sbplib: +scheme/Hypsyst3dCurve.m comparison

comparison +scheme/Hypsyst3dCurve.m @ 1033:037f203b9bf5 feature/burgers1d

Merge with branch feature/advectioRV to utilize the +rv package

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Thu, 17 Jan 2019 10:44:12 +0100
parents	706d1c2b4199
children	0652b34f9f27

comparison

equal deleted inserted replaced

-:18162a0a5bb5
+:037f203b9bf5
 m % Number of points in each direction, possibly a vector
 n %size of system
 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.
 Hxi,Heta,Hzeta
 I_xi,I_eta,I_zeta, I_N,onesN
 e_w, e_e, e_s, e_n, e_b, e_t
 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
 m_xi = m(1);
 m_eta = m(2);
 m_zeta = m(3);
 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);
 ops_eta = sbp.D1Upwind(m_eta,etalim,order);
 ops_zeta = sbp.D1Upwind(m_zeta,zetalim,order);
 ops_eta = sbp.D2Standard(m_eta,etalim,order);
 ops_zeta = sbp.D2Standard(m_zeta,zetalim,order);
 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;
 I_eta = speye(m_eta);
 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);
 D1_eta = kr(I_xi, (ops_eta.Dp+ops_eta.Dm)/2,I_zeta);
 D1_zeta = kr(I_xi, I_eta,(ops_zeta.Dp+ops_zeta.Dm)/2);
 otherwise
 D1_xi = kr(ops_xi.D1, I_eta,I_zeta);
 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;
 obj.Y_xi = D1_xi*Y;
 obj.Y_eta = D1_eta*Y;
 obj.Y_zeta = D1_zeta*Y;
 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 = [];
 Dpzeta = kr(I_n, I_xi, I_eta,ops_zeta.Dp);
 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);
 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'.
 %       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.
 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);
 case{'general'}
 [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');
+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;
 side = max(length(X),length(Y));
 if isa(mat,'function_handle')
 side = max(length(X),length(Y));
 cols = cols/side;
 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));
 end
 end
 ret = cell2mat(ret);
 end
 function [BM] = boundary_matrices(obj,boundary)
 params = obj.params;
 BM.boundary = boundary;
 switch boundary
 case {'w','W','west'}
 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.X(BM.index),obj.Y(BM.index),obj.Z(BM.index),...
 BM.x_1,BM.x_2,BM.y_1,BM.y_2,BM.z_1,BM.z_2);
 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;
 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;
 Vi = BM.Vi;
 Hi = BM.Hi;
 D = BM.D;
 e_ = BM.e_;
 index = BM.index;
 switch BM.boundary
 case{'b','B','bottom'}
 Ji_vec = diag(obj.Ji);
 Ji = diag(Ji_vec(index));
 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);
 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-]
 if(sum(abs(x_1))>eps)
 syms x_1s
 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);
 xs = x;
 ys = y;
 x_2s = x_2;
 y_1s = y_1;
 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));
 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,x_1,x_2,y_1,y_2,z_1,z_2);
 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,:)];
 signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
 end

Mercurial > repos > public > sbplib

comparison +scheme/Hypsyst3dCurve.m @ 1033:037f203b9bf5 feature/burgers1d