Mercurial > repos > public > sbplib
changeset 717:8e4274ee6dd8 feature/utux2D
Merge with feature/poroelastic
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Sat, 03 Mar 2018 14:58:21 -0800 |
| parents | 2d85f17a8aec (current diff) 60eb7f46d8d9 (diff) |
| children | 71aa5828cbbf |
| files | diffSymfun.m |
| diffstat | 29 files changed, 1320 insertions(+), 76 deletions(-) [+] |
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diff -r 2d85f17a8aec -r 8e4274ee6dd8 +blockmatrix/toMatrix.m --- a/+blockmatrix/toMatrix.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+blockmatrix/toMatrix.m Sat Mar 03 14:58:21 2018 -0800 @@ -12,12 +12,9 @@ A = sparse(N,M); - n_ind = [0 cumsum(n)]; - m_ind = [0 cumsum(m)]; - for i = 1:size(bm,1) for j = 1:size(bm,2) - if(isempty(bm{i,j})) + if isempty(bm{i,j}) bm{i,j} = sparse(n(i),m(j)); end end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +grid/Cartesian.m --- a/+grid/Cartesian.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+grid/Cartesian.m Sat Mar 03 14:58:21 2018 -0800 @@ -5,6 +5,7 @@ m % Number of points in each direction x % Cell array of vectors with node placement for each dimension. h % Spacing/Scaling + lim % Cell array of left and right boundaries for each dimension. end % General d dimensional grid with n points @@ -27,6 +28,7 @@ end obj.h = []; + obj.lim = []; end % n returns the number of points in the grid function o = N(obj)
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +grid/TODO.txt --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+grid/TODO.txt Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,1 @@ +% TODO: Rename grid package. name conflicts with built in function
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +grid/evalOn.m --- a/+grid/evalOn.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+grid/evalOn.m Sat Mar 03 14:58:21 2018 -0800 @@ -7,68 +7,34 @@ function gf = evalOn(g, func) if ~isa(func, 'function_handle') % We should have a constant. - if size(func,2) ~= 1 - error('grid:evalOn:VectorValuedWrongDim', 'A vector valued function must be given as a column vector') - end + assert(size(func,2) == 1,'grid:evalOn:VectorValuedWrongDim', 'A vector valued function must be given as a column vector'); gf = repmat(func,[g.N, 1]); return end % func should now be a function_handle + assert(g.D == nargin(func),'grid:evalOn:WrongNumberOfInputs', 'The number of inputs of the function must match the dimension of the domain.') - if g.D ~= nargin(func) - g.D - nargin(func) - error('grid:evalOn:WrongNumberOfInputs', 'The number of inputs of the function must match the dimension of the domain.') - end + x = num2cell(g.points(),1); + k = numberOfComponents(func); + gf = func(x{:}); + gf = reorderComponents(gf, k); +end - % Get coordinates - x = g.points(); +% Find the number of vector components of func +function k = numberOfComponents(func) + x0 = num2cell(ones(1,nargin(func))); + f0 = func(x0{:}); + assert(size(f0,2) == 1, 'grid:evalOn:VectorValuedWrongDim', 'A vector valued function must be given as a column vector'); + k = length(f0); +end - % Find the number of components - if size(x,1) ~= 0 - x0 = x(1,:); - else - x0 = num2cell(ones(1,size(x,2))); +% Reorder the components of the function to sit together +function gf = reorderComponents(a, k) + N = length(a)/k; + gf = zeros(N*k, 1); + for i = 1:k + gf(i:k:end) = a((i-1)*N + 1 : i*N); end - - dim = length(x0); - % Evaluate f0 = func(x0(1),x0(2),...,x0(dim)); - if(dim == 1) - f0 = func(x0); - else - eval_str = 'f0 = func(x0(1)'; - for i = 2:dim - eval_str = [eval_str, sprintf(',x0(%d)',i)]; - end - eval_str = [eval_str, ');']; - eval(eval_str); - end - - % k = number of components - k = length(f0); - - if size(f0,2) ~= 1 - error('grid:evalOn:VectorValuedWrongDim', 'A vector valued function must be given as a column vector') - end - - % Evaluate gf = func(x(:,1),x(:,2),...,x(:,dim)); - if(dim == 1) - gf = func(x); - else - eval_str = 'gf = func(x(:,1)'; - for i = 2:dim - eval_str = [eval_str, sprintf(',x(:,%d)',i)]; - end - eval_str = [eval_str, ');']; - eval(eval_str); - end - - % Reorganize gf - gf_temp = gf; - gf = zeros(g.N*k, 1); - for i = 1:k - gf(i:k:end) = gf_temp((i-1)*g.N + 1 : i*g.N); - end -end \ No newline at end of file +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +grid/evalOnTest.m --- a/+grid/evalOnTest.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+grid/evalOnTest.m Sat Mar 03 14:58:21 2018 -0800 @@ -31,7 +31,7 @@ cases = { {getTestGrid('1d'), @(x,y)x-y}, {getTestGrid('2d'), @(x)x }, - } + }; for i = 1:length(cases) g = cases{i}{1}; @@ -111,9 +111,9 @@ function testInputErrorVectorValued(testCase) - in = { + in = { [1,2,3], - @(x,y)[x,-y]; + @(x,y)[x,-y], }; g = getTestGrid('2d');
