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annotate +scheme/hypsyst2d.m @ 293:2d604d16842c feature/hypsyst

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Works with varying coefficients and char boundary condition
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 23 Sep 2016 16:30:51 +0200
parents 3d275c5e45b3
children 8ff6ec6249e8
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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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23 methods
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24 function obj = hypsyst2d(m,lim,order,matrices,params)
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25
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26 xlim = lim{1};
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27 ylim = lim{2};
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28
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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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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.matrixBuild(matrices.A);
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49 obj.B=obj.matrixBuild(matrices.B);
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50 obj.E=obj.matrixBuild(matrices.E);
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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);
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55 I_x = speye(m_x); obj.I_x=I_x;
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56 I_y = speye(m_y); obj.I_y=I_y;
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59 D1_x = kr(kr(I_n,ops_x.D1),I_y);
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60 obj.Hxi= kr(kr(I_n,ops_x.HI),I_y);
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61 D1_y=kr(I_n,kr(I_x,ops_y.D1));
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62 obj.Hyi=kr(I_n,kr(I_x,ops_y.HI));
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63
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64 obj.e_w=kr(I_n,kr(ops_x.e_l,I_y));
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65 obj.e_e=kr(I_n,kr(ops_x.e_r,I_y));
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66 obj.e_s=kr(I_n,kr(I_x,ops_y.e_l));
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67 obj.e_n=kr(I_n,kr(I_x,ops_y.e_r));
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68
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69 obj.m=m;
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70 obj.h=[ops_x.h ops_y.h];
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71 obj.order=order;
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73 obj.D=-obj.A*D1_x-obj.B*D1_y-obj.E;
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75 end
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76 % Closure functions return the opertors applied to the own doamin to close the boundary
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77 % 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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78 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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79 % type is a string specifying the type of boundary condition if there are several.
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80 % data is a function returning the data that should be applied at the boundary.
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81 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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82 % neighbour_boundary is a string specifying which boundary to interface to.
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83 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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84 default_arg('type','neumann');
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85 default_arg('data',0);
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86
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87 switch type
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88 case{'c','char'}
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89 [closure,penalty]=GetBoundarydata_char(obj,boundary);
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90 case{'general'}
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91 [closure,penalty]=GeneralBoundaryCond(obj,boundary,L);
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92 otherwise
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93 error('No such boundary condition')
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94 end
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95 end
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96
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97 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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98 error('An interface function does not exist yet');
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99 end
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100
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101 function N = size(obj)
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102 N = obj.m;
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103 end
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104
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105 function [ret]=matrixBuild(obj,mat,x,y)
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106 %extra info for coordinate transfomration mult my y_ny and
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107 %x,ny osv...
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108 params=obj.params;
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109 X=obj.X;
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110 Y=obj.Y;
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111
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112 if isa(mat,'function_handle')
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113 [rows,cols]=size(mat(params,0,0));
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114 matVec=mat(params,X',Y');
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115 matVec=sparse(matVec);
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116 side=max(length(X),length(Y));
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117 else
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118 matVec=mat;
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119 [rows,cols]=size(matVec);
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120 side=max(length(x),length(y));
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121 cols=cols/side;
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122 end
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123
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124
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125 ret=kron(ones(rows,cols),speye(side));
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126
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127 for ii=1:rows
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128 for jj=1:cols
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diff changeset
129 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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130 end
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131 end
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diff changeset
132
291
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133 end
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134
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135
292
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diff changeset
136 function [closure, penalty]=GetBoundarydata_char(obj,boundary)
291
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137 params=obj.params;
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diff changeset
138 x=obj.x;
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139 y=obj.y;
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140
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diff changeset
141 side=max(length(x),length(y));
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142
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143 switch boundary
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144 case {'w','W','west'}
292
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diff changeset
145 e_=obj.e_w;
291
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146 mat=obj.matrices.A;
292
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147 boundPos='l';
291
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148 Hi=obj.Hxi;
292
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149 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
291
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150 case {'e','E','east'}
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151 e_=obj.e_e;
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152 mat=obj.matrices.A;
292
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153 boundPos='r';
291
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154 Hi=obj.Hxi;
292
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155 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
291
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156 case {'s','S','south'}
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157 e_=obj.e_s;
292
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158 mat=obj.matrices.B;
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159 boundPos='l';
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160 Hi=obj.Hxi;
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161 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
291
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162 case {'n','N','north'}
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163 e_=obj.e_n;
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164 mat=obj.matrices.B;
292
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165 boundPos='r';
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166 Hi=obj.Hxi;
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167 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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168 end
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169
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170 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
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171
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172 switch boundPos
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173 case {'l'}
293
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174 tau=sparse(obj.n*side,pos*side);
292
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175 Vi_plus=Vi(1:pos*side,:);
