = size(obj) end - - methods(Static) - % Calculates the matrcis need for the inteface coupling between - % boundary bound_u of scheme schm_u and bound_v of scheme schm_v. - % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l') - function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) - [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); - [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); - end - end end
--- a/+scheme/Schrodinger.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Schrodinger.m Tue Feb 12 17:12:42 2019 +0100 @@ -67,7 +67,8 @@ default_arg('type','dirichlet'); default_arg('data',0); - [e,d,s] = obj.get_boundary_ops(boundary); + [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary); + s = obj.getBoundarySign(boundary); switch type % Dirichlet boundary condition @@ -90,11 +91,14 @@ end end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) % u denotes the solution in the own domain % v denotes the solution in the neighbour domain - [e_u,d_u,s_u] = obj.get_boundary_ops(boundary); - [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); + [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary); + s_u = obj.getBoundarySign(boundary); + + [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary); + s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); a = -s_u* 1/2 * 1i ; b = a'; @@ -106,20 +110,60 @@ penalty = obj.Hi * (-tau*e_v' - sig*d_v'); end - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e,d,s] = get_boundary_ops(obj,boundary) + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'l', 'r'}) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'l' + e = obj.e_l; + case 'r' + e = obj.e_r; + end + varargout{i} = e; + + case 'd' + switch boundary + case 'l' + d = obj.d1_l; + case 'r' + d = obj.d1_r; + end + varargout{i} = d; + end + end + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + % Note: for 1d diffOps, the boundary quadrature is the scalar 1. + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + H_b = 1; + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + switch boundary - case 'l' - e = obj.e_l; - d = obj.d1_l; + case {'r'} + s = 1; + case {'l'} s = -1; - case 'r' - e = obj.e_r; - d = obj.d1_r; - s = 1; - otherwise - error('No such boundary: boundary = %s',boundary); end end @@ -128,14 +172,4 @@ end end - - methods(Static) - % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u - % and bound_v of scheme schm_v. - % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') - function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) - [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); - [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); - end - end -end \ No newline at end of file +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Schrodinger2d.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,366 @@ +classdef Schrodinger2d < scheme.Scheme + +% Discretizes the Laplacian with constant coefficent, +% in the Schrödinger equation way (i.e., the discretization matrix is not necessarily +% definite) +% u_t = a*i*Laplace u +% opSet should be cell array of opSets, one per dimension. This +% is useful if we have periodic BC in one direction. + + properties + m % Number of points in each direction, possibly a vector + h % Grid spacing + + grid + dim + + order % Order of accuracy for the approximation + + % Diagonal matrix for variable coefficients + a % Constant coefficient + + D % Total operator + D1 % First derivatives + + % Second derivatives + D2 + + H, Hi % Inner products + e_l, e_r + d1_l, d1_r % Normal derivatives at the boundary + e_w, e_e, e_s, e_n + d_w, d_e, d_s, d_n + + H_boundary % Boundary inner products + + end + + methods + + function obj = Schrodinger2d(g ,order, a, opSet) + default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable}); + default_arg('a',1); + dim = 2; + + assertType(g, 'grid.Cartesian'); + if isa(a, 'function_handle') + a = grid.evalOn(g, a); + a = spdiag(a); + end + + m = g.size(); + m_tot = g.N(); + + h = g.scaling(); + xlim = {g.x{1}(1), g.x{1}(end)}; + ylim = {g.x{2}(1), g.x{2}(end)}; + lim = {xlim, ylim}; + + % 1D operators + ops = cell(dim,1); + for i = 1:dim + ops{i} = opSet{i}(m(i), lim{i}, order); + end + + I = cell(dim,1); + D1 = cell(dim,1); + D2 = cell(dim,1); + H = cell(dim,1); + Hi = cell(dim,1); + e_l = cell(dim,1); + e_r = cell(dim,1); + d1_l = cell(dim,1); + d1_r = cell(dim,1); + + for i = 1:dim + I{i} = speye(m(i)); + D1{i} = ops{i}.D1; + D2{i} = ops{i}.D2; + H{i} = ops{i}.H; + Hi{i} = ops{i}.HI; + e_l{i} = ops{i}.e_l; + e_r{i} = ops{i}.e_r; + d1_l{i} = ops{i}.d1_l; + d1_r{i} = ops{i}.d1_r; + end + + % Constant coeff D2 + for i = 1:dim + D2{i} = D2{i}(ones(m(i),1)); + end + + %====== Assemble full operators ======== + obj.D1 = cell(dim,1); + obj.D2 = cell(dim,1); + obj.e_l = cell(dim,1); + obj.e_r = cell(dim,1); + obj.d1_l = cell(dim,1); + obj.d1_r = cell(dim,1); + + % D1 + obj.D1{1} = kron(D1{1},I{2}); + obj.D1{2} = kron(I{1},D1{2}); + + % Boundary operators + obj.e_l{1} = kron(e_l{1},I{2}); + obj.e_l{2} = kron(I{1},e_l{2}); + obj.e_r{1} = kron(e_r{1},I{2}); + obj.e_r{2} = kron(I{1},e_r{2}); + + obj.d1_l{1} = kron(d1_l{1},I{2}); + obj.d1_l{2} = kron(I{1},d1_l{2}); + obj.d1_r{1} = kron(d1_r{1},I{2}); + obj.d1_r{2} = kron(I{1},d1_r{2}); + + % D2 + obj.D2{1} = kron(D2{1},I{2}); + obj.D2{2} = kron(I{1},D2{2}); + + % Quadratures + obj.H = kron(H{1},H{2}); + obj.Hi = inv(obj.H); + obj.H_boundary = cell(dim,1); + obj.H_boundary{1} = H{2}; + obj.H_boundary{2} = H{1}; + + % Differentiation matrix D (without SAT) + D2 = obj.D2; + D = sparse(m_tot,m_tot); + for j = 1:dim + D = D + a*1i*D2{j}; + end + obj.D = D; + %=========================================% + + % Misc. + obj.m = m; + obj.h = h; + obj.order = order; + obj.grid = g; + obj.dim = dim; + obj.a = a; + obj.e_w = obj.e_l{1}; + obj.e_e = obj.e_r{1}; + obj.e_s = obj.e_l{2}; + obj.e_n = obj.e_r{2}; + obj.d_w = obj.d1_l{1}; + obj.d_e = obj.d1_r{1}; + obj.d_s = obj.d1_l{2}; + obj.d_n = obj.d1_r{2}; + + end + + + % Closure functions return the operators applied to the own domain to close the boundary + % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin. + % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. + % type is a string specifying the type of boundary condition. + % data is a function returning the data that should be applied at the boundary. + % neighbour_scheme is an instance of Scheme that should be interfaced to. + % neighbour_boundary is a string specifying which boundary to interface to. + function [closure, penalty] = boundary_condition(obj, boundary, type, parameter) + default_arg('type','Neumann'); + default_arg('parameter', []); + + % nj: outward unit normal component. + % nj = -1 for west, south, bottom boundaries + % nj = 1 for east, north, top boundaries + nj = obj.getBoundarySign(boundary); + [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary); + H_gamma = obj.getBoundaryQuadrature(boundary); + Hi = obj.Hi; + a = e'*obj.a*e; + + switch type + + % Dirichlet boundary condition + case {'D','d','dirichlet','Dirichlet'} + closure = nj*Hi*d*a*1i*H_gamma*(e' ); + penalty = -nj*Hi*d*a*1i*H_gamma; + + % Free boundary condition + case {'N','n','neumann','Neumann'} + closure = -nj*Hi*e*a*1i*H_gamma*(d' ); + penalty = nj*Hi*e*a*1i*H_gamma; + + % Unknown boundary condition + otherwise + error('No such boundary condition: type = %s',type); + end + end + + % type Struct that specifies the interface coupling. + % Fields: + % -- interpolation: type of interpolation, default 'none' + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + defaultType.interpolation = 'none'; + default_struct('type', defaultType); + + switch type.interpolation + case {'none', ''} + [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type); + case {'op','OP'} + [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type); + otherwise + error('Unknown type of interpolation: %s ', type.interpolation); + end + end + + function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type) + % u denotes the solution in the own domain + % v denotes the solution in the neighbour domain + + % Get boundary operators + [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary); + [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary); + H_gamma = obj.getBoundaryQuadrature(boundary); + Hi = obj.Hi; + a = obj.a; + + % Get outward unit normal component + n = obj.getBoundarySign(boundary); + + Hi = obj.Hi; + sigma = -n*1i*a/2; + tau = -n*(1i*a)'/2; + + closure = tau*Hi*d*H_gamma*e' + sigma*Hi*e*H_gamma*d'; + penalty = -tau*Hi*d*H_gamma*e_neighbour' ... + -sigma*Hi*e*H_gamma*d_neighbour'; + + end + + function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + % User can request special interpolation operators by specifying type.interpOpSet + default_field(type, 'interpOpSet', @sbp.InterpOpsOP); + interpOpSet = type.interpOpSet; + + % u denotes the solution in the own domain + % v denotes the solution in the neighbour domain + [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary); + [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary); + H_gamma = obj.getBoundaryQuadrature(boundary); + Hi = obj.Hi; + a = obj.a; + + % Get outward unit normal component + n = obj.getBoundarySign(boundary); + + % Find the number of grid points along the interface + m_u = size(e_u, 2); + m_v = size(e_v, 2); + + % Build interpolation operators + intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order); + Iu2v = intOps.Iu2v; + Iv2u = intOps.Iv2u; + + sigma = -n*1i*a/2; + tau = -n*(1i*a)'/2; + + closure = tau*Hi*d_u*H_gamma*e_u' + sigma*Hi*e_u*H_gamma*d_u'; + penalty = -tau*Hi*d_u*H_gamma*Iv2u.good*e_v' ... + -sigma*Hi*e_u*H_gamma*Iv2u.bad*d_v'; + + end + + % Returns the coordinate number and outward normal component for the boundary specified by the string boundary. + function [j, nj] = get_boundary_number(obj, boundary) + + switch boundary + case {'w','W','west','West', 'e', 'E', 'east', 'East'} + j = 1; + case {'s','S','south','South', 'n', 'N', 'north', 'North'} + j = 2; + otherwise + error('No such boundary: boundary = %s',boundary); + end + + switch boundary + case {'w','W','west','West','s','S','south','South'} + nj = -1; + case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'} + nj = 1; + end + end + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_w; + case 'e' + e = obj.e_e; + case 's' + e = obj.e_s; + case 'n' + e = obj.e_n; + end + varargout{i} = e; + + case 'd' + switch boundary + case 'w' + d = obj.d_w; + case 'e' + d = obj.d_e; + case 's' + d = obj.d_s; + case 'n' + d = obj.d_n; + end + varargout{i} = d; + end + end + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case 'w' + H_b = obj.H_boundary{1}; + case 'e' + H_b = obj.H_boundary{1}; + case 's' + H_b = obj.H_boundary{2}; + case 'n' + H_b = obj.H_boundary{2}; + end + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'e','n'} + s = 1; + case {'w','s'} + s = -1; + end + end + + function N = size(obj) + N = prod(obj.m); + end + end +end
--- a/+scheme/TODO.txt Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1 +0,0 @@ -% TODO: Rename package and abstract class to diffOp
--- a/+scheme/Utux.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Utux.m Tue Feb 12 17:12:42 2019 +0100 @@ -2,7 +2,7 @@ properties m % Number of points in each direction, possibly a vector h % Grid spacing - x % Grid + grid % Grid order % Order accuracy for the approximation H % Discrete norm @@ -16,42 +16,30 @@ end - methods - function obj = Utux(m,xlim,order,operator) - default_arg('a',1); - - %Old operators - % [x, h] = util.get_grid(xlim{:},m); - %ops = sbp.Ordinary(m,h,order); - - - switch operator - case 'NonEquidistant' - ops = sbp.D1Nonequidistant(m,xlim,order); - obj.D1 = ops.D1; - case 'Standard' - ops = sbp.D2Standard(m,xlim,order); - obj.D1 = ops.D1; - case 'Upwind' - ops = sbp.D1Upwind(m,xlim,order); - obj.D1 = ops.Dm; - otherwise - error('Unvalid operator') - end - obj.x=ops.x; + methods + function obj = Utux(g, order, opSet) + default_arg('opSet',@sbp.D2Standard); - + m = g.size(); + xl = g.getBoundary('l'); + xr = g.getBoundary('r'); + xlim = {xl, xr}; + + ops = opSet(m, xlim, order); + obj.D1 = ops.D1; + + obj.grid = g; + obj.H = ops.H; obj.Hi = ops.HI; - + obj.e_l = ops.e_l; obj.e_r = ops.e_r; - obj.D=obj.D1; + obj.D = -obj.D1; obj.m = m; obj.h = ops.h; obj.order = order; - obj.x = ops.x; end % Closure functions return the opertors applied to the own doamin to close the boundary @@ -61,32 +49,53 @@ % data is a function returning the data that should be applied at the boundary. % neighbour_scheme is an instance of Scheme that should be interfaced to. % neighbour_boundary is a string specifying which boundary to interface to. - function [closure, penalty] = boundary_condition(obj,boundary,type,data) - default_arg('type','neumann'); - default_arg('data',0); - tau =-1*obj.e_l; - closure = obj.Hi*tau*obj.e_l'; - penalty = 0*obj.e_l; - + function [closure, penalty] = boundary_condition(obj,boundary,type) + default_arg('type','dirichlet'); + tau =-1*obj.e_l; + closure = obj.Hi*tau*obj.e_l'; + penalty = -obj.Hi*tau; + + end + + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) + switch boundary + % Upwind coupling + case {'l','left'} + tau = -1*obj.e_l; + closure = obj.Hi*tau*obj.e_l'; + penalty = -obj.Hi*tau*neighbour_scheme.e_r'; + case {'r','right'} + tau = 0*obj.e_r; + closure = obj.Hi*tau*obj.e_r'; + penalty = -obj.Hi*tau*neighbour_scheme.e_l'; + end + end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - error('An interface function does not exist yet'); - end - + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string + % boundary -- string + function o = getBoundaryOperator(obj, op, boundary) + assertIsMember(op, {'e'}) + assertIsMember(boundary, {'l', 'r'}) + + o = obj.([op, '_', boundary]); + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + % Note: for 1d diffOps, the boundary quadrature is the scalar 1. + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'l', 'r'}) + + H_b = 1; + end + function N = size(obj) N = obj.m; end end - - methods(Static) - % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u - % and bound_v of scheme schm_v. - % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') - function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) - [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); - [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); - end - end -end \ No newline at end of file +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Utux2d.