annotate +scheme/Hypsyst2d.m @ 297:cd30b22cee56 feature/hypsyst

Have tried to make a curvelinear sheme for hypsysts. Does not really work yet...
author Ylva Rydin <ylva.rydin@telia.com>
date Mon, 03 Oct 2016 08:33:47 +0200
parents a6ae1b104391
children d9860ebc3148
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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
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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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21
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22 methods
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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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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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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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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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65
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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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70
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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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95
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96 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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97 error('An interface function does not exist yet');
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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=kron(ones(rows,cols),speye(side));
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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-1)*side+1:ii*side,(jj-1)*side+1:jj*side)=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 end
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127
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128 function [closure, penalty]=boundary_condition_char(obj,boundary)
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129 params=obj.params;
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130 x=obj.x; y=obj.y;
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131 side=max(length(x),length(y));
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132
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133 switch boundary
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134 case {'w','W','west'}
294
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diff changeset
135 e_=obj.e_w;
297
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diff changeset
136 mat=obj.A;
292
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diff changeset
137 boundPos='l';
291
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diff changeset
138 Hi=obj.Hxi;
292
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diff changeset
139 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
291
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diff changeset
140 case {'e','E','east'}
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diff changeset
141 e_=obj.e_e;
297
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diff changeset
142 mat=obj.A;
292
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diff changeset
143 boundPos='r';
291
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diff changeset
144 Hi=obj.Hxi;
294
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diff changeset
145 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
291
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diff changeset
146 case {'s','S','south'}
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parents: 290
diff changeset
147 e_=obj.e_s;
297
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diff changeset
148 mat=obj.B;
292
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diff changeset
149 boundPos='l';
297
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diff changeset
150 Hi=obj.Hyi;
294
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diff changeset
151 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
291
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diff changeset
152 case {'n','N','north'}
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diff changeset
153 e_=obj.e_n;
297
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diff changeset
154 mat=obj.B;
292
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diff changeset
155 boundPos='r';
297
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diff changeset
156 Hi=obj.Hyi;
292
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diff changeset
157 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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diff changeset
158 end
295
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diff changeset
159
294
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diff changeset
160 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
295
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diff changeset
161
292
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diff changeset
162 switch boundPos
294
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diff changeset
163 case {'l'}
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diff changeset
164 tau=sparse(obj.n*side,pos*side);
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diff changeset
165 Vi_plus=Vi(1:pos*side,:);
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diff changeset
166 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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diff changeset
167 closure=Hi*e_*V*tau*Vi_plus*e_';
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diff changeset
168 penalty=-Hi*e_*V*tau*Vi_plus;
294
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diff changeset
169 case {'r'}
293
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diff changeset
170 tau=sparse(obj.n*side,neg*side);
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diff changeset
171 tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side));
294
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diff changeset
172 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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diff changeset
173 closure=Hi*e_*V*tau*Vi_minus*e_';
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diff changeset
174 penalty=-Hi*e_*V*tau*Vi_minus;
294
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diff changeset
175 end
292
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diff changeset
176 end
295
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diff changeset
177
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diff changeset
178
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diff changeset
179 function [closure,penalty]=boundary_condition_general(obj,boundary,L)
294
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diff changeset
180 params=obj.params;
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diff changeset
181 x=obj.x; y=obj.y;
292
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diff changeset
182 side=max(length(x),length(y));
295
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diff changeset
183
292
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diff changeset
184 switch boundary
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diff changeset
185 case {'w','W','west'}
294
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diff changeset
186 e_=obj.e_w;
297
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diff changeset
187 mat=obj.A;
292
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diff changeset
188 boundPos='l';
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diff changeset
189 Hi=obj.Hxi;
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diff changeset
190 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
295
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diff changeset
191 L=obj.evaluateCoefficientMatrix(L,x(1),y);
292
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diff changeset
192 case {'e','E','east'}
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diff changeset
193 e_=obj.e_e;
297
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diff changeset
194 mat=obj.A;
292
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195 boundPos='r';
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diff changeset
196 Hi=obj.Hxi;
294
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diff changeset
