sbplib: +scheme/Hypsyst3d.m comparison

comparison +scheme/Hypsyst3d.m @ 905:459eeb99130f feature/utux2D

Include type as (optional) input parameter in the interface method of all schemes.

author	Martin Almquist <malmquist@stanford.edu>
date	Thu, 22 Nov 2018 22:03:44 -0800
parents	0fd6561964b0
children	b9c98661ff5d

comparison

equal deleted inserted replaced

-:14b093a344eb
+:459eeb99130f
 h % Grid spacing
 x, y, z % Grid
 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.
 I_x,I_y, I_z, I_N
 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)
 default_arg('E', [])
 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;
 obj.E = E;
 m_x = m(1);
 m_y = m(2);
 m_z = m(3);
 obj.params = params;
 switch operator
 case 'upwind'
 ops_x = sbp.D1Upwind(m_x,xlim,order);
 ops_y = sbp.D1Upwind(m_y,ylim,order);
 ops_z = sbp.D1Upwind(m_z,zlim,order);
 otherwise
 ops_x = sbp.D2Standard(m_x,xlim,order);
 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;
 I_y = speye(m_y);
 obj.I_y = I_y;
 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);
 Dmx = kr(I_n, ops_x.Dm, I_y,I_z);
 obj.D = -Am*Dpx;
 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);
 Dmy = kr(I_n, I_x, ops_y.Dm,I_z);
 temp = Bm*Dpy;
 obj.D = obj.D-temp;
 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);
 D1_z = kr(I_n, I_x, I_y,ops_z.D1);
 obj.D = -obj.Aevaluated*D1_x-obj.Bevaluated*D1_y-obj.Cevaluated*D1_z-obj.Eevaluated;
 otherwise
 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'.
 %       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.
 [closure,penalty] = boundary_condition_general(obj,BM,boundary,L);
 otherwise
 error('No such boundary condition')
 end
 end
-function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
+function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
 error('An interface function does not exist yet');
 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));
 if isa(mat,'function_handle')
 [rows,cols] = size(mat(params,0,0,0));
 matVec = mat;
 [rows,cols] = size(matVec);
 side = max(length(X),length(Y));
 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));
 end
 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;
 mat = obj.A;
 BM.boundpos = 'l';
 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.Xz,obj.Yz,obj.Z(end));
 BM.side = length(obj.Xz);
 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;
 pos = BM.pos;
 neg = BM.neg;
 V = BM.V;
 Vi = BM.Vi;
 Hi = BM.Hi;
 D = BM.D;
 e_ = BM.e_;
 switch BM.boundpos
 case {'l'}
 tau = sparse(obj.n*side,pos);
 Vi_plus = Vi(1:pos,:);
 tau(1:pos,:) = -abs(D(1:pos,1:pos));
 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
 % General boundary condition in the form Lu=g(x)
 function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L)
 side = BM.side;
 pos = BM.pos;
 neg = BM.neg;
 zeroval=BM.zeroval;
 V = BM.V;
 Vi = BM.Vi;
 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);
 case {'e','E','east'}
 L = obj.evaluateCoefficientMatrix(L,obj.x(end),obj.Yx,obj.Zx);
 case {'b','B','bottom'}
 L = obj.evaluateCoefficientMatrix(L,obj.Xz,obj.Yz,obj.z(1));
 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);
 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);
 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_';
 penalty = -Hi*e_*V*tau*inv(L*V_plus)*L;
 case {'r'}
 tau = sparse(obj.n*side,neg);
 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);
 closure = Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
 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-]
 [V, D] = eig(mat(params,xs,ys,zs));
 Vi=inv(V);
 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));
 Vret(jj,(ii-1)*side+1:side*ii) = eval(V(jj,ii));
 Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii));
 end
 end
 D = sparse(Dret);
 V = sparse(Vret);
 Vi = sparse(Viret);
 V = obj.evaluateCoefficientMatrix(V,x,y,z);
 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,:)];
 signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
 end

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comparison +scheme/Hypsyst3d.m @ 905:459eeb99130f feature/utux2D