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,305 @@ +classdef Utux2d < scheme.Scheme + properties + m % Number of points in each direction, possibly a vector + h % Grid spacing + grid % Grid + order % Order accuracy for the approximation + v0 % Initial data + + a % Wave speed a = [a1, a2]; + % Can either be a constant vector or a cell array of function handles. + + H % Discrete norm + H_x, H_y % Norms in the x and y directions + Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms + H_w, H_e, H_s, H_n % Boundary quadratures + + % Derivatives + Dx, Dy + + % Boundary operators + e_w, e_e, e_s, e_n + + D % Total discrete operator + end + + + methods + function obj = Utux2d(g ,order, opSet, a) + + default_arg('a',1/sqrt(2)*[1, 1]); + default_arg('opSet',@sbp.D2Standard); + + assertType(g, 'grid.Cartesian'); + if iscell(a) + a1 = grid.evalOn(g, a{1}); + a2 = grid.evalOn(g, a{2}); + a = {spdiag(a1), spdiag(a2)}; + else + a = {a(1), a(2)}; + end + + m = g.size(); + m_x = m(1); + m_y = m(2); + m_tot = g.N(); + + xlim = {g.x{1}(1), g.x{1}(end)}; + ylim = {g.x{2}(1), g.x{2}(end)}; + obj.grid = g; + + % Operator sets + ops_x = opSet(m_x, xlim, order); + ops_y = opSet(m_y, ylim, order); + Ix = speye(m_x); + Iy = speye(m_y); + + % Norms + Hx = ops_x.H; + Hy = ops_y.H; + Hxi = ops_x.HI; + Hyi = ops_y.HI; + + obj.H_w = Hy; + obj.H_e = Hy; + obj.H_s = Hx; + obj.H_n = Hx; + obj.H_x = Hx; + obj.H_y = Hy; + obj.H = kron(Hx,Hy); + obj.Hi = kron(Hxi,Hyi); + obj.Hx = kron(Hx,Iy); + obj.Hy = kron(Ix,Hy); + obj.Hxi = kron(Hxi,Iy); + obj.Hyi = kron(Ix,Hyi); + + % Derivatives + Dx = ops_x.D1; + Dy = ops_y.D1; + obj.Dx = kron(Dx,Iy); + obj.Dy = kron(Ix,Dy); + + % Boundary operators + obj.e_w = kr(ops_x.e_l, Iy); + obj.e_e = kr(ops_x.e_r, Iy); + obj.e_s = kr(Ix, ops_y.e_l); + obj.e_n = kr(Ix, ops_y.e_r); + + obj.m = m; + obj.h = [ops_x.h ops_y.h]; + obj.order = order; + obj.a = a; + obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy); + + end + % Closure functions return the opertors applied to the own domain to close the boundary + % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. + % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. + % type is a string specifying the type of boundary condition if there are several. + % data is a function returning the data that should be applied at the boundary. + % neighbour_scheme is an instance of Scheme that should be interfaced to. + % neighbour_boundary is a string specifying which boundary to interface to. + function [closure, penalty] = boundary_condition(obj,boundary,type) + default_arg('type','dirichlet'); + + sigma = -1; % Scalar penalty parameter + switch boundary + case {'w','W','west','West'} + tau = sigma*obj.a{1}*obj.e_w*obj.H_y; + closure = obj.Hi*tau*obj.e_w'; + + case {'s','S','south','South'} + tau = sigma*obj.a{2}*obj.e_s*obj.H_x; + closure = obj.Hi*tau*obj.e_s'; + end + penalty = -obj.Hi*tau; + + end + + % type Struct that specifies the interface coupling. + % Fields: + % -- couplingType String, type of interface coupling + % % Default: 'upwind'. Other: 'centered' + % -- interpolation: type of interpolation, default 'none' + % -- interpolationDamping: damping on upstream and downstream sides, when using interpolation. + % Default {0,0} gives zero damping. + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + defaultType.couplingType = 'upwind'; + defaultType.interpolation = 'none'; + defaultType.interpolationDamping = {0,0}; + default_struct('type', defaultType); + + switch type.interpolation + case {'none', ''} + [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type); + case {'op','OP'} + [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type); + otherwise + error('Unknown type of interpolation: %s ', type.interpolation); + end + end + + function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type) + couplingType = type.couplingType; + + % Get neighbour boundary operator + e_neighbour = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + + switch couplingType + + % Upwind coupling (energy dissipation) + case 'upwind' + sigma_ds = -1; %"Downstream" penalty + sigma_us = 0; %"Upstream" penalty + + % Energy-preserving coupling (no energy dissipation) + case 'centered' + sigma_ds = -1/2; %"Downstream" penalty + sigma_us = 1/2; %"Upstream" penalty + + otherwise + error(['Interface coupling type ' couplingType ' is not available.']) + end + + switch boundary + case {'w','W','west','West'} + tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y; + closure = obj.Hi*tau*obj.e_w'; + penalty = -obj.Hi*tau*e_neighbour'; + case {'e','E','east','East'} + tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y; + closure = obj.Hi*tau*obj.e_e'; + penalty = -obj.Hi*tau*e_neighbour'; + case {'s','S','south','South'} + tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x; + closure = obj.Hi*tau*obj.e_s'; + penalty = -obj.Hi*tau*e_neighbour'; + case {'n','N','north','North'} + tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x; + closure = obj.Hi*tau*obj.e_n'; + penalty = -obj.Hi*tau*e_neighbour'; + end + + end + + function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type) + + % User can request special interpolation operators by specifying type.interpOpSet + default_field(type, 'interpOpSet', @sbp.InterpOpsOP); + + interpOpSet = type.interpOpSet; + couplingType = type.couplingType; + interpolationDamping = type.interpolationDamping; + + % Get neighbour boundary operator + e_neighbour = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); + + switch couplingType + + % Upwind coupling (energy dissipation) + case 'upwind' + sigma_ds = -1; %"Downstream" penalty + sigma_us = 0; %"Upstream" penalty + + % Energy-preserving coupling (no energy dissipation) + case 'centered' + sigma_ds = -1/2; %"Downstream" penalty + sigma_us = 1/2; %"Upstream" penalty + + otherwise + error(['Interface coupling type ' couplingType ' is not available.']) + end + + int_damp_us = interpolationDamping{1}; + int_damp_ds = interpolationDamping{2}; + + % u denotes the solution in the own domain + % v denotes the solution in the neighbour domain + % Find the number of grid points along the interface + switch boundary + case {'w','e'} + m_u = obj.m(2); + case {'s','n'} + m_u = obj.m(1); + end + m_v = size(e_neighbour, 2); + + % Build interpolation operators + intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order); + Iu2v = intOps.Iu2v; + Iv2u = intOps.Iv2u; + + I_local2neighbour_ds = intOps.Iu2v.bad; + I_local2neighbour_us = intOps.Iu2v.good; + I_neighbour2local_ds = intOps.Iv2u.good; + I_neighbour2local_us = intOps.Iv2u.bad; + + I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us; + I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds; + + + switch boundary + case {'w','W','west','West'} + tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y; + closure = obj.Hi*tau*obj.e_w'; + penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour'; + + beta = int_damp_ds*obj.a{1}... + *obj.e_w*obj.H_y; + closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_w' - obj.Hi*beta*obj.e_w'; + case {'e','E','east','East'} + tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y; + closure = obj.Hi*tau*obj.e_e'; + penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour'; + + beta = int_damp_us*obj.a{1}... + *obj.e_e*obj.H_y; + closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_e' - obj.Hi*beta*obj.e_e'; + case {'s','S','south','South'} + tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x; + closure = obj.Hi*tau*obj.e_s'; + penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour'; + + beta = int_damp_ds*obj.a{2}... + *obj.e_s*obj.H_x; + closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_s' - obj.Hi*beta*obj.e_s'; + case {'n','N','north','North'} + tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x; + closure = obj.Hi*tau*obj.e_n'; + penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour'; + + beta = int_damp_us*obj.a{2}... + *obj.e_n*obj.H_x; + closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_n' - obj.Hi*beta*obj.e_n'; + end + + + end + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string + % boundary -- string + function o = getBoundaryOperator(obj, op, boundary) + assertIsMember(op, {'e'}) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + o = obj.([op, '_', boundary]); + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + H_b = obj.(['H_', boundary]); + end + + function N = size(obj) + N = obj.m; + end + + end +end
--- a/+scheme/Wave.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,175 +0,0 @@ -classdef Wave < scheme.Scheme - properties - m % Number of points in each direction, possibly a vector - h % Grid spacing - x % Grid - order % Order accuracy for the approximation - - D % non-stabalized scheme operator - H % Discrete norm - M % Derivative norm - alpha - - D2 - Hi - e_l - e_r - d1_l - d1_r - gamm - end - - methods - function obj = Wave(m,xlim,order,alpha) - default_arg('a',1); - [x, h] = util.get_grid(xlim{:},m); - - ops = sbp.Ordinary(m,h,order); - - obj.D2 = sparse(ops.derivatives.D2); - obj.H = sparse(ops.norms.H); - obj.Hi = sparse(ops.norms.HI); - obj.M = sparse(ops.norms.M); - obj.e_l = sparse(ops.boundary.e_1); - obj.e_r = sparse(ops.boundary.e_m); - obj.d1_l = sparse(ops.boundary.S_1); - obj.d1_r = sparse(ops.boundary.S_m); - - - obj.m = m; - obj.h = h; - obj.order = order; - - obj.alpha = alpha; - obj.D = alpha*obj.D2; - obj.x = x; - - obj.gamm = h*ops.borrowing.M.S; - - end - - - % Closure functions return the opertors applied to the own doamin to close the boundary - % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. - % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. - % type is a string specifying the type of boundary condition if there are several. - % data is a function returning the data that should be applied at the boundary. - % neighbour_scheme is an instance of Scheme that should be interfaced to. - % neighbour_boundary is a string specifying which boundary to interface to. - function [closure, penalty] = boundary_condition(obj,boundary,type,data) - default_arg('type','neumann'); - default_arg('data',0); - - [e,d,s] = obj.get_boundary_ops(boundary); - - switch type - % Dirichlet boundary condition - case {'D','dirichlet'} - alpha = obj.alpha; - - % tau1 < -alpha^2/gamma - tuning = 1.1; - tau1 = -tuning*alpha/obj.gamm; - tau2 = s*alpha; - - p = tau1*e + tau2*d; - - closure = obj.Hi*p*e'; - - pp = obj.Hi*p; - switch class(data) - case 'double' - penalty = pp*data; - case 'function_handle' - penalty = @(t)pp*data(t); - otherwise - error('Wierd data argument!') - end - - - % Neumann boundary condition - case {'N','neumann'} - alpha = obj.alpha; - tau1 = -s*alpha; - tau2 = 0; - tau = tau1*e + tau2*d; - - closure = obj.Hi*tau*d'; - - pp = obj.Hi*tau; - switch class(data) - case 'double' - penalty = pp*data; - case 'function_handle' - penalty = @(t)pp*data(t); - otherwise - error('Wierd data argument!') - end - - % Unknown, boundary condition - otherwise - error('No such boundary condition: type = %s',type); - end - end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - % u denotes the solution in the own domain - % v denotes the solution in the neighbour domain - [e_u,d_u,s_u] = obj.get_boundary_ops(boundary); - [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); - - tuning = 1.1; - - alpha_u = obj.alpha; - alpha_v = neighbour_scheme.alpha; - - gamm_u = obj.gamm; - gamm_v = neighbour_scheme.gamm; - - % tau1 < -(alpha_u/gamm_u + alpha_v/gamm_v) - - tau1 = -(alpha_u/gamm_u + alpha_v/gamm_v) * tuning; - tau2 = s_u*1/2*alpha_u; - sig1 = s_u*(-1/2); - sig2 = 0; - - tau = tau1*e_u + tau2*d_u; - sig = sig1*e_u + sig2*d_u; - - closure = obj.Hi*( tau*e_u' + sig*alpha_u*d_u'); - penalty = obj.Hi*(-tau*e_v' - sig*alpha_v*d_v'); - end - - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e,d,s] = get_boundary_ops(obj,boundary) - switch boundary - case 'l' - e = obj.e_l; - d = obj.d1_l; - s = -1; - case 'r' - e = obj.e_r; - d = obj.d1_r; - s = 1; - otherwise - error('No such boundary: boundary = %s',boundary); - end - end - - function N = size(obj) - N = obj.m; - end - - end - - methods(Static) - % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u - % and bound_v of scheme schm_v. - % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') - function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) - [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); - [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); - end - end -end \ No newline at end of file
--- a/+scheme/Wave2d.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/Wave2d.m Tue Feb 12 17:12:42 2019 +0100 @@ -106,7 +106,10 @@ default_arg('type','neumann'); default_arg('data',0); - [e,d,s,gamm,halfnorm_inv] = obj.get_boundary_ops(boundary); + [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary); + gamm = obj.getBoundaryBorrowing(boundary); + s = obj.getBoundarySign(boundary); + halfnorm_inv = obj.getHalfnormInv(boundary); switch type % Dirichlet boundary condition @@ -158,12 +161,21 @@ end end - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) % u denotes the solution in the own domain % v denotes the solution in the neighbour domain [e_u,d_u,s_u,gamm_u, halfnorm_inv] = obj.get_boundary_ops(boundary); [e_v,d_v,s_v,gamm_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); + [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary); + gamm_u = obj.getBoundaryBorrowing(boundary); + s_u = obj.getBoundarySign(boundary); + halfnorm_inv = obj.getHalfnormInv(boundary); + + [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary); + gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary); + s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); + tuning = 1.1; alpha_u = obj.alpha; @@ -183,36 +195,107 @@ penalty = halfnorm_inv*(-tau*e_v' - sig*alpha_v*d_v'); end - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - function [e,d,s,gamm, halfnorm_inv] = get_boundary_ops(obj,boundary) + + % Returns the boundary operator op for the boundary specified by the string boundary. + % op -- string or a cell array of strings + % boundary -- string + function varargout = getBoundaryOperator(obj, op, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + if ~iscell(op) + op = {op}; + end + + for i = 1:numel(op) + switch op{i} + case 'e' + switch boundary + case 'w' + e = obj.e_w; + case 'e' + e = obj.e_e; + case 's' + e = obj.e_s; + case 'n' + e = obj.e_n; + end + varargout{i} = e; + + case 'd' + switch boundary + case 'w' + d = obj.d1_w; + case 'e' + d = obj.d1_e; + case 's' + d = obj.d1_s; + case 'n' + d = obj.d1_n; + end + varargout{i} = d; + end + end + + end + + % Returns square boundary quadrature matrix, of dimension + % corresponding to the number of boundary points + % + % boundary -- string + function H_b = getBoundaryQuadrature(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + switch boundary case 'w' - e = obj.e_w; - d = obj.d1_w; - s = -1; - gamm = obj.gamm_x; - halfnorm_inv = obj.Hix; + H_b = obj.H_y; case 'e' - e = obj.e_e; - d = obj.d1_e; - s = 1; - gamm = obj.gamm_x; - halfnorm_inv = obj.Hix; + H_b = obj.H_y; case 's' - e = obj.e_s; - d = obj.d1_s; - s = -1; - gamm = obj.gamm_y; - halfnorm_inv = obj.Hiy; + H_b = obj.H_x; case 'n' - e = obj.e_n; - d = obj.d1_n; - s = 1; + H_b = obj.H_x; + end + end + + % Returns borrowing constant gamma + % boundary -- string + function gamm = getBoundaryBorrowing(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'w','e'} + gamm = obj.gamm_x; + case {'s','n'} gamm = obj.gamm_y; - halfnorm_inv = obj.Hiy; - otherwise - error('No such boundary: boundary = %s',boundary); + end + end + + % Returns the boundary sign. The right boundary is considered the positive boundary + % boundary -- string + function s = getBoundarySign(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case {'e','n'} + s = 1; + case {'w','s'} + s = -1; + end + end + + % Returns the halfnorm_inv used in SATs. TODO: better notation + function Hinv = getHalfnormInv(obj, boundary) + assertIsMember(boundary, {'w', 'e', 's', 'n'}) + + switch boundary + case 'w' + Hinv = obj.Hix; + case 'e' + Hinv = obj.Hix; + case 's' + Hinv = obj.Hiy; + case 'n' + Hinv = obj.Hiy; end end @@ -221,14 +304,4 @@ end end - - methods(Static) - % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u - % and bound_v of scheme schm_v. - % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') - function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) - [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); - [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); - end - end -end \ No newline at end of file +end
--- a/+scheme/Wave2dCurve.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,359 +0,0 @@ -classdef Wave2dCurve < scheme.Scheme - properties - m % Number of points in each direction, possibly a vector - h % Grid spacing - - grid - - order % Order accuracy for the approximation - - D % non-stabalized scheme operator - M % Derivative norm - c - J, Ji - a11, a12, a22 - - H % Discrete norm - Hi - H_u, H_v % Norms in the x and y directions - Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. - Hi_u, Hi_v - Hiu, Hiv - e_w, e_e, e_s, e_n - du_w, dv_w - du_e, dv_e - du_s, dv_s - du_n, dv_n - gamm_u, gamm_v - lambda - - Dx, Dy % Physical derivatives - - x_u - x_v - y_u - y_v - end - - methods - function obj = Wave2dCurve(g ,order, c, opSet) - default_arg('opSet',@sbp.D2Variable); - default_arg('c', 1); - - warning('Use LaplaceCruveilinear instead') - - assert(isa(g, 'grid.Curvilinear')) - - m = g.size(); - m_u = m(1); - m_v = m(2); - m_tot = g.N(); - - h = g.scaling(); - h_u = h(1); - h_v = h(2); - - % Operators - ops_u = opSet(m_u, {0, 1}, order); - ops_v = opSet(m_v, {0, 1}, order); - - I_u = speye(m_u); - I_v = speye(m_v); - - D1_u = ops_u.D1; - D2_u = ops_u.D2; - H_u = ops_u.H; - Hi_u = ops_u.HI; - e_l_u = ops_u.e_l; - e_r_u = ops_u.e_r; - d1_l_u = ops_u.d1_l; - d1_r_u = ops_u.d1_r; - - D1_v = ops_v.D1; - D2_v = ops_v.D2; - H_v = ops_v.H; - Hi_v = ops_v.HI; - e_l_v = ops_v.e_l; - e_r_v = ops_v.e_r; - d1_l_v = ops_v.d1_l; - d1_r_v = ops_v.d1_r; - - Du = kr(D1_u,I_v); - Dv = kr(I_u,D1_v); - - % Metric derivatives - coords = g.points(); - x = coords(:,1); - y = coords(:,2); - - x_u = Du*x; - x_v = Dv*x; - y_u = Du*y; - y_v = Dv*y; - - J = x_u.*y_v - x_v.*y_u; - a11 = 1./J .* (x_v.^2 + y_v.^2); - a12 = -1./J .* (x_u.*x_v + y_u.*y_v); - a22 = 1./J .* (x_u.^2 + y_u.^2); - lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); - - % Assemble full operators - L_12 = spdiags(a12, 0, m_tot, m_tot); - Duv = Du*L_12*Dv; - Dvu = Dv*L_12*Du; - - Duu = sparse(m_tot); - Dvv = sparse(m_tot); - ind = grid.funcToMatrix(g, 1:m_tot); - - for i = 1:m_v - D = D2_u(a11(ind(:,i))); - p = ind(:,i); - Duu(p,p) = D; - end - - for i = 1:m_u - D = D2_v(a22(ind(i,:))); - p = ind(i,:); - Dvv(p,p) = D; - end - - obj.H = kr(H_u,H_v); - obj.Hi = kr(Hi_u,Hi_v); - obj.Hu = kr(H_u,I_v); - obj.Hv = kr(I_u,H_v); - obj.Hiu = kr(Hi_u,I_v); - obj.Hiv = kr(I_u,Hi_v); - - obj.e_w = kr(e_l_u,I_v); - obj.e_e = kr(e_r_u,I_v); - obj.e_s = kr(I_u,e_l_v); - obj.e_n = kr(I_u,e_r_v); - obj.du_w = kr(d1_l_u,I_v); - obj.dv_w = (obj.e_w'*Dv)'; - obj.du_e = kr(d1_r_u,I_v); - obj.dv_e = (obj.e_e'*Dv)'; - obj.du_s = (obj.e_s'*Du)'; - obj.dv_s = kr(I_u,d1_l_v); - obj.du_n = (obj.e_n'*Du)'; - obj.dv_n = kr(I_u,d1_r_v); - - obj.x_u = x_u; - obj.x_v = x_v; - obj.y_u = y_u; - obj.y_v = y_v; - - obj.m = m; - obj.h = [h_u h_v]; - obj.order = order; - obj.grid = g; - - obj.c = c; - obj.J = spdiags(J, 0, m_tot, m_tot); - obj.Ji = spdiags(1./J, 0, m_tot, m_tot); - obj.a11 = a11; - obj.a12 = a12; - obj.a22 = a22; - obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); - obj.lambda = lambda; - - obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv; - obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv; - - obj.gamm_u = h_u*ops_u.borrowing.M.d1; - obj.gamm_v = h_v*ops_v.borrowing.M.d1; - end - - - % Closure functions return the opertors applied to the own doamin to close the boundary - % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. - % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. - % type is a string specifying the type of boundary condition if there are several. - % data is a function returning the data that should be applied at the boundary. - % neighbour_scheme is an instance of Scheme that should be interfaced to. - % neighbour_boundary is a string specifying which boundary to interface to. - function [closure, penalty] = boundary_condition(obj, boundary, type, parameter) - default_arg('type','neumann'); - default_arg('parameter', []); - - [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv , ~, ~, ~, scale_factor] = obj.get_boundary_ops(boundary); - switch type - % Dirichlet boundary condition - case {'D','d','dirichlet'} - % v denotes the solution in the neighbour domain - tuning = 1.2; - % tuning = 20.2; - [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t] = obj.get_boundary_ops(boundary); - - a_n = spdiag(coeff_n); - a_t = spdiag(coeff_t); - - F = (s * a_n * d_n' + s * a_t*d_t')'; - - u = obj; - - b1 = gamm*u.lambda./u.a11.^2; - b2 = gamm*u.lambda./u.a22.^2; - - tau = -1./b1 - 1./b2; - tau = tuning * spdiag(tau); - sig1 = 1; - - penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; - - closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; - penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; - - - % Neumann boundary condition - case {'N','n','neumann'} - c = obj.c; - - a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); - a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); - d = (a_n * d_n' + a_t*d_t')'; - - tau1 = -s; - tau2 = 0; - tau = c.