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annotate +scheme/Hypsyst2d.m @ 1316:bd8e607768ce feature/poroelastic

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Add interfaceForcing method in multiblock.DiffOp to facilitate mms forcing
author Martin Almquist <malmquist@stanford.edu>
date Sun, 26 Jul 2020 20:05:10 -0700
parents 706d1c2b4199
children 78db023a7fe3
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1 classdef Hypsyst2d < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 n %size of system
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5 h % Grid spacing
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6 x,y % Grid
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7 X,Y % Values of x and y for each grid point
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8 order % Order accuracy for the approximation
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9
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10 D % non-stabalized scheme operator
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11 A, B, E %Coefficient matrices
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12
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13 H % Discrete norm
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14 % Norms in the x and y directions
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15 Hxi,Hyi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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16 I_x,I_y, I_N
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17 e_w, e_e, e_s, e_n
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18 params %parameters for the coeficient matrice
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19 end
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20
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21 methods
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22 %Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Eu
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23 function obj = Hypsyst2d(m, lim, order, A, B, E, params)
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24 default_arg('E', [])
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25 xlim = lim{1};
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26 ylim = lim{2};
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27
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28 if length(m) == 1
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29 m = [m m];
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30 end
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31
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32 obj.A=A;
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33 obj.B=B;
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34 obj.E=E;
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35
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36 m_x = m(1);
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37 m_y = m(2);
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38 obj.params = params;
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39
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40 ops_x = sbp.D2Standard(m_x,xlim,order);
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41 ops_y = sbp.D2Standard(m_y,ylim,order);
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42
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43 obj.x = ops_x.x;
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44 obj.y = ops_y.x;
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45
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46 obj.X = kr(obj.x,ones(m_y,1));
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47 obj.Y = kr(ones(m_x,1),obj.y);
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48
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49 Aevaluated = obj.evaluateCoefficientMatrix(A, obj.X, obj.Y);
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50 Bevaluated = obj.evaluateCoefficientMatrix(B, obj.X, obj.Y);
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51 Eevaluated = obj.evaluateCoefficientMatrix(E, obj.X, obj.Y);
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52
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53 obj.n = length(A(obj.params,0,0));
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54
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55 I_n = eye(obj.n);I_x = speye(m_x);
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56 obj.I_x = I_x;
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57 I_y = speye(m_y);
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58 obj.I_y = I_y;
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60
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61 D1_x = kr(I_n, ops_x.D1, I_y);
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62 obj.Hxi = kr(I_n, ops_x.HI, I_y);
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63 D1_y = kr(I_n, I_x, ops_y.D1);
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64 obj.Hyi = kr(I_n, I_x, ops_y.HI);
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66 obj.e_w = kr(I_n, ops_x.e_l, I_y);
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67 obj.e_e = kr(I_n, ops_x.e_r, I_y);
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68 obj.e_s = kr(I_n, I_x, ops_y.e_l);
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69 obj.e_n = kr(I_n, I_x, ops_y.e_r);
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71 obj.m = m;
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72 obj.h = [ops_x.h ops_y.h];
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73 obj.order = order;
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75 obj.D = -Aevaluated*D1_x-Bevaluated*D1_y-Eevaluated;
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77 end
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78
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79 % Closure functions return the opertors applied to the own doamin to close the boundary
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80 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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81 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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82 % type is a string specifying the type of boundary condition if there are several.
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83 % data is a function returning the data that should be applied at the boundary.