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +multiblock/DiffOp.m --- a/+multiblock/DiffOp.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+multiblock/DiffOp.m Sat Mar 03 14:58:21 2018 -0800 @@ -194,6 +194,7 @@ 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);
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +noname/Animation.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+noname/Animation.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,75 @@ +classdef Animation < handle + properties + timeStepper + representationMaker + updaters + end + + % add input validation + + methods + function obj = Animation(timeStepper, representationMaker, updaters); + obj.timeStepper = timeStepper; + obj.updaters = updaters; + obj.representationMaker = representationMaker; + end + + function update(obj, r) + for i = 1:length(obj.updaters) + obj.updaters{i}(r); + end + drawnow + end + + function run(obj, tEnd, timeModifier, do_pause) + default_arg('do_pause', false) + + function next_t = G(next_t) + obj.timeStepper.evolve(next_t); + r = obj.representationMaker(obj.timeStepper); + obj.update(r); + + if do_pause + pause + end + end + + anim.animate(@G, obj.timeStepper.t, tEnd, timeModifier); + end + + function step(obj, tEnd, do_pause) + default_arg('do_pause', false) + + while obj.timeStepper.t < tEnd + obj.timeStepper.step(); + + r = obj.representationMaker(obj.timeStepper); + obj.update(r); + + % TODO: Make it never go faster than a certain fram rate + + if do_pause + pause + end + end + end + + function saveMovie(obj, tEnd, timeModifier, figureHandle, dirname) + save_frame = anim.setup_fig_mov(figureHandle, dirname); + + function next_t = G(next_t) + obj.timeStepper.evolve(next_t); + r = obj.representationMaker(obj.timeStepper); + obj.update(r); + + save_frame(); + end + + fprintf('Generating and saving frames to: ..\n') + anim.animate(@G, obj.timeStepper.t, tEnd, timeModifier); + fprintf('Generating movies...\n') + cmd = sprintf('bash %s/+anim/make_movie.sh %s', sbplibLocation(),dirname); + system(cmd); + end + end +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +noname/calculateErrors.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+noname/calculateErrors.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,40 @@ +% [discr, trueSolution] = schemeFactory(m) +% where trueSolution should be a timeSnapshot of the true solution a time T +% T is the end time +% m are grid size parameters. +% N are number of timesteps to use for each gird size +% timeOpt are options for the timeStepper +function e = calculateErrors(schemeFactory, T, m, N, errorFun, timeOpt) + assertType(schemeFactory, 'function_handle'); + assertNumberOfArguments(schemeFactory, 1); + assertScalar(T); + assert(length(m) == length(N), 'Vectors m and N must have the same length'); + assertType(errorFun, 'function_handle'); + assertNumberOfArguments(errorFun, 2); + default_arg('timeOpt'); + + e = []; + for i = 1:length(m) + done = timeTask('m = %3d ', m(i)); + + [discr, trueSolution] = schemeFactory(m(i)); + + timeOpt.k = T/N(i); + ts = discr.getTimestepper(timeOpt); + ts.stepTo(N(i), true); + approxSolution = discr.getTimeSnapshot(ts); + + e(i) = errorFun(trueSolution, approxSolution); + + fprintf('e = %.4e', e(i)) + done() + end + fprintf('\n') +end + + +%% Example error function +% u_true = grid.evalOn(dr.grid, @(x,y)trueSolution(T,x,y)); +% err = u_true-u_false; +% e(i) = norm(err)/norm(u_true); +% % e(i) = sqrt(err'*d.H*d.J*err/(u_true'*d.H*d.J*u_true));