^2 * obj.Ji*(tau1*e + tau2*d); - - closure = halfnorm_inv*tau*d'; - penalty = -halfnorm_inv*tau; - - % Characteristic boundary condition - case {'characteristic', 'char', 'c'} - default_arg('parameter', 1); - beta = parameter; - c = obj.c; - - a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); - a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); - d = s*(a_n * d_n' + a_t*d_t')'; % outward facing normal derivative - - tau = -c.^2 * 1/beta*obj.Ji*e; - - warning('is this right?! /c?') - closure{1} = halfnorm_inv*tau/c*spdiag(scale_factor)*e'; - closure{2} = halfnorm_inv*tau*beta*d'; - penalty = -halfnorm_inv*tau; - - % Unknown, boundary condition - otherwise - error('No such boundary condition: type = %s',type); - end - end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - % u denotes the solution in the own domain - % v denotes the solution in the neighbour domain - tuning = 1.2; - % tuning = 20.2; - [e_u, d_n_u, d_t_u, coeff_n_u, coeff_t_u, s_u, gamm_u, halfnorm_inv_u_n, halfnorm_inv_u_t, halfnorm_u_t, I_u] = obj.get_boundary_ops(boundary); - [e_v, d_n_v, d_t_v, coeff_n_v, coeff_t_v, s_v, gamm_v, halfnorm_inv_v_n, halfnorm_inv_v_t, halfnorm_v_t, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); - - a_n_u = spdiag(coeff_n_u); - a_t_u = spdiag(coeff_t_u); - a_n_v = spdiag(coeff_n_v); - a_t_v = spdiag(coeff_t_v); - - F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; - F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; - - u = obj; - v = neighbour_scheme; - - b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; - b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; - b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; - b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; - - tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); - tau = tuning * spdiag(tau); - sig1 = 1/2; - sig2 = -1/2; - - penalty_parameter_1 = halfnorm_inv_u_n*(e_u*tau + sig1*halfnorm_inv_u_t*F_u*e_u'*halfnorm_u_t*e_u); - penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; - - - closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); - penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); - end - - % Ruturns the boundary ops and sign for the boundary specified by the string boundary. - % The right boundary is considered the positive boundary - % - % I -- the indecies of the boundary points in the grid matrix - function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I, scale_factor] = get_boundary_ops(obj, boundary) - - % gridMatrix = zeros(obj.m(2),obj.m(1)); - % gridMatrix(:) = 1:numel(gridMatrix); - - ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); - - switch boundary - case 'w' - e = obj.e_w; - d_n = obj.du_w; - d_t = obj.dv_w; - s = -1; - - I = ind(1,:); - coeff_n = obj.a11(I); - coeff_t = obj.a12(I); - scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); - case 'e' - e = obj.e_e; - d_n = obj.du_e; - d_t = obj.dv_e; - s = 1; - - I = ind(end,:); - coeff_n = obj.a11(I); - coeff_t = obj.a12(I); - scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); - case 's' - e = obj.e_s; - d_n = obj.dv_s; - d_t = obj.du_s; - s = -1; - - I = ind(:,1)'; - coeff_n = obj.a22(I); - coeff_t = obj.a12(I); - scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); - case 'n' - e = obj.e_n; - d_n = obj.dv_n; - d_t = obj.du_n; - s = 1; - - I = ind(:,end)'; - coeff_n = obj.a22(I); - coeff_t = obj.a12(I); - scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); - otherwise - error('No such boundary: boundary = %s',boundary); - end - - switch boundary - case {'w','e'} - halfnorm_inv_n = obj.Hiu; - halfnorm_inv_t = obj.Hiv; - halfnorm_t = obj.Hv; - gamm = obj.gamm_u; - case {'s','n'} - halfnorm_inv_n = obj.Hiv; - halfnorm_inv_t = obj.Hiu; - halfnorm_t = obj.Hu; - gamm = obj.gamm_v; - end - end - - function N = size(obj) - N = prod(obj.m); - end - - - end -end \ No newline at end of file
--- a/+scheme/bcSetup.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+scheme/bcSetup.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,10 +1,9 @@ -% function [closure, S] = bcSetup(diffOp, bc) % Takes a diffOp and a cell array of boundary condition definitions. % Each bc is a struct with the fields % * type -- Type of boundary condition % * boundary -- Boundary identifier % * data -- A function_handle for a function which provides boundary data.(see below) -% Also takes S_sign which modifies the sign of S, [-1,1] +% Also takes S_sign which modifies the sign of the penalty function, [-1,1] % Returns a closure matrix and a forcing function S. % % The boundary data function can either be a function of time or a function of time and space coordinates. @@ -16,97 +15,6 @@ assertType(bcs, 'cell'); assert(S_sign == 1 || S_sign == -1, 'S_sign must be either 1 or -1'); - verifyBcFormat(bcs, diffOp); - - % Setup storage arrays - closure = spzeros(size(diffOp)); - gridData = {}; - symbolicData = {}; - - % Collect closures, penalties and data - for i = 1:length(bcs) - [localClosure, penalty] = diffOp.boundary_condition(bcs{i}.boundary, bcs{i}.type); - closure = closure + localClosure; - - [ok, isSymbolic, data] = parseData(bcs{i}, penalty, diffOp.grid); - - if ~ok - % There was no data - continue - end - - if isSymbolic - symbolicData{end+1} = data; - else - gridData{end+1} = data; - end - end - - % Setup penalty function - O = spzeros(size(diffOp),1); - function v = S_fun(t) - v = O; - for i = 1:length(gridData) - v = v + gridData{i}.penalty*gridData{i}.func(t); - end - - for i = 1:length(symbolicData) - v = v + symbolicData{i}.penalty*symbolicData{i}.func(t, symbolicData{i}.coords{:}); - end - - v = S_sign * v; - end - S = @S_fun; + [closure, penalties] = scheme.bc.closureSetup(diffOp, bcs); + S = scheme.bc.forcingSetup(diffOp, penalties, bcs, S_sign); end - -function verifyBcFormat(bcs, diffOp) - for i = 1:length(bcs) - assertType(bcs{i}, 'struct'); - assertStructFields(bcs{i}, {'type', 'boundary'}); - - if ~isfield(bcs{i}, 'data') || isempty(bcs{i}.data) - continue - end - - if ~isa(bcs{i}.data, 'function_handle') - error('bcs{%d}.data should be a function of time or a function of time and space',i); - end - - b = diffOp.grid.getBoundary(bcs{i}.boundary); - - dim = size(b,2); - - if nargin(bcs{i}.data) == 1 - % Grid data (only function of time) - assertSize(bcs{i}.data(0), 1, size(b)); - elseif nargin(bcs{i}.data) ~= 1+dim - error('sbplib:scheme:bcSetup:DataWrongNumberOfArguments', 'bcs{%d}.data has the wrong number of input arguments. Must be either only time or time and space.', i); - end - end -end - -function [ok, isSymbolic, dataStruct] = parseData(bc, penalty, grid) - if ~isfield(bc,'data') || isempty(bc.data) - isSymbolic = []; - dataStruct = struct(); - ok = false; - return - end - ok = true; - - nArg = nargin(bc.data); - - if nArg > 1 - % Symbolic data - isSymbolic = true; - coord = grid.getBoundary(bc.boundary); - dataStruct.penalty = penalty; - dataStruct.func = bc.data; - dataStruct.coords = num2cell(coord, 1); - else - % Grid data - isSymbolic = false; - dataStruct.penalty = penalty; - dataStruct.func = bcs{i}.data; - end -end
--- a/+scheme/error1d.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,4 +0,0 @@ -function e = error1d(discr, v1, v2) - h = discr.h; - e = sqrt(h*sum((v1-v2).^2)); -end \ No newline at end of file