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84 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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85 default_arg('type','char');
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86 switch type
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87 case{'c','char'}
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88 [closure,penalty] = boundary_condition_char(obj,boundary);
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89 case{'general'}
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90 [closure,penalty] = boundary_condition_general(obj,boundary,L);
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91 otherwise
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92 error('No such boundary condition')
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93 end
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94 end
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96 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type)
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97 error('Not implemented');
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98 end
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99
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100 function N = size(obj)
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101 N = obj.m;
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102 end
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103
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104 function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y)
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105 params = obj.params;
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106
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107 if isa(mat,'function_handle')
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108 [rows,cols] = size(mat(params,0,0));
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109 matVec = mat(params,X',Y');
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110 matVec = sparse(matVec);
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111 side = max(length(X),length(Y));
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112 else
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113 matVec = mat;
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114 [rows,cols] = size(matVec);
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115 side = max(length(X),length(Y));
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116 cols = cols/side;
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117 end
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118 ret = cell(rows,cols);
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119
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120 for ii = 1:rows
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121 for jj=1:cols
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122 ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side));
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123 end
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124 end
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125 ret = cell2mat(ret);
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126 end
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parents: 369
diff changeset
127
369
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diff changeset
128 %Characteristic boundary conditions
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diff changeset
129 function [closure, penalty] = boundary_condition_char(obj,boundary)
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diff changeset
130 params = obj.params;
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diff changeset
131 x = obj.x;
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diff changeset
132 y = obj.y;
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parents: 369
diff changeset
133
291
807dfe8be3ec Have made a lot of stupid changes in hypsyst in order to find a stupid bug
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diff changeset
134 switch boundary
807dfe8be3ec Have made a lot of stupid changes in hypsyst in order to find a stupid bug
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parents: 290
diff changeset
135 case {'w','W','west'}
369
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diff changeset
136 e_ = obj.e_w;
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diff changeset
137 mat = obj.A;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
138 boundPos = 'l';
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
139 Hi = obj.Hxi;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
140 [V,Vi,D,signVec] = obj.matrixDiag(mat,x(1),y);
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parents: 352
diff changeset
141 side = max(length(y));
291
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parents: 290
diff changeset
142 case {'e','E','east'}
369
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diff changeset
143 e_ = obj.e_e;
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diff changeset
144 mat = obj.A;
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diff changeset
145 boundPos = 'r';
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diff changeset
146 Hi = obj.Hxi;
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diff changeset
147 [V,Vi,D,signVec] = obj.matrixDiag(mat,x(end),y);
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diff changeset
148 side = max(length(y));
291
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parents: 290
diff changeset
149 case {'s','S','south'}
369
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diff changeset
150 e_ = obj.e_s;
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diff changeset
151 mat = obj.B;
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parents: 352
diff changeset
152 boundPos = 'l';
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Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
153 Hi = obj.Hyi;
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parents: 352
diff changeset
154 [V,Vi,D,signVec] = obj.matrixDiag(mat,x,y(1));
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parents: 352
diff changeset
155 side = max(length(x));
291
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parents: 290
diff changeset
156 case {'n','N','north'}
369
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diff changeset
157 e_ = obj.e_n;
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diff changeset
158 mat = obj.B;
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diff changeset
159 boundPos = 'r';
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parents: 352
diff changeset
160 Hi = obj.Hyi;
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diff changeset
161 [V,Vi,D,signVec] = obj.matrixDiag(mat,x,y(end));
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diff changeset
162 side = max(length(x));
292
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163 end
369
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diff changeset
164 pos = signVec(1);
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parents: 352
diff changeset
165 zeroval = signVec(2);
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parents: 352
diff changeset
166 neg = signVec(3);
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parents: 369
diff changeset
167
292
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diff changeset
168 switch boundPos
294
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Ylva Rydin <ylva.rydin@telia.com>
parents: 293
diff changeset
169 case {'l'}
369
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diff changeset
170 tau = sparse(obj.n*side,pos);
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diff changeset
171 Vi_plus = Vi(1:pos,:);
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diff changeset
172 tau(1:pos,:) = -abs(D(1:pos,1:pos));
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diff changeset
173 closure = Hi*e_*V*tau*Vi_plus*e_';
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parents: 352
diff changeset
174 penalty = -Hi*e_*V*tau*Vi_plus;
294
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parents: 293
diff changeset
175 case {'r'}
369
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diff changeset
176 tau = sparse(obj.n*side,neg);
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diff changeset
177 tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
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diff changeset
178 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
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diff changeset
179 closure = Hi*e_*V*tau*Vi_minus*e_';
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diff changeset
180 penalty = -Hi*e_*V*tau*Vi_minus;
294
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parents: 293
diff changeset
181 end
292
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diff changeset
182 end
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parents: 369
diff changeset
183
369
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diff changeset
184 % General boundary condition in the form Lu=g(x)
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diff changeset
185 function [closure,penalty] = boundary_condition_general(obj,boundary,L)
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diff changeset
186 params = obj.params;
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diff changeset
187 x = obj.x;
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188 y = obj.y;
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diff changeset
189
292
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diff changeset
190 switch boundary
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diff changeset
191 case {'w','W','west'}
369
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diff changeset
192 e_ = obj.e_w;
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diff changeset
193 mat = obj.A;
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diff changeset