197 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
295
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diff changeset
198 L=obj.evaluateCoefficientMatrix(L,x(end),y);
292
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199 case {'s','S','south'}
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diff changeset
200 e_=obj.e_s;
297
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diff changeset
201 mat=obj.B;
292
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diff changeset
202 boundPos='l';
297
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diff changeset
203 Hi=obj.Hyi;
294
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diff changeset
204 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
295
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diff changeset
205 L=obj.evaluateCoefficientMatrix(L,x,y(1));
292
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diff changeset
206 case {'n','N','north'}
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diff changeset
207 e_=obj.e_n;
297
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diff changeset
208 mat=obj.B;
292
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diff changeset
209 boundPos='r';
297
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diff changeset
210 Hi=obj.Hyi;
292
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diff changeset
211 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
295
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diff changeset
212 L=obj.evaluateCoefficientMatrix(L,x,y(end));
292
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diff changeset
213 end
295
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diff changeset
214
294
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diff changeset
215 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
295
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diff changeset
216
292
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diff changeset
217 switch boundPos
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diff changeset
218 case {'l'}
294
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diff changeset
219 tau=sparse(obj.n*side,pos*side);
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diff changeset
220 Vi_plus=Vi(1:pos*side,:);
293
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parents: 292
diff changeset
221 Vi_minus=Vi(pos*side+1:obj.n*side,:);
294
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diff changeset
222 V_plus=V(:,1:pos*side);
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diff changeset
223 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
295
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diff changeset
224
294
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diff changeset
225 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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diff changeset
226 R=-inv(L*V_plus)*(L*V_minus);
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diff changeset
227 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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diff changeset
228 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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diff changeset
229 case {'r'}
293
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diff changeset
230 tau=sparse(obj.n*side,neg*side);
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diff changeset
231 tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side));
294
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diff changeset
232 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
233 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
295
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diff changeset
234
294
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diff changeset
235 V_plus=V(:,1:pos*side);
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diff changeset
236 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
292
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diff changeset
237 R=-inv(L*V_minus)*(L*V_plus);
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diff changeset
238 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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diff changeset
239 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
294
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diff changeset
240 end
292
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diff changeset
241 end
295
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diff changeset
242
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diff changeset
243
292
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diff changeset
244 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y)
291
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diff changeset
245 params=obj.params;
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diff changeset
246 syms xs ys;
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diff changeset
247 [V, D]=eig(mat(params,xs,ys));
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diff changeset
248 xs=1;ys=1;
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diff changeset
249 DD=eval(diag(D));
295
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diff changeset
250
294
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diff changeset
251 poseig=find(DD>0);
292
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diff changeset
252 zeroeig=find(DD==0);
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diff changeset
253 negeig=find(DD<0);
291
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diff changeset
254 syms xs ys
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diff changeset
255 DD=diag(D);
295
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diff changeset
256
292
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diff changeset
257 D=diag([DD(poseig);DD(zeroeig); DD(negeig)]);
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parents: 291
diff changeset
258 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
291
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diff changeset
259 xs=x; ys=y;
295
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diff changeset
260
291
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261 side=max(length(x),length(y));
293
2d604d16842c Works with varying coefficients and char boundary condition
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262 Dret=zeros(obj.n,side*obj.n);
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263 Vret=zeros(obj.n,side*obj.n);
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264 for ii=1:obj.n
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265 for jj=1:obj.n
291
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266 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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267 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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268 end
807dfe8be3ec Have made a lot of stupid changes in hypsyst in order to find a stupid bug
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parents: 290
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269 end
295
da0131655035 Fixed some formatting and naming.
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parents: 294
diff changeset
270
291
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diff changeset
271 D=sparse(Dret);
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272 V=sparse(normc(Vret));
295
da0131655035 Fixed some formatting and naming.
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diff changeset
273 V=obj.evaluateCoefficientMatrix(V,x,y);
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diff changeset
274 D=obj.evaluateCoefficientMatrix(D,x,y);
291
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diff changeset
275 Vi=inv(V);
292
3d275c5e45b3 Changed how the matrices are built
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parents: 291
diff changeset
276 signVec=[length(poseig),length(zeroeig),length(negeig)];
291
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277 end
295
da0131655035 Fixed some formatting and naming.
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278
290
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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parents:
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279 end
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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parents:
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280 end