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annotate +scheme/hypsyst2d.m @ 295:da0131655035 feature/hypsyst

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Fixed some formatting and naming.
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 26 Sep 2016 14:19:34 +0200
parents 8ff6ec6249e8
children
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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 matrices
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19 matrices
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20 end
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22
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23 methods
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24 function obj = Hypsyst2d(m, lim, order, A, B, E, params)
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25 default_arg('E', [])
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26 xlim = lim{1};
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27 ylim = lim{2};
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29 if length(m) == 1
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30 m = [m m];
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31 end
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32
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33 m_x = m(1);
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34 m_y = m(2);
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35 obj.params = params;
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36
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37 obj.matrices = matrices;
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38
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39 ops_x = sbp.D2Standard(m_x,xlim,order);
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40 ops_y = sbp.D2Standard(m_y,ylim,order);
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41
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42 obj.x = ops_x.x;
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43 obj.y = ops_y.x;
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44
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45 obj.X = kr(obj.x,ones(m_y,1));
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46 obj.Y = kr(ones(m_x,1),obj.y);
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47
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48 obj.A = obj.evaluateCoefficientMatrix(matrices.A, obj.X, obj.Y);
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49 obj.B = obj.evaluateCoefficientMatrix(matrices.B, obj.X, obj.Y);
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50 obj.E = obj.evaluateCoefficientMatrix(matrices.E, obj.X, obj.Y);
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51
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52 obj.n = length(matrices.A(obj.params,0,0));
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53
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54 I_n = eye(obj.n);I_x = speye(m_x);
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55 obj.I_x = I_x;
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56 I_y = speye(m_y);
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57 obj.I_y = I_y;
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58
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59
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60 D1_x = kr(I_n, ops_x.D1, I_y);
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61 obj.Hxi = kr(I_n, ops_x.HI, I_y);
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62 D1_y = kr(I_n, I_x, ops_y.D1));
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63 obj.Hyi = kr(I_n, I_x, ops_y.HI));
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64
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65 obj.e_w = kr(I_n, ops_x.e_l, I_y);
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66 obj.e_e = kr(I_n, ops_x.e_r, I_y);
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67 obj.e_s = kr(I_n, I_x, ops_y.e_l);
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68 obj.e_n = kr(I_n, I_x, ops_y.e_r);
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69
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70 obj.m=m;
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71 obj.h=[ops_x.h ops_y.h];
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72 obj.order=order;
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73
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74 obj.D=-obj.A*D1_x-obj.B*D1_y-obj.E;
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75
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76 end
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77
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78 % Closure functions return the opertors applied to the own doamin to close the boundary
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79 % 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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80 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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81 % type is a string specifying the type of boundary condition if there are several.
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82 % data is a function returning the data that should be applied at the boundary.
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83 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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84 default_arg('type','char');
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85 switch type
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86 case{'c','char'}
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87 [closure,penalty]=boundary_condition_char(obj,boundary);
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88 case{'general'}
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89 [closure,penalty]=boundary_condition_general(obj,boundary,L);
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90 otherwise
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91 error('No such boundary condition')
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92 end
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93 end
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94
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95 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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96 error('An interface function does not exist yet');
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97 end
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98
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99 function N = size(obj)
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100 N = obj.m;
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101 end
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102
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103 function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y)
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104 params=obj.params;
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105
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106 if isa(mat,'function_handle')
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107 [rows,cols]=size(mat(params,0,0));
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108 matVec=mat(params,X',Y');
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109 matVec=sparse(matVec);
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110 side=max(length(X),length(Y));
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111 else
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112 matVec=mat;
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113 [rows,cols]=size(matVec);
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114 side=max(length(X),length(Y));
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115 cols=cols/side;
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116 end
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117 ret=kron(ones(rows,cols),speye(side));
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118
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119 for ii=1:rows
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120 for jj=1:cols
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121 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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122 end
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123 end
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124 end
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125
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126
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127 function [closure, penalty]=boundary_condition_char(obj,boundary)
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128 params=obj.params;
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129 x=obj.x; y=obj.y;
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130 side=max(length(x),length(y));
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131
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132 switch boundary
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133 case {'w','W','west'}
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134 e_=obj.e_w;
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135 mat=obj.matrices.A;
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136 boundPos='l';
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137 Hi=obj.Hxi;
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138 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
291
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diff changeset
139 case {'e','E','east'}
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diff changeset
140 e_=obj.e_e;
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diff changeset
141 mat=obj.matrices.A;
292
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diff changeset
142 boundPos='r';
291
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diff changeset
143 Hi=obj.Hxi;
294
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diff changeset
144 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
291
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diff changeset
145 case {'s','S','south'}
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diff changeset
146 e_=obj.e_s;
294
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diff changeset
147 mat=obj.matrices.B;
292
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diff changeset
148 boundPos='l';
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diff changeset
149 Hi=obj.Hxi;
294
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diff changeset
150 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
291
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diff changeset
151 case {'n','N','north'}
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diff changeset
152 e_=obj.e_n;
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diff changeset
153 mat=obj.matrices.B;
292
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diff changeset
154 boundPos='r';
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diff changeset
155 Hi=obj.Hxi;
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diff changeset
156 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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diff changeset
157 end
295
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diff changeset
158
294
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diff changeset
159 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