194 boundPos = 'l';
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diff changeset
195 Hi = obj.Hxi;
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diff changeset
196 [V,Vi,D,signVec] = obj.matrixDiag(mat,x(1),y);
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diff changeset
197 L = obj.evaluateCoefficientMatrix(L,x(1),y);
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diff changeset
198 side = max(length(y));
292
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diff changeset
199 case {'e','E','east'}
369
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diff changeset
200 e_ = obj.e_e;
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diff changeset
201 mat = obj.A;
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parents: 352
diff changeset
202 boundPos = 'r';
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Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
203 Hi = obj.Hxi;
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parents: 352
diff changeset
204 [V,Vi,D,signVec] = obj.matrixDiag(mat,x(end),y);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
205 L = obj.evaluateCoefficientMatrix(L,x(end),y);
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parents: 352
diff changeset
206 side = max(length(y));
292
3d275c5e45b3 Changed how the matrices are built
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parents: 291
diff changeset
207 case {'s','S','south'}
369
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parents: 352
diff changeset
208 e_ = obj.e_s;
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parents: 352
diff changeset
209 mat = obj.B;
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
210 boundPos = 'l';
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
211 Hi = obj.Hyi;
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
212 [V,Vi,D,signVec] = obj.matrixDiag(mat,x,y(1));
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
213 L = obj.evaluateCoefficientMatrix(L,x,y(1));
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
214 side = max(length(x));
292
3d275c5e45b3 Changed how the matrices are built
Ylva Rydin <ylva.rydin@telia.com>
parents: 291
diff changeset
215 case {'n','N','north'}
369
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Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
216 e_ = obj.e_n;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
217 mat = obj.B;
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
218 boundPos = 'r';
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
219 Hi = obj.Hyi;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
220 [V,Vi,D,signVec] = obj.matrixDiag(mat,x,y(end));
905
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Martin Almquist <malmquist@stanford.edu>
parents: 369
diff changeset
221 L = obj.evaluateCoefficientMatrix(L,x,y(end));
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
222 side = max(length(x));
292
3d275c5e45b3 Changed how the matrices are built
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parents: 291
diff changeset
223 end
905
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Martin Almquist <malmquist@stanford.edu>
parents: 369
diff changeset
224
369
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parents: 352
diff changeset
225 pos = signVec(1);
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
226 zeroval = signVec(2);
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parents: 352
diff changeset
227 neg = signVec(3);
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parents: 369
diff changeset
228
292
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diff changeset
229 switch boundPos
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parents: 291
diff changeset
230 case {'l'}
369
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parents: 352
diff changeset
231 tau = sparse(obj.n*side,pos);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
232 Vi_plus = Vi(1:pos,:);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
233 Vi_minus = Vi(pos+zeroval+1:obj.n*side,:);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
234 V_plus = V(:,1:pos);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
235 V_minus = V(:,(pos+zeroval)+1:obj.n*side);
905
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Martin Almquist <malmquist@stanford.edu>
parents: 369
diff changeset
236
369
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
237 tau(1:pos,:) = -abs(D(1:pos,1:pos));
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
238 R = -inv(L*V_plus)*(L*V_minus);
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
239 closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
240 penalty = -Hi*e_*V*tau*inv(L*V_plus)*L;
292
3d275c5e45b3 Changed how the matrices are built
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parents: 291
diff changeset
241 case {'r'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
242 tau = sparse(obj.n*side,neg);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
243 tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
244 Vi_plus = Vi(1:pos,:);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
245 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
905
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Martin Almquist <malmquist@stanford.edu>
parents: 369
diff changeset
246
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
247 V_plus = V(:,1:pos);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
248 V_minus = V(:,(pos+zeroval)+1:obj.n*side);
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parents: 352
diff changeset
249 R = -inv(L*V_minus)*(L*V_plus);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
250 closure = Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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Ylva Rydin <ylva.rydin@telia.com>
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251 penalty = -Hi*e_*V*tau*inv(L*V_minus)*L;
294
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252 end
292
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253 end
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254
369
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255 % Function that diagonalizes a symbolic matrix A as A=V*D*Vi
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256 % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign
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257 % [d+ ]
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258 % D = [ d0 ]
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259 % [ d-]
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260 % signVec is a vector specifying the number of possitive, zero and negative eigenvalues of D
369
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261 function [V,Vi, D,signVec] = matrixDiag(obj,mat,x,y)
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262 params = obj.params;
301
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263 syms xs ys
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264 [V, D]= eig(mat(params,xs,ys));
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265 Vi = inv(V);
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266 xs = x;
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267 ys = y;
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268
369
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269 side = max(length(x),length(y));
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270 Dret = zeros(obj.n,side*obj.n);
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271 Vret = zeros(obj.n,side*obj.n);
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272 Viret = zeros(obj.n,side*obj.n);
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273
369
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274 for ii = 1:obj.n
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275 for jj = 1:obj.n
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276 Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii));
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277 Vret(jj,(ii-1)*side+1:side*ii) = eval(V(jj,ii));
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278 Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii));
291
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279 end
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280 end
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281
369
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282 D = sparse(Dret);
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283 V = sparse(Vret);
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284 Vi = sparse(Viret);
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285 V = obj.evaluateCoefficientMatrix(V,x,y);
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286 Vi = obj.evaluateCoefficientMatrix(Vi,x,y);
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287 D = obj.evaluateCoefficientMatrix(D,x,y);
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288 DD = diag(D);
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289
369
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290 poseig = (DD>0);
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291 zeroeig = (DD==0);
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292 negeig = (DD<0);
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293
369
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294 D = diag([DD(poseig); DD(zeroeig); DD(negeig)]);
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295 V = [V(:,poseig) V(:,zeroeig) V(:,negeig)];
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296 Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
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297 signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
291
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298 end
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299
290
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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300 end
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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301 end