--- a/+scheme/error2d.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,5 +0,0 @@ -function e = error2d(discr, v1, v2) - % If v1 and v2 are more complex types, something like grid functions... Then we may use .getVectorFrom here! - h = discr.h; - e = sqrt(h.^2*sum((v1-v2).^2)); -end \ No newline at end of file
--- a/+scheme/errorMax.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -function e = errorMax(~, v1, v2) - e = max(abs(v1-v2)); -end
--- a/+scheme/errorRelative.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -function e = errorRelative(~,v1,v2) - e = sqrt(sum((v1-v2).^2)/sum(v2.^2)); -end \ No newline at end of file
--- a/+scheme/errorSbp.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,6 +0,0 @@ -function e = errorSbp(discr, v1, v2) - % If v1 and v2 are more complex types, something like grid functions... Then we may use .getVectorFrom here! - H = discr.H; - err = v2 - v1; - e = sqrt(err'*H*err); -end \ No newline at end of file
--- a/+scheme/errorVector.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -function e = errorVector(~, v1, v2) - e = v2-v1; -end \ No newline at end of file
--- a/+time/+cdiff/cdiff.m Thu Sep 20 12:05:20 2018 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -% Takes a step of -% v_tt = Dv+Ev_t+S -% -% 1/k^2 * (v_next - 2v + v_prev) = Dv + E 1/(2k)(v_next - v_prev) + S -% -function [v_next, v] = cdiff(v, v_prev, k, D, E, S) - % 1/k^2 * (v_next - 2v + v_prev) = Dv + E 1/(2k)(v_next - v_prev) + S - % ekv to - % A v_next = B v + C v_prev + S - I = speye(size(D)); - A = 1/k^2 * I - 1/(2*k)*E; - B = 2/k^2 * I + D; - C = -1/k^2 * I - 1/(2*k)*E; - - v_next = A\(B*v + C*v_prev + S); -end \ No newline at end of file
--- a/+time/Cdiff.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+time/Cdiff.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,36 +1,45 @@ classdef Cdiff < time.Timestepper properties - D - E - S + A, B, C + AA, BB, CC + G k t - v - v_prev + v, v_prev n end methods - % Solves u_tt = Du + Eu_t + S - % D, E, S can either all be constants or all be function handles, - % They can also be omitted by setting them equal to the empty matrix. - % Cdiff(D, E, S, k, t0, n0, v, v_prev) - function obj = Cdiff(D, E, S, k, t0, n0, v, v_prev) - m = length(v); - default_arg('E',sparse(m,m)); - default_arg('S',sparse(m,1)); + % Solves + % A*v_tt + B*v_t + C*v = G(t) + % v(t0) = v0 + % v_t(t0) = v0t + % starting at time t0 with timestep k + % Using + % A*Dp*Dm*v_n + B*D0*v_n + C*v_n = G(t_n) + function obj = Cdiff(A, B, C, G, v0, v0t, k, t0) + m = length(v0); + default_arg('A', speye(m)); + default_arg('B', sparse(m,m)); + default_arg('G', @(t) sparse(m,1)); + default_arg('t0', 0); - obj.D = D; - obj.E = E; - obj.S = S; + obj.A = A; + obj.B = B; + obj.C = C; + obj.G = G; + % Rewrite as AA*v_(n+1) + BB*v_n + CC*v_(n-1) = G(t_n) + obj.AA = A/k^2 + B/(2*k); + obj.BB = -2*A/k^2 + C; + obj.CC = A/k^2 - B/(2*k); obj.k = k; - obj.t = t0; - obj.n = n0; - obj.v = v; - obj.v_prev = v_prev; + obj.v_prev = v0; + obj.v = v0 + k*v0t; + obj.t = t0+k; + obj.n = 1; end function [v,t] = getV(obj) @@ -43,10 +52,21 @@ t = obj.t; end + function E = getEnergy(obj) + v = obj.v; + vp = obj.v_prev; + vt = (obj.v - obj.v_prev)/obj.k; + + E = vt'*obj.A*vt + v'*obj.C*vp; + end + function obj = step(obj) - [obj.v, obj.v_prev] = time.cdiff.cdiff(obj.v, obj.v_prev, obj.k, obj.D, obj.E, obj.S); + v_next = obj.AA\(-obj.BB*obj.v - obj.CC*obj.v_prev + obj.G(obj.t)); + + obj.v_prev = obj.v; + obj.v = v_next; obj.t = obj.t + obj.k; obj.n = obj.n + 1; end end -end \ No newline at end of file +end
--- a/+time/CdiffImplicit.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+time/CdiffImplicit.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,7 +1,8 @@ classdef CdiffImplicit < time.Timestepper properties - A, B, C, G + A, B, C AA, BB, CC + G k t v, v_prev @@ -13,59 +14,36 @@ methods % Solves - % A*u_tt + B*u + C*v_t = G(t) - % u(t0) = f1 - % u_t(t0) = f2 - % starting at time t0 with timestep k - function obj = CdiffImplicit(A, B, C, G, f1, f2, k, t0) - default_arg('A', []); - default_arg('C', []); - default_arg('G', []); - default_arg('f1', 0); - default_arg('f2', 0); + % A*v_tt + B*v_t + C*v = G(t) + % v(t0) = v0 + % v_t(t0) = v0t + % starting at time t0 with timestep + % Using + % A*Dp*Dm*v_n + B*D0*v_n + C*I0*v_n = G(t_n) + function obj = CdiffImplicit(A, B, C, G, v0, v0t, k, t0) + m = length(v0); + default_arg('A', speye(m)); + default_arg('B', sparse(m,m)); + default_arg('G', @(t) sparse(m,1)); default_arg('t0', 0); - m = size(B,1); - - if isempty(A) - A = speye(m); - end - - if isempty(C) - C = sparse(m,m); - end - - if isempty(G) - G = @(t) sparse(m,1); - end - - if isempty(f1) - f1 = sparse(m,1); - end - - if isempty(f2) - f2 = sparse(m,1); - end - obj.A = A; obj.B = B; obj.C = C; obj.G = G; - AA = 1/k^2*A + 1/2*B + 1/(2*k)*C; - BB = -2/k^2*A; - CC = 1/k^2*A + 1/2*B - 1/(2*k)*C; - % AA*v_next + BB*v + CC*v_prev == G(t_n) + % Rewrite as AA*v_(n+1) + BB*v_n + CC*v_(n-1) = G(t_n) + AA = A/k^2 + B/(2*k) + C/2; + BB = -2*A/k^2; + CC = A/k^2 - B/(2*k) + C/2; obj.AA = AA; obj.BB = BB; obj.CC = CC; - v_prev = f1; + v_prev = v0; I = speye(m); - % v = (1/k^2*A)\((1/k^2*A - 1/2*B)*f1 + (1/k*I - 1/2*C)*f2 + 1/2*G(0)); - v = f1 + k*f2; - + v = v0 + k*v0t; if ~issparse(A) || ~issparse(B) || ~issparse(C) error('LU factorization with full pivoting only works for sparse matrices.') @@ -78,7 +56,6 @@ obj.p = p; obj.q = q; - obj.k = k; obj.t = t0+k; obj.n = 1; @@ -92,17 +69,17 @@ end function [vt,t] = getVt(obj) - % Calculate next time step to be able to do centered diff. - v_next = zeros(size(obj.v)); - b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev; + vt = (obj.v-obj.v_prev)/obj.k; % Could be improved using u_tt = f(u)) + t = obj.t; + end - y = obj.L\b(obj.p); - z = obj.U\y; - v_next(obj.q) = z; + % Calculate the conserved energy (Dm*v_n)^2_A + Im*v_n^2_B + function E = getEnergy(obj) + v = obj.v; + vp = obj.v_prev; + vt = (obj.v - obj.v_prev)/obj.k; - - vt = (v_next-obj.v_prev)/(2*obj.k); - t = obj.t; + E = vt'*obj.A*vt + 1/2*(v'*obj.C*v + vp'*obj.C*vp); end function obj = step(obj) @@ -123,30 +100,3 @@ end end end - - - - - -%%% Derivation -% syms A B C G -% syms n k -% syms f1 f2 - -% v = symfun(sym('v(n)'),n); - - -% d = A/k^2 * (v(n+1) - 2*v(n) +v(n-1)) + B/2*(v(n+1)+v(n-1)) + C/(2*k)*(v(n+1) - v(n-1)) == G -% ic1 = v(0) == f1 -% ic2 = A/k*(v(1)-f1) + k/2*(B*f1 + C*f2 - G) - f2 == 0 - -% c = collect(d, [v(n) v(n-1) v(n+1)]) % (-(2*A)/k^2)*v(n) + (B/2 + A/k^2 - C/(2*k))*v(n - 1) + (B/2 + A/k^2 + C/(2*k))*v(n + 1) == G -% syms AA BB CC -% % AA = B/2 + A/k^2 + C/(2*k) -% % BB = -(2*A)/k^2 -% % CC = B/2 + A/k^2 - C/(2*k) -% s = subs(c, [B/2 + A/k^2 + C/(2*k), -(2*A)/k^2, B/2 + A/k^2 - C/(2*k)], [AA, BB, CC]) - - -% ic2_a = collect(ic2, [v(1) f1 f2]) % (A/k)*v(1) + ((B*k)/2 - A/k)*f1 + ((C*k)/2 - 1)*f2 - (G*k)/2 == 0 -
--- a/+util/ReplaceableString.m Thu Sep 20 12:05:20 2018 +0200 +++ b/+util/ReplaceableString.m Tue Feb 12 17:12:42 2019 +0100 @@ -58,3 +58,5 @@ function b = padStr(a, n) b = sprintf('%-*s', n, a); end + +% TODO: Add a debug mode which prints without replacing?