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +parametrization/Ti.m --- a/+parametrization/Ti.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+parametrization/Ti.m Sat Mar 03 14:58:21 2018 -0800 @@ -21,16 +21,29 @@ D = g4(0); function o = S_fun(u,v) + if isrow(u) && isrow(v) + flipped = false; + else + flipped = true; + u = u'; + v = v'; + end + x1 = g1(u); x2 = g2(v); x3 = g3(1-u); x4 = g4(1-v); + o1 = (1-v).*x1(1,:) + u.*x2(1,:) + v.*x3(1,:) + (1-u).*x4(1,:) ... - -((1-u)*(1-v).*A(1,:) + u*(1-v).*B(1,:) + u*v.*C(1,:) + (1-u)*v.*D(1,:)); + -((1-u).*(1-v).*A(1,:) + u.*(1-v).*B(1,:) + u.*v.*C(1,:) + (1-u).*v.*D(1,:)); o2 = (1-v).*x1(2,:) + u.*x2(2,:) + v.*x3(2,:) + (1-u).*x4(2,:) ... - -((1-u)*(1-v).*A(2,:) + u*(1-v).*B(2,:) + u*v.*C(2,:) + (1-u)*v.*D(2,:)); + -((1-u).*(1-v).*A(2,:) + u.*(1-v).*B(2,:) + u.*v.*C(2,:) + (1-u).*v.*D(2,:)); - o = [o1;o2]; + if ~flipped + o = [o1;o2]; + else + o = [o1'; o2']; + end end obj.S = @S_fun;
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +parametrization/TiTest.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+parametrization/TiTest.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,52 @@ +function tests = TiTest() + tests = functiontests(localfunctions); +end + +function testScalarInput(testCase) + ti = getMinimumTi(); + + cases = { + % {u, v, out}, + {0, 0, [1; 2]}, + {0, 1, [1; 4]}, + {1, 0, [3; 2]}, + {1, 1, [3; 4]}, + {0.5, 0.5, [2; 3]}, + }; + + for i = 1:length(cases) + u = cases{i}{1}; + v = cases{i}{2}; + expected = cases{i}{3}; + + testCase.verifyEqual(ti.S(u,v), expected, sprintf('Case: %d',i)); + end +end + +function testRowVectorInput(testCase) + ti = getMinimumTi(); + + u = [0, 0.5, 1]; + v = [0, 0, 0.5]; + expected = [ + 1, 2, 3; + 2, 2, 3; + ]; + + testCase.verifyEqual(ti.S(u,v), expected); +end + +function testColumnvectorInput(testCase) + ti = getMinimumTi(); + + u = [0; 0.5; 1]; + v = [0; 0; 0.5]; + expected = [1; 2; 3; 2; 2; 3]; + + testCase.verifyEqual(ti.S(u,v), expected); +end + + +function ti = getMinimumTi() + ti = parametrization.Ti.rectangle([1; 2], [3; 4]); +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +sbp/+implementations/d2_variable_periodic_2.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/d2_variable_periodic_2.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,50 @@ +function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_2(m,h) + % m = number of unique grid points, i.e. h = L/m; + + if(m<3) + error(['Operator requires at least ' num2str(3) ' grid points']); + end + + % Norm + Hv = ones(m,1); + Hv = h*Hv; + H = spdiag(Hv, 0); + HI = spdiag(1./Hv, 0); + + + % Dummy boundary operators + e_l = sparse(m,1); + e_r = rot90(e_l, 2); + + d1_l = sparse(m,1); + d1_r = -rot90(d1_l, 2); + + % D1 operator + diags = -1:1; + stencil = [-1/2 0 1/2]; + D1 = stripeMatrixPeriodic(stencil, diags, m); + D1 = D1/h; + + scheme_width = 3; + scheme_radius = (scheme_width-1)/2; + + r = 1:m; + offset = scheme_width; + r = r + offset; + + function D2 = D2_fun(c) + c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ]; + + Mm1 = -c(r-1)/2 - c(r)/2; + M0 = c(r-1)/2 + c(r) + c(r+1)/2; + Mp1 = -c(r)/2 - c(r+1)/2; + + vals = [Mm1,M0,Mp1]; + diags = -scheme_radius : scheme_radius; + M = spdiagsVariablePeriodic(vals,diags); + + M=M/h; + D2=HI*(-M ); + end + D2 = @D2_fun; +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +sbp/+implementations/d2_variable_periodic_4.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/d2_variable_periodic_4.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,57 @@ +function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_4(m,h) + % m = number of unique grid points, i.e. h = L/m; + + if(m<5) + error(['Operator requires at least ' num2str(5) ' grid points']); + end + + % Norm + Hv = ones(m,1); + Hv = h*Hv; + H = spdiag(Hv, 0); + HI = spdiag(1./Hv, 0); + + + % Dummy boundary operators + e_l = sparse(m,1); + e_r = rot90(e_l, 2); + + d1_l = sparse(m,1); + d1_r = -rot90(d1_l, 2); + + S = d1_l*d1_l' + d1_r*d1_r'; + + % D1 operator + stencil = [1/12 -2/3 0 2/3 -1/12]; + diags = -2:2; + Q = stripeMatrixPeriodic(stencil, diags, m); + D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r'); + + + scheme_width = 5; + scheme_radius = (scheme_width-1)/2; + + r = 1:m; + offset = scheme_width; + r = r + offset; + + function D2 = D2_fun(c) + c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ]; + + % Note: these coefficients are for -M. + Mm2 = -1/8*c(r-2) + 1/6*c(r-1) - 1/8*c(r); + Mm1 = 1/6 *c(r-2) + 1/2*c(r-1) + 1/2*c(r) + 1/6*c(r+1); + M0 = -1/24*c(r-2)- 5/6*c(r-1) - 3/4*c(r) - 5/6*c(r+1) - 1/24*c(r+2); + Mp1 = 0 * c(r-2) + 1/6*c(r-1) + 1/2*c(r) + 1/2*c(r+1) + 1/6 *c(r+2); + Mp2 = 0 * c(r-2) + 0 * c(r-1) - 1/8*c(r) + 1/6*c(r+1) - 1/8 *c(r+2); + + vals = -[Mm2,Mm1,M0,Mp1,Mp2]; + diags = -scheme_radius : scheme_radius; + M = spdiagsVariablePeriodic(vals,diags); + + M=M/h; + D2=HI*(-M ); + + end + D2 = @D2_fun; +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +sbp/+implementations/d2_variable_periodic_6.