295
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diff changeset
160
292
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diff changeset
161 switch boundPos
294
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diff changeset
162 case {'l'}
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diff changeset
163 tau=sparse(obj.n*side,pos*side);
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diff changeset
164 Vi_plus=Vi(1:pos*side,:);
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diff changeset
165 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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diff changeset
166 closure=Hi*e_*V*tau*Vi_plus*e_';
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diff changeset
167 penalty=-Hi*e_*V*tau*Vi_plus;
294
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diff changeset
168 case {'r'}
293
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diff changeset
169 tau=sparse(obj.n*side,neg*side);
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diff changeset
170 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
171 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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diff changeset
172 closure=Hi*e_*V*tau*Vi_minus*e_';
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diff changeset
173 penalty=-Hi*e_*V*tau*Vi_minus;
294
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diff changeset
174 end
292
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175 end
295
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diff changeset
176
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177
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diff changeset
178 function [closure,penalty]=boundary_condition_general(obj,boundary,L)
294
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diff changeset
179 params=obj.params;
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diff changeset
180 x=obj.x; y=obj.y;
292
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diff changeset
181 side=max(length(x),length(y));
295
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diff changeset
182
292
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diff changeset
183 switch boundary
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diff changeset
184 case {'w','W','west'}
294
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diff changeset
185 e_=obj.e_w;
292
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diff changeset
186 mat=obj.matrices.A;
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diff changeset
187 boundPos='l';
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diff changeset
188 Hi=obj.Hxi;
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diff changeset
189 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
295
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diff changeset
190 L=obj.evaluateCoefficientMatrix(L,x(1),y);
292
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diff changeset
191 case {'e','E','east'}
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diff changeset
192 e_=obj.e_e;
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193 mat=obj.matrices.A;
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194 boundPos='r';
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diff changeset
195 Hi=obj.Hxi;
294
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diff changeset
196 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
295
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diff changeset
197 L=obj.evaluateCoefficientMatrix(L,x(end),y);
292
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diff changeset
198 case {'s','S','south'}
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diff changeset
199 e_=obj.e_s;
294
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diff changeset
200 mat=obj.matrices.B;
292
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diff changeset
201 boundPos='l';
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diff changeset
202 Hi=obj.Hxi;
294
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diff changeset
203 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
295
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diff changeset
204 L=obj.evaluateCoefficientMatrix(L,x,y(1));
292
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diff changeset
205 case {'n','N','north'}
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diff changeset
206 e_=obj.e_n;
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diff changeset
207 mat=obj.matrices.B;
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208 boundPos='r';
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diff changeset
209 Hi=obj.Hxi;
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diff changeset
210 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
295
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diff changeset
211 L=obj.evaluateCoefficientMatrix(L,x,y(end));
292
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diff changeset
212 end
295
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diff changeset
213
294
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diff changeset
214 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
295
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diff changeset
215
292
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diff changeset
216 switch boundPos
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diff changeset
217 case {'l'}
294
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diff changeset
218 tau=sparse(obj.n*side,pos*side);
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diff changeset
219 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
220 Vi_minus=Vi(pos*side+1:obj.n*side,:);
294
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diff changeset
221 V_plus=V(:,1:pos*side);
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diff changeset
222 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
295
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diff changeset
223
294
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diff changeset
224 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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diff changeset
225 R=-inv(L*V_plus)*(L*V_minus);
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diff changeset
226 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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diff changeset
227 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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diff changeset
228 case {'r'}
293
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diff changeset
229 tau=sparse(obj.n*side,neg*side);
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diff changeset
230 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
231 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
232 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
295
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diff changeset
233
294
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diff changeset
234 V_plus=V(:,1:pos*side);
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diff changeset
235 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
292
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diff changeset
236 R=-inv(L*V_minus)*(L*V_plus);
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diff changeset
237 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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parents: 291
diff changeset
238 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
294
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diff changeset
239 end
292
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diff changeset
240 end
295
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diff changeset
241
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diff changeset
242
292
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diff changeset
243 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y)
291
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diff changeset
244 params=obj.params;
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diff changeset
245 syms xs ys;
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diff changeset
246 [V, D]=eig(mat(params,xs,ys));
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diff changeset
247 xs=1;ys=1;
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diff changeset
248 DD=eval(diag(D));
295
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diff changeset
249
294
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diff changeset
250 poseig=find(DD>0);
292
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diff changeset
251 zeroeig=find(DD==0);
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diff changeset
252 negeig=find(DD<0);
291
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diff changeset
253 syms xs ys
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diff changeset
254 DD=diag(D);
295
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diff changeset
255
292
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diff changeset
256 D=diag([DD(poseig);DD(zeroeig); DD(negeig)]);
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diff changeset
257 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
291
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diff changeset
258 xs=x; ys=y;
295
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diff changeset
259
291
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diff changeset
260 side=max(length(x),length(y));
293
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diff changeset
261 Dret=zeros(obj.n,side*obj.n);
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diff changeset
262 Vret=zeros(obj.n,side*obj.n);
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diff changeset
263 for ii=1:obj.n
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diff changeset
264 for jj=1:obj.n
291
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diff changeset
265 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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diff changeset
266 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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267 end
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268 end
295
da0131655035 Fixed some formatting and naming.
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269
291
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270 D=sparse(Dret);
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271 V=sparse(normc(Vret));
295
da0131655035 Fixed some formatting and naming.
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272 V=obj.evaluateCoefficientMatrix(V,x,y);
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273 D=obj.evaluateCoefficientMatrix(D,x,y);
291
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274 Vi=inv(V);
292
3d275c5e45b3 Changed how the matrices are built
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parents: 291
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275 signVec=[length(poseig),length(zeroeig),length(negeig)];
291
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276 end
295
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277
290
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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278 end
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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parents:
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279 end