--- a/Map.m Thu Sep 20 12:05:20 2018 +0200 +++ b/Map.m Tue Feb 12 17:12:42 2019 +0100 @@ -59,6 +59,9 @@ function v = subsref(obj, S) switch S(1).type case '()' + if length(S.subs) > 1 + error('sbplib:Map:multipleKeys', 'Multiple dimensions are not supported. Use a cell array as a key instead.'); + end k = S.subs{1}; try v = get(obj, k); @@ -81,6 +84,9 @@ function obj = subsasgn(obj, S, v); switch S(1).type case '()' + if length(S.subs) > 1 + error('sbplib:Map:multipleKeys', 'Multiple dimensions are not supported. Use a cell array as a key instead.'); + end k = S.subs{1}; set(obj, k, v); otherwise
--- a/MapTest.m Thu Sep 20 12:05:20 2018 +0200 +++ b/MapTest.m Tue Feb 12 17:12:42 2019 +0100 @@ -12,6 +12,21 @@ }; end +function testMultiKey(testCase) + map = Map + + function setMultiKey() + map(1,2) = 1; + end + + function getMultiKey() + v = map(1,2); + end + + testCase.verifyError(@setMultiKey,'sbplib:Map:multipleKeys') + testCase.verifyError(@getMultiKey,'sbplib:Map:multipleKeys') +end + function testSetAndGet(testCase) keyValuePairs = getKeyValuePairs();
--- a/TextTable.m Thu Sep 20 12:05:20 2018 +0200 +++ b/TextTable.m Tue Feb 12 17:12:42 2019 +0100 @@ -41,6 +41,14 @@ obj.fmtArray{i,j} = fmt; end + function formatGrid(obj, I, J, fmt) + for i = I + for j = J + obj.fmtArray{i,j} = fmt; + end + end + end + function formatRow(obj, i, fmt) obj.fmtArray(i,:) = {fmt}; end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/arrowAnnotation.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,23 @@ +% Draw an arrow from p1 to p2, with text attached +function [h] = arrowAnnotation(p1,p2) + ah = gca; + xl = ah.XLim(1); + xr = ah.XLim(2); + + yl = ah.YLim(1); + yr = ah.YLim(2); + + dx = xr - xl; + dy = yr - yl; + + s = [ + ah.Position(1) + (p1(1) - xl)/dx*ah.Position(3), + ah.Position(1) + (p2(1) - xl)/dx*ah.Position(3), + ]; + t = [ + ah.Position(2) + (p1(2) - yl)/dy*ah.Position(4), + ah.Position(2) + (p2(2) - yl)/dy*ah.Position(4), + ]; + + h = annotation('arrow', s, t); +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/assertLength.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,4 @@ +function assertLength(A,l) + assert(isvector(A), sprintf('Expected ''%s'' to be a vector, got matrix of size %s',inputname(1), toString(size(A)))); + assert(length(A) == l, sprintf('Expected ''%s'' to have length %d, got %d', inputname(1), l, length(A))); +end
--- a/assertSize.m Thu Sep 20 12:05:20 2018 +0200 +++ b/assertSize.m Tue Feb 12 17:12:42 2019 +0100 @@ -2,13 +2,13 @@ function assertSize(A,varargin) if length(varargin) == 1 s = varargin{1}; - errmsg = sprintf('Expected %s to have size %s, got: %s',inputname(1), toString(s), toString(size(A))); - assert(all(size(A) == s), errmsg); + assert(length(size(A)) == length(s), sprintf('Expected ''%s'' to have dimension %d, got %d', inputname(1), length(s), length(size(A)))); + assert(all(size(A) == s), sprintf('Expected ''%s'' to have size %s, got: %s',inputname(1), toString(s), toString(size(A)))); elseif length(varargin) == 2 dim = varargin{1}; s = varargin{2}; - errmsg = sprintf('Expected %s to have size %d along dimension %d, got: %d',inputname(1), s, dim, size(A,dim)); + errmsg = sprintf('Expected ''%s'' to have size %d along dimension %d, got: %d',inputname(1), s, dim, size(A,dim)); assert(size(A,dim) == s, errmsg); else error('Expected 2 or 3 arguments to assertSize()');
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/dealStruct.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,18 @@ +function varargout = dealStruct(s, fields) + default_arg('fields', []); + + if isempty(fields) + out = dealFields(s, fieldnames(s)); + varargout = out(1:nargout); + else + assert(nargout == length(fields), 'Number of output arguements must match the number of fieldnames provided'); + varargout = dealFields(s, fields); + end +end + +function out = dealFields(s, fields) + out = cell(1, length(fields)); + for i = 1:length(fields) + out{i} = s.(fields{i}); + end +end
--- a/default_field.m Thu Sep 20 12:05:20 2018 +0200 +++ b/default_field.m Tue Feb 12 17:12:42 2019 +0100 @@ -1,7 +1,7 @@ function default_field(s, f, val) - if isfield(s,f) + if isfield(s,f) && ~isempty(s.(f)) return end s.(f) = val; assignin('caller', inputname(1),s); -end \ No newline at end of file +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/hgRevision.m Tue Feb 12 17:12:42 2019 +0100 @@ -0,0 +1,8 @@ +% Returns the short mercurial revision Id. +% ok is false if there are uncommited changes. +function [revId, ok] = hgRevision() + [~, s] = system('hg id -i'); + revId = strtrim(s); + + ok = s(end) ~= '+'; +end