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/d2_variable_periodic_6.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,58 @@ +function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_6(m,h) + % m = number of unique grid points, i.e. h = L/m; + + if(m<7) + error(['Operator requires at least ' num2str(7) ' grid points']); + end + + % Norm + Hv = ones(m,1); + Hv = h*Hv; + H = spdiag(Hv, 0); + HI = spdiag(1./Hv, 0); + + + % Dummy boundary operators + e_l = sparse(m,1); + e_r = rot90(e_l, 2); + + d1_l = sparse(m,1); + d1_r = -rot90(d1_l, 2); + + + % D1 operator + diags = -3:3; + stencil = [-1/60 9/60 -45/60 0 45/60 -9/60 1/60]; + D1 = stripeMatrixPeriodic(stencil, diags, m); + D1 = D1/h; + + % D2 operator + scheme_width = 7; + scheme_radius = (scheme_width-1)/2; + + r = 1:m; + offset = scheme_width; + r = r + offset; + + function D2 = D2_fun(c) + c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ]; + + Mm3 = c(r-2)/0.40e2 + c(r-1)/0.40e2 - 0.11e2/0.360e3 * c(r-3) - 0.11e2/0.360e3 * c(r); + Mm2 = c(r-3)/0.20e2 - 0.3e1/0.10e2 * c(r-1) + c(r+1)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r-2); + Mm1 = -c(r-3)/0.40e2 - 0.3e1/0.10e2 * c(r-2) - 0.3e1/0.10e2 * c(r+1) - c(r+2)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r-1); + M0 = c(r-3)/0.180e3 + c(r-2)/0.8e1 + 0.19e2/0.20e2 * c(r-1) + 0.19e2/0.20e2 * c(r+1) + c(r+2)/0.8e1 + c(r+3)/0.180e3 + 0.101e3/0.180e3 * c(r); + Mp1 = -c(r-2)/0.40e2 - 0.3e1/0.10e2 * c(r-1) - 0.3e1/0.10e2 * c(r+2) - c(r+3)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r+1); + Mp2 = c(r-1)/0.20e2 - 0.3e1/0.10e2 * c(r+1) + c(r+3)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r+2); + Mp3 = c(r+1)/0.40e2 + c(r+2)/0.40e2 - 0.11e2/0.360e3 * c(r) - 0.11e2/0.360e3 * c(r+3); + + vals = [Mm3,Mm2,Mm1,M0,Mp1,Mp2,Mp3]; + diags = -scheme_radius : scheme_radius; + M = spdiagsVariablePeriodic(vals,diags); + + M=M/h; + D2=HI*(-M ); + end + D2 = @D2_fun; + + +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +sbp/D2Variable.m --- a/+sbp/D2Variable.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+sbp/D2Variable.m Sat Mar 03 14:58:21 2018 -0800 @@ -26,22 +26,39 @@ obj.x = linspace(x_l,x_r,m)'; switch order + + case 6 + + [obj.H, obj.HI, obj.D1, obj.D2, ... + ~, obj.e_l, obj.e_r, ~, ~, ~, ~, ~,... + obj.d1_l, obj.d1_r] = ... + sbp.implementations.d4_variable_6(m, obj.h); + obj.borrowing.M.d1 = 0.1878; + obj.borrowing.R.delta_D = 0.3696; + % Borrowing e^T*D1 - d1 from R + case 4 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,... obj.e_r, obj.d1_l, obj.d1_r] = ... sbp.implementations.d2_variable_4(m,obj.h); obj.borrowing.M.d1 = 0.2505765857; + + obj.borrowing.R.delta_D = 0.577587500088313; + % Borrowing e^T*D1 - d1 from R case 2 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,... obj.e_r, obj.d1_l, obj.d1_r] = ... sbp.implementations.d2_variable_2(m,obj.h); obj.borrowing.M.d1 = 0.3636363636; % Borrowing const taken from Virta 2014 + + obj.borrowing.R.delta_D = 1.000000538455350; + % Borrowing e^T*D1 - d1 from R otherwise error('Invalid operator order %d.',order); end - + obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h, obj.m = m; obj.M = []; end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +sbp/D2VariablePeriodic.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/D2VariablePeriodic.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,71 @@ +classdef D2VariablePeriodic < sbp.OpSet + properties + D1 % SBP operator approximating first derivative + H % Norm matrix + HI % H^-1 + Q % Skew-symmetric matrix + e_l % Left boundary operator + e_r % Right boundary operator + D2 % SBP operator for second derivative + M % Norm matrix, second derivative + d1_l % Left boundary first derivative + d1_r % Right boundary first derivative + m % Number of grid points. + h % Step size + x % grid + borrowing % Struct with borrowing limits for different norm matrices + end + + methods + function obj = D2VariablePeriodic(m,lim,order) + + x_l = lim{1}; + x_r = lim{2}; + L = x_r-x_l; + obj.h = L/m; + x = linspace(x_l,x_r,m+1)'; + obj.x = x(1:end-1); + + switch order + + case 