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176 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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177 closure=Hi*e_*V*tau*Vi_plus*e_';
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178 penalty=-Hi*e_*V*tau*Vi_plus;
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179
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180 case {'r'}
293
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181 tau=sparse(obj.n*side,neg*side);
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182 tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side));
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183 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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184 closure=Hi*e_*V*tau*Vi_minus*e_';
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185 penalty=-Hi*e_*V*tau*Vi_minus;
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186
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187 end
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188 end
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189
291
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190
292
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191 function [closure,penalty]=GeneralBoundaryCond(obj,boundary,L)
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192 params=obj.params;
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193 x=obj.x;
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194 y=obj.y;
293
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195 L=obj.matrixBuild(L,x,y);
292
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196 side=max(length(x),length(y));
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197
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198
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199 switch boundary
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200 case {'w','W','west'}
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201 e_=obj.e_w;
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202 mat=obj.matrices.A;
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203 boundPos='l';
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204 Hi=obj.Hxi;
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205 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
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206 case {'e','E','east'}
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207 e_=obj.e_e;
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208 mat=obj.matrices.A;
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209 boundPos='r';
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210 Hi=obj.Hxi;
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211 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
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212 case {'s','S','south'}
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213 e_=obj.e_s;
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214 mat=obj.matrices.B;
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215 boundPos='l';
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216 Hi=obj.Hxi;
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217 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
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diff changeset
218 case {'n','N','north'}
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219 e_=obj.e_n;
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220 mat=obj.matrices.B;
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221 boundPos='r';
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222 Hi=obj.Hxi;
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diff changeset
223 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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diff changeset
224 end
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diff changeset
225
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diff changeset
226 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
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diff changeset
227
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diff changeset
228
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diff changeset
229
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diff changeset
230 switch boundPos
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diff changeset
231 case {'l'}
293
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diff changeset
232 tau=sparse(obj.n*side,pos*side);
292
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diff changeset
233 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
234 Vi_minus=Vi(pos*side+1:obj.n*side,:);
292
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diff changeset
235
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diff changeset
236 V_plus=Vi(:,1:pos*side);
293
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diff changeset
237 V_minus=Vi(:,(pos+zeroval)*side+1:obj.n*side);
292
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diff changeset
238
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diff changeset
239 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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diff changeset
240 R=-inv(L*V_plus)*(L*V_minus);
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diff changeset
241 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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diff changeset
242 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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diff changeset
243
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diff changeset
244
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diff changeset
245 case {'r'}
293
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diff changeset
246 tau=sparse(obj.n*side,neg*side);
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diff changeset
247 tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side));
292
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diff changeset
248 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
249 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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diff changeset
250
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diff changeset
251 V_plus=Vi(:,1:pos*side);
293
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diff changeset
252 V_minus=Vi(:,(pos+zeroval)*side+1:obj.n*side);
292
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diff changeset
253 R=-inv(L*V_minus)*(L*V_plus);
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diff changeset
254 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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diff changeset
255 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
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diff changeset
256
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258 end
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261
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262 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y)
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263 params=obj.params;
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264 syms xs ys;
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265 [V, D]=eig(mat(params,xs,ys));
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266 xs=1;ys=1;
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267 DD=eval(diag(D));
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268
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269 poseig=find(DD>0);
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270 zeroeig=find(DD==0);
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271 negeig=find(DD<0);
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272 syms xs ys
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273 DD=diag(D);
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274
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275 D=diag([DD(poseig);DD(zeroeig); DD(negeig)]);
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276 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
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278 xs=x; ys=y;
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280
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281 side=max(length(x),length(y));
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282 Dret=zeros(obj.n,side*obj.n);
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283 Vret=zeros(obj.n,side*obj.n);
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284 for ii=1:obj.n
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285 for jj=1:obj.n
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286 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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287 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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288 end
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289 end
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291 D=sparse(Dret);
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292 V=sparse(normc(Vret));
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293 V=obj.matrixBuild(V,x,y);
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294 D=obj.matrixBuild(D,x,y);
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295 Vi=inv(V);
292
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296 signVec=[length(poseig),length(zeroeig),length(negeig)];
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297 end
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298
290
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300
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301 methods(Static)
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302 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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303 % and bound_v of scheme schm_v.
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304 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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305 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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306 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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307 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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308 end
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309
291
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310
290
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311 end
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312 end