Mercurial > repos > public > sbplib
annotate +scheme/Hypsyst2d.m @ 349:cd6a29ab3746 feature/hypsyst
A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
author | Ylva Rydin <ylva.rydin@telia.com> |
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date | Thu, 13 Oct 2016 09:34:30 +0200 |
parents | d9860ebc3148 |
children | 9b3d7fc61a36 |
rev | line source |
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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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20 |
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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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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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59 |
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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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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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74 |
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75 obj.D=-Aevaluated*D1_x-Bevaluated*D1_y-Eevaluated; |
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76 |
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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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126 |
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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 |
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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.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); |
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139 side=max(length(y)); |
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140 case {'e','E','east'} |
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141 e_=obj.e_e; |
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142 mat=obj.A; |
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143 boundPos='r'; |
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144 Hi=obj.Hxi; |
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145 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); |
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146 side=max(length(y)); |
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147 case {'s','S','south'} |
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148 e_=obj.e_s; |
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149 mat=obj.B; |
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150 boundPos='l'; |
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151 Hi=obj.Hyi; |
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152 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); |
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153 side=max(length(x)); |
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154 case {'n','N','north'} |
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155 e_=obj.e_n; |
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156 mat=obj.B; |
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157 boundPos='r'; |
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158 Hi=obj.Hyi; |
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159 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); |
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160 side=max(length(x)); |
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161 end |
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162 |
294
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163 pos=signVec(1); zeroval=signVec(2); neg=signVec(3); |
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164 |
292
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165 switch boundPos |
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166 case {'l'} |
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167 tau=sparse(obj.n*side,pos); |
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168 Vi_plus=Vi(1:pos,:); |
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169 tau(1:pos,:)=-abs(D(1:pos,1:pos)); |
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170 closure=Hi*e_*V*tau*Vi_plus*e_'; |
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171 penalty=-Hi*e_*V*tau*Vi_plus; |
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172 case {'r'} |
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173 tau=sparse(obj.n*side,neg); |
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174 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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175 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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176 closure=Hi*e_*V*tau*Vi_minus*e_'; |
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177 penalty=-Hi*e_*V*tau*Vi_minus; |
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178 end |
292
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179 end |
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180 |
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181 |
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182 function [closure,penalty]=boundary_condition_general(obj,boundary,L) |
294
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183 params=obj.params; |
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184 x=obj.x; y=obj.y; |
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185 |
292
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186 switch boundary |
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187 case {'w','W','west'} |
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188 e_=obj.e_w; |
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189 mat=obj.A; |
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190 boundPos='l'; |
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191 Hi=obj.Hxi; |
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192 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y); |
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193 L=obj.evaluateCoefficientMatrix(L,x(1),y); |
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194 side=max(length(y)); |
292
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195 case {'e','E','east'} |
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196 e_=obj.e_e; |
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197 mat=obj.A; |
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198 boundPos='r'; |
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199 Hi=obj.Hxi; |
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200 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); |
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201 L=obj.evaluateCoefficientMatrix(L,x(end),y); |
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202 side=max(length(y)); |
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203 case {'s','S','south'} |
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204 e_=obj.e_s; |
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205 mat=obj.B; |
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206 boundPos='l'; |
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207 Hi=obj.Hyi; |
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208 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); |
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209 L=obj.evaluateCoefficientMatrix(L,x,y(1)); |
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210 side=max(length(x)); |
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211 case {'n','N','north'} |
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212 e_=obj.e_n; |
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213 mat=obj.B; |
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214 boundPos='r'; |
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215 Hi=obj.Hyi; |
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216 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); |
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217 L=obj.evaluateCoefficientMatrix(L,x,y(end)); |
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218 side=max(length(x)); |
292
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219 end |
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220 |
294
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221 pos=signVec(1); zeroval=signVec(2); neg=signVec(3); |
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222 |
292
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223 switch boundPos |
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224 case {'l'} |
301
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225 tau=sparse(obj.n*side,pos); |
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226 Vi_plus=Vi(1:pos,:); |
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227 Vi_minus=Vi(pos+zeroval+1:obj.n*side,:); |
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228 V_plus=V(:,1:pos); |
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229 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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230 |
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231 tau(1:pos,:)=-abs(D(1:pos,1:pos)); |
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232 R=-inv(L*V_plus)*(L*V_minus); |
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233 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; |
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234 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L; |
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235 case {'r'} |
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236 tau=sparse(obj.n*side,neg); |
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237 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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238 Vi_plus=Vi(1:pos,:); |
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239 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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240 |
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241 V_plus=V(:,1:pos); |
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242 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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243 R=-inv(L*V_minus)*(L*V_plus); |
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244 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_'; |
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245 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L; |
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246 end |
292
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247 end |
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248 |
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249 |
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250 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y) |
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251 params=obj.params; |
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252 syms xs ys |
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253 [V, D]=eig(mat(params,xs,ys)); |
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254 xs=x; |
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255 ys=y; |
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256 |
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257 side=max(length(x),length(y)); |
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258 Dret=zeros(obj.n,side*obj.n); |
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259 Vret=zeros(obj.n,side*obj.n); |
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260 for ii=1:obj.n |
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261 for jj=1:obj.n |
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262 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii)); |
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263 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii)); |
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264 end |
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265 end |
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266 |
291
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267 D=sparse(Dret); |
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268 V=sparse(Vret); |
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269 V=obj.evaluateCoefficientMatrix(V,x,y); |
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270 D=obj.evaluateCoefficientMatrix(D,x,y); |
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271 DD=diag(D); |
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272 |
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273 poseig=(DD>0); |
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274 zeroeig=(DD==0); |
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275 negeig=(DD<0); |
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276 |
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277 D=diag([DD(poseig); DD(zeroeig); DD(negeig)]); |
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278 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)]; |
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279 Vi=inv(V); |
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280 signVec=[sum(poseig),sum(zeroeig),sum(negeig)]; |
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281 end |
295
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282 |
290
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A first attempt to make a general scheme fo hyperbolic systems
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283 end |
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284 end |