6 + [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,... + obj.e_r, obj.d1_l, obj.d1_r] = ... + sbp.implementations.d2_variable_periodic_6(m,obj.h); + obj.borrowing.M.d1 = 0.1878; + obj.borrowing.R.delta_D = 0.3696; + % Borrowing e^T*D1 - d1 from R + + case 4 + [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,... + obj.e_r, obj.d1_l, obj.d1_r] = ... + sbp.implementations.d2_variable_periodic_4(m,obj.h); + obj.borrowing.M.d1 = 0.2505765857; + + obj.borrowing.R.delta_D = 0.577587500088313; + % Borrowing e^T*D1 - d1 from R + case 2 + [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,... + obj.e_r, obj.d1_l, obj.d1_r] = ... + sbp.implementations.d2_variable_periodic_2(m,obj.h); + obj.borrowing.M.d1 = 0.3636363636; + % Borrowing const taken from Virta 2014 + + obj.borrowing.R.delta_D = 1.000000538455350; + % Borrowing e^T*D1 - d1 from R + + otherwise + error('Invalid operator order %d.',order); + end + obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h, + + obj.m = m; + obj.M = []; + end + function str = string(obj) + str = [class(obj) '_' num2str(obj.order)]; + end + end + + +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +scheme/Beam.m --- a/+scheme/Beam.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+scheme/Beam.m Sat Mar 03 14:58:21 2018 -0800 @@ -126,6 +126,44 @@ penalty{1} = -obj.Hi*tau; penalty{1} = -obj.Hi*sig; + case 'e' + alpha = obj.alpha; + tuning = 1.1; + + tau1 = tuning * alpha/delt; + tau4 = s*alpha; + + tau = tau1*e+tau4*d3; + + closure = obj.Hi*tau*e'; + penalty = -obj.Hi*tau; + case 'd1' + alpha = obj.alpha; + + tuning = 1.1; + + sig2 = tuning * alpha/gamm; + sig3 = -s*alpha; + + sig = sig2*d1+sig3*d2; + + closure = obj.Hi*sig*d1'; + penalty = -obj.Hi*sig; + + case 'd2' + a = obj.alpha; + + tau = s*a*d1; + + closure = obj.Hi*tau*d2'; + penalty = -obj.Hi*tau; + case 'd3' + a = obj.alpha; + + sig = -s*a*e; + + closure = obj.Hi*sig*d3'; + penalty = -obj.Hi*sig; otherwise % Unknown, boundary condition error('No such boundary condition: type = %s',type);
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +scheme/Elastic2dVariable.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Elastic2dVariable.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,420 @@ +classdef Elastic2dVariable < scheme.Scheme + +% Discretizes the elastic wave equation: +% rho u_{i,tt} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i +% 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 matrices for varible coefficients + LAMBDA % Variable coefficient, related to dilation + MU % Shear modulus, variable coefficient + RHO, RHOi % Density, variable + + D % Total operator + D1 % First derivatives + + % Second derivatives + D2_lambda + D2_mu + + % Traction operators used for BC + 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 + e_l, e_r + d1_l, d1_r % Normal derivatives at the boundary + E % E{i}^T picks out component i + + H_boundary % Boundary inner products + + % Kroneckered norms and coefficients + RHOi_kron + Hi_kron + end + + methods + + function obj = Elastic2dVariable(g ,order, lambda_fun, mu_fun, rho_fun, 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); + 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); + m = g.size(); + m_tot = g.N(); + + h = g.scaling(); + lim = g.lim; + + % 1D operators + ops = cell(dim,1); + for i = 1:dim + ops{i} = opSet{i}(m(i), lim{i}, order); + end + + % 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; + 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 + + %====== Assemble full operators ======== + LAMBDA = spdiag(lambda); + obj.LAMBDA = LAMBDA; + MU = spdiag(mu); + obj.MU = MU; + RHO = spdiag(rho); + obj.RHO = RHO; + obj.RHOi = inv(RHO); + + obj.D1 = cell(dim,1); + obj.D2_lambda = cell(dim,1); + obj.D2_mu = 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 + for i = 1:dim + obj.D2_lambda{i} = sparse(m_tot); + obj.D2_mu{i} = sparse(m_tot); + end + ind = grid.funcToMatrix(g, 1:m_tot); + + for i = 1:m(2) + D_lambda = D2{1}(lambda(ind(:,i))); + D_mu = D2{1}(mu(ind(:,i))); + + p = ind(:,i); + obj.D2_lambda{1}(p,p) = D_lambda; + obj.D2_mu{1}(p,p) = D_mu; + end + + for i = 1:m(1) + D_lambda = D2{2}(lambda(ind(i,:))); + D_mu = D2{2}(mu(ind(i,:))); + + p = ind(i,:); + obj.D2_lambda{2}(p,p) = D_lambda; + obj.D2_mu{2}(p,p) = D_mu; + end + + % 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}; + + % E{i}^T