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annotate +scheme/hypsyst2d.m @ 294:8ff6ec6249e8 feature/hypsyst

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"General" boundary conditions implemented
author Ylva Rydin <ylva.rydin@telia.com>
date Mon, 26 Sep 2016 09:54:43 +0200
parents 2d604d16842c
children da0131655035
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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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29 if length(m) == 1
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30 m = [m m];
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31 end
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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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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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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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77 % Closure functions return the opertors applied to the own doamin to close the boundary
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78 % 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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79 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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80 % type is a string specifying the type of boundary condition if there are several.
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81 % data is a function returning the data that should be applied at the boundary.
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82 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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83 % neighbour_boundary is a string specifying which boundary to interface to.
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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]=GetBoundarydata_char(obj,boundary);
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89 case{'general'}
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90 [closure,penalty]=GeneralBoundaryCond(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]=matrixBuild(obj,mat,X,Y)
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105 params=obj.params;
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106 default_arg('X',obj.X);
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107 default_arg('Y',obj.Y)
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109 if isa(mat,'function_handle')
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110 [rows,cols]=size(mat(params,0,0));
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111 matVec=mat(params,X',Y');
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112 matVec=sparse(matVec);
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113 side=max(length(X),length(Y));
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114 else
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115 matVec=mat;
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116 [rows,cols]=size(matVec);
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117 side=max(length(X),length(Y));
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118 cols=cols/side;
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119 end
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120 ret=kron(ones(rows,cols),speye(side));
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121
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122 for ii=1:rows
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123 for jj=1:cols
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124 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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125 end
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126 end
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127 end
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130 function [closure, penalty]=GetBoundarydata_char(obj,boundary)
291
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131 params=obj.params;
294
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132 x=obj.x; y=obj.y;
291
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133 side=max(length(x),length(y));
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134
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135 switch boundary
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136 case {'w','W','west'}
294
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diff changeset
137 e_=obj.e_w;
291
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138 mat=obj.matrices.A;
292
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139 boundPos='l';
291
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140 Hi=obj.Hxi;
292
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141 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
291
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142 case {'e','E','east'}
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143 e_=obj.e_e;
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144 mat=obj.matrices.A;
292
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145 boundPos='r';
291
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146 Hi=obj.Hxi;
294
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147 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
291
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148 case {'s','S','south'}
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149 e_=obj.e_s;
294
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150 mat=obj.matrices.B;
292
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151 boundPos='l';
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152 Hi=obj.Hxi;
294
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153 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
291
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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.matrices.B;
292
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157 boundPos='r';
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158 Hi=obj.Hxi;
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159 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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160 end
294
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161
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162 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
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163
292
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164 switch boundPos
294
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165 case {'l'}
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166 tau=sparse(obj.n*side,pos*side);
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167 Vi_plus=Vi(1:pos*side,:);
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168 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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169 closure=Hi*e_*V*tau*Vi_plus*e_';
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170 penalty=-Hi*e_*V*tau*Vi_plus;
294
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171 case {'r'}
293
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172 tau=sparse(obj.n*side,neg*side);
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173 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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174 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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175 closure=Hi*e_*V*tau*Vi_minus*e_';
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176 penalty=-Hi*e_*V*tau*Vi_minus;
294
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177 end
292
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178 end
294
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179
291
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180
292
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181 function [closure,penalty]=GeneralBoundaryCond(obj,boundary,L)
294
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182 params=obj.params;
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183 x=obj.x; y=obj.y;
292
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184 side=max(length(x),length(y));
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185
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186 switch boundary
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187 case {'w','W','west'}
294
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188 e_=obj.e_w;
292
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189 mat=obj.matrices.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);
294
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193 L=obj.matrixBuild(L,x(1),y);
292
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194 case {'e','E','east'}
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195 e_=obj.e_e;
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196 mat=obj.matrices.A;
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197 boundPos='r';
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198 Hi=obj.Hxi;
294
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199 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
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200 L=obj.matrixBuild(L,x(end),y);
292
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201 case {'s','S','south'}
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202 e_=obj.e_s;
294
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203 mat=obj.matrices.B;
292
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204 boundPos='l';
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205 Hi=obj.Hxi;
294
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206 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
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207 L=obj.matrixBuild(L,x,y(1));
292
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208 case {'n','N','north'}
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209 e_=obj.e_n;
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210 mat=obj.matrices.B;
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211 boundPos='r';
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212 Hi=obj.Hxi;
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213 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
294
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diff changeset
214 L=obj.matrixBuild(L,x,y(end));
292
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diff changeset
215 end
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216
294
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diff changeset
217 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
292
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218
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219 switch boundPos
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diff changeset
220 case {'l'}
294
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221 tau=sparse(obj.n*side,pos*side);
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222 Vi_plus=Vi(1:pos*side,:);
293
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diff changeset
223 Vi_minus=Vi(pos*side+1:obj.n*side,:);
294
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diff changeset
224 V_plus=V(:,1:pos*side);
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diff changeset
225 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
292
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diff changeset
226
294
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diff changeset
227 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
292
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228 R=-inv(L*V_plus)*(L*V_minus);
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229 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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230 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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diff changeset
231 case {'r'}
293
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232 tau=sparse(obj.n*side,neg*side);
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diff changeset
233 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
234 Vi_plus=Vi(1:pos*side,:);
293
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235 Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:);
292
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diff changeset
236
294
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237 V_plus=V(:,1:pos*side);
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238 V_minus=V(:,(pos+zeroval)*side+1:obj.n*side);
292
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239 R=-inv(L*V_minus)*(L*V_plus);
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diff changeset
240 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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diff changeset
241 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
294
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diff changeset
242 end
292
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243 end
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244
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245
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diff changeset
246 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y)
291
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diff changeset
247 params=obj.params;
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diff changeset
248 syms xs ys;
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diff changeset
249 [V, D]=eig(mat(params,xs,ys));
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diff changeset
250 xs=1;ys=1;
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diff changeset
251 DD=eval(diag(D));
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diff changeset
252
294
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diff changeset
253 poseig=find(DD>0);
292
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diff changeset
254 zeroeig=find(DD==0);
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diff changeset
255 negeig=find(DD<0);
291
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256 syms xs ys
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257 DD=diag(D);
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258
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259 D=diag([DD(poseig);DD(zeroeig); DD(negeig)]);
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260 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
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261 xs=x; ys=y;
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262
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263 side=max(length(x),length(y));
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264 Dret=zeros(obj.n,side*obj.n);
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265 Vret=zeros(obj.n,side*obj.n);
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266 for ii=1:obj.n
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267 for jj=1:obj.n
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268 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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269 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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270 end
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271 end
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272
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273 D=sparse(Dret);
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274 V=sparse(normc(Vret));
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275 V=obj.matrixBuild(V,x,y);
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276 D=obj.matrixBuild(D,x,y);
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277 Vi=inv(V);
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278 signVec=[length(poseig),length(zeroeig),length(negeig)];
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279 end
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280
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281 end
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282
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283 methods(Static)
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284 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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285 % and bound_v of scheme schm_v.
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286 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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287 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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288 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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289 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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290 end
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293 end
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294 end