picks out component i. + E = cell(dim,1); + I = speye(m_tot,m_tot); + for i = 1:dim + e = sparse(dim,1); + e(i) = 1; + E{i} = kron(I,e); + end + obj.E = E; + + % Differentiation matrix D (without SAT) + D2_lambda = obj.D2_lambda; + D2_mu = obj.D2_mu; + D1 = obj.D1; + D = sparse(dim*m_tot,dim*m_tot); + d = @kroneckerDelta; % Kronecker delta + db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta + for i = 1:dim + for j = 1:dim + D = D + E{i}*inv(RHO)*( d(i,j)*D2_lambda{i}*E{j}' +... + db(i,j)*D1{i}*LAMBDA*D1{j}*E{j}' ... + ); + D = D + E{i}*inv(RHO)*( d(i,j)*D2_mu{i}*E{j}' +... + db(i,j)*D1{j}*MU*D1{i}*E{j}' + ... + D2_mu{j}*E{i}' ... + ); + end + end + obj.D = D; + %=========================================% + + % Numerical traction operators for BC. + % Because d1 =/= e0^T*D1, the numerical tractions are different + % at every boundary. + T_l = cell(dim,1); + T_r = cell(dim,1); + tau_l = cell(dim,1); + tau_r = cell(dim,1); + % tau^{j}_i = sum_k T^{j}_{ik} u_k + + d1_l = obj.d1_l; + d1_r = obj.d1_r; + e_l = obj.e_l; + e_r = obj.e_r; + D1 = obj.D1; + + % Loop over boundaries + for j = 1:dim + T_l{j} = cell(dim,dim); + T_r{j} = cell(dim,dim); + tau_l{j} = cell(dim,1); + tau_r{j} = cell(dim,1); + + % 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); + 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}'; + + 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}'; + + 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}'; + end + + end + end + obj.T_l = T_l; + obj.T_r = T_r; + obj.tau_l = tau_l; + obj.tau_r = tau_r; + + % Kroneckered norms and coefficients + I_dim = speye(dim); + obj.RHOi_kron = kron(obj.RHOi, I_dim); + obj.Hi_kron = kron(obj.Hi, I_dim); + + % Misc. + obj.m = m; + obj.h = h; + obj.order = order; + obj.grid = g; + obj.dim = dim; + + 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 cell array of strings specifying the type of boundary condition for each component. + % 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',{'free','free'}); + default_arg('parameter', []); + + % j is the coordinate direction of the boundary + % 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; + tau = obj.tau_r{j}; + T = obj.T_r{j}; + case -1 + e = obj.e_l; + d = obj.d1_l; + tau = obj.tau_l{j}; + T = obj.T_l{j}; + end + + E = obj.E; + Hi = obj.Hi; + H_gamma = obj.H_boundary{j}; + LAMBDA = obj.LAMBDA; + MU = obj.MU; + RHOi = obj.RHOi; + + dim = obj.dim; + m_tot = obj.grid.N(); + + RHOi_kron = obj.RHOi_kron; + Hi_kron = obj.Hi_kron; + + % Preallocate + closure = sparse(dim*m_tot, dim*m_tot); + penalty = cell(dim,1); + for k = 1:dim + penalty{k} = sparse(dim*m_tot, m_tot/obj.m(j)); + end + + % Loop over components that we (potentially) have different BC on + for k = 1:dim + switch type{k} + + % Dirichlet boundary condition + case {'D','d','dirichlet','Dirichlet'} + + tuning = 1.2; + 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 ); + + % 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*B'*e{j}*H_gamma*(e{j}'*E{k}' ); + penalty{k} = penalty{k} - E{i}*RHOi*Hi*B'*e{j}*H_gamma; + end + + % Free boundary condition + case {'F','f','Free','free','traction','Traction','t','T'} + closure = closure - E{k}*RHOi*Hi*e{j}*H_gamma* (e{j}'*tau{k} ); + penalty{k} = penalty{k} + E{k}*RHOi*Hi*e{j}*H_gamma; + + % Unknown boundary condition + otherwise + error('No such boundary condition: type = %s',type); + end + 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; + 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) + + 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 coordinate number and outward normal component for the boundary specified by the string boundary. + function [return_op] = get_boundary_operator(obj, op, 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 op + 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]); + end + + end + + function N = size(obj) + N = prod(obj.m); + end + end +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +scheme/Heat2dVariable.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Heat2dVariable.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,262 @@ +classdef Heat2dVariable < scheme.Scheme + +% Discretizes the Laplacian with variable coefficent, +% In the Heat equation way (i.e., the discretization matrix is not necessarily +% symmetric) +% 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. + + 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 + KAPPA % Variable coefficient + + D % Total operator + D1 % First derivatives + + % Second derivatives + D2_kappa + + H, Hi % Inner products + e_l, e_r + d1_l, d1_r % Normal derivatives at the boundary + + H_boundary % Boundary inner products + + end + + methods + + function obj = Heat2dVariable(g ,order, kappa_fun, opSet) + default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable}); + default_arg('kappa_fun', @(x,y) 0*x+1); + dim = 2; + + assert(isa(g, 'grid.Cartesian')) + + kappa = grid.evalOn(g, kappa_fun); + m = g.size(); + m_tot = g.N(); + + h = g.scaling(); + lim = g.lim; + + % 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 + + %====== Assemble full operators ======== + KAPPA = spdiag(kappa); + obj.KAPPA = KAPPA; + + obj.D1 = cell(dim,1); + obj.D2_kappa = 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 + for i = 1:dim + obj.D2_kappa{i} = sparse(m_tot); + end + ind = grid.funcToMatrix(g, 1:m_tot); + + for i = 1:m(2) + D_kappa = D2{1}(kappa(ind(:,i))); + p = ind(:,i); + obj.D2_kappa{1}(p,p) = D_kappa; + end + + for i = 1:m(1) + D_kappa = D2{2}(kappa(ind(i,:))); + p = ind(i,:); + obj.D2_kappa{2}(p,p) = D_kappa; + end + + % 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_kappa = obj.D2_kappa; + D1 = obj.D1; + D = sparse(m_tot,m_tot); + for i = 1:dim + D = D + D2_kappa{i}; + end + obj.D = D; + %=========================================% + + % Misc. + obj.m = m; + obj.h = h; + obj.order = order; + obj.grid = g; + obj.dim = dim; + + 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', []); + + % j is the coordinate direction of the boundary + % 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 + + Hi = obj.Hi; + H_gamma = obj.H_boundary{j}; + KAPPA = obj.KAPPA; + kappa_gamma = e{j}'*KAPPA*e{j}; + + switch type + + % Dirichlet boundary condition + case {'D','d','dirichlet','Dirichlet'} + closure = -nj*Hi*d{j}*kappa_gamma*H_gamma*(e{j}' ); + penalty = nj*Hi*d{j}*kappa_gamma*H_gamma; + + % Free boundary condition + case {'N','n','neumann','Neumann'} + closure = -nj*Hi*e{j}*kappa_gamma*H_gamma*(d{j}' ); + penalty = nj*Hi*e{j}*kappa_gamma*H_gamma; + + % 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 + 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) + + 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 coordinate number and outward normal component for the boundary specified by the string boundary. + function [return_op] = get_boundary_operator(obj, op, 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 op + 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]); + end + + end + + function N = size(obj) + N = prod(obj.m); + end + end +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +scheme/TODO.txt --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/TODO.txt Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,1 @@ +% TODO: Rename package and abstract class to diffOp
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +scheme/bcSetup.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/bcSetup.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,48 @@ +% 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 with time and space coordinates as a parameters, for example f(t,x,y) for a 2D problem +% Also takes S_sign which modifies the sign of S, [-1,1] +% Returns a closure matrix and a forcing function S +function [closure, S] = bcSetup(diffOp, bc, S_sign) + default_arg('S_sign', 1); + assertType(bc, 'cell'); + assert(S_sign == 1 || S_sign == -1, 'S_sign must be either 1 or -1'); + + + closure = spzeros(size(diffOp)); + penalties = {}; + dataFunctions = {}; + dataParams = {}; + + for i = 1:length(bc) + assertType(bc{i}, 'struct'); + [localClosure, penalty] = diffOp.boundary_condition(bc{i}.boundary, bc{i}.type); + closure = closure + localClosure; + + if isempty(bc{i}.data) + continue + end + assertType(bc{i}.data, 'function_handle'); + + coord = diffOp.grid.getBoundary(bc{i}.boundary); + assertNumberOfArguments(bc{i}.data, 1+size(coord,2)); + + penalties{end+1} = penalty; + dataFunctions{end+1} = bc{i}.data; + dataParams{end+1} = num2cell(coord ,1); + end + + O = spzeros(size(diffOp),1); + function v = S_fun(t) + v = O; + for i = 1:length(dataFunctions) + v = v + penalties{i}*dataFunctions{i}(t, dataParams{i}{:}); + end + + v = S_sign * v; + end + S = @S_fun; +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 +time/Timestepper.m --- a/+time/Timestepper.m Mon Oct 16 21:56:12 2017 -0700 +++ b/+time/Timestepper.m Sat Mar 03 14:58:21 2018 -0800 @@ -62,6 +62,7 @@ function [v, t] = stepTo(obj, n, progress_bar) + assertScalar(n); default_arg('progress_bar',false); [v, t] = obj.stepN(n-obj.n, progress_bar);
diff -r 2d85f17a8aec -r 8e4274ee6dd8 assertScalar.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/assertScalar.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,5 @@ +function assertScalar(obj) + if ~isscalar(obj) + error('sbplib:assertScalar:notScalar', '"%s" must be scalar, found size "%s"', inputname(1), toString(size(obj))); + end +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 diffSymfun.m --- a/diffSymfun.m Mon Oct 16 21:56:12 2017 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,7 +0,0 @@ -% Differentiates a symbolic function like diff does, but keeps the function as a symfun -function g = diffSymfun(f, varargin) - assertType(f, 'symfun'); - - args = argnames(f); - g = symfun(diff(f,varargin{:}), args); -end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 kroneckerDelta.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/kroneckerDelta.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,6 @@ +function d = kroneckerDelta(i,j) + +d = 0; +if i==j + d = 1; +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 sbplibLocation.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/sbplibLocation.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,4 @@ +function location = sbplibLocation() + scriptname = mfilename('fullpath'); + [location, ~, ~] = fileparts(scriptname); +end
diff -r 2d85f17a8aec -r 8e4274ee6dd8 sbplibVersion.m --- a/sbplibVersion.m Mon Oct 16 21:56:12 2017 -0700 +++ b/sbplibVersion.m Sat Mar 03 14:58:21 2018 -0800 @@ -1,11 +1,10 @@ % Prints the version and location of the sbplib currently in use. function sbplibVersion() - scriptname = mfilename('fullpath'); - [folder,~,~] = fileparts(scriptname); + location = sbplibLocation(); name = 'sbplib (feature/grids)'; ver = '0.0.x'; fprintf('%s %s\n', name, ver); - fprintf('Running in:\n%s\n',folder); + fprintf('Running in:\n%s\n', location); end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 spdiagVariable.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/spdiagVariable.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,17 @@ +function A = spdiagVariable(a,i) + default_arg('i',0); + + if isrow(a) + a = a'; + end + + n = length(a)+abs(i); + + if i > 0 + a = [sparse(i,1); a]; + elseif i < 0 + a = [a; sparse(abs(i),1)]; + end + + A = spdiags(a,i,n,n); +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 spdiagsVariablePeriodic.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/spdiagsVariablePeriodic.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,42 @@ +function A = spdiagsVariablePeriodic(vals,diags) + % Creates an m x m periodic discretization matrix. + % vals - m x ndiags matrix of values + % diags - 1 x ndiags vector of the 'center diagonals' that vals end up on + % vals that are not on main diagonal are going to spill over to + % off-diagonal corners. + + default_arg('diags',0); + + [m, ~] = size(vals); + + A = sparse(m,m); + + for i = 1:length(diags) + + d = diags(i); + a = vals(:,i); + + % Sub-diagonals + if d < 0 + a_bulk = a(1+abs(d):end); + a_corner = a(1:1+abs(d)-1); + corner_diag = m-abs(d); + A = A + spdiagVariable(a_bulk, d); + A = A + spdiagVariable(a_corner, corner_diag); + + % Super-diagonals + elseif d > 0 + a_bulk = a(1:end-d); + a_corner = a(end-d+1:end); + corner_diag = -m + d; + A = A + spdiagVariable(a_bulk, d); + A = A + spdiagVariable(a_corner, corner_diag); + + % Main diagonal + else + A = A + spdiagVariable(a, 0); + end + + end + +end \ No newline at end of file
diff -r 2d85f17a8aec -r 8e4274ee6dd8 stripeMatrixPeriodic.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/stripeMatrixPeriodic.m Sat Mar 03 14:58:21 2018 -0800 @@ -0,0 +1,8 @@ +% Creates a periodic discretization matrix of size n x n +% with the values of val on the diagonals diag. +% A = stripeMatrix(val,diags,n) +function A = stripeMatrixPeriodic(val,diags,n) + + D = ones(n,1)*val; + A = spdiagsVariablePeriodic(D,diags); +end \ No newline at end of file