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annotate +scheme/hypsyst2d.m @ 292:3d275c5e45b3 feature/hypsyst

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Changed how the matrices are built
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 23 Sep 2016 14:48:54 +0200
parents 807dfe8be3ec
children 2d604d16842c
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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 h % Grid spacing
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5 x,y % Grid
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6 X,Y % Values of x and y for each grid point
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7 order % Order accuracy for the approximation
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8
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9 D % non-stabalized scheme operator
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10 A, B, E
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11
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12 H % Discrete norm
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13 % Norms in the x and y directions
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14 Hxi,Hyi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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15 I_x,I_y, I_N
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16 e_w, e_e, e_s, e_n
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17 params %parameters for the coeficient matrices
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18 matrices
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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,matrices,params)
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24
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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 m_x = m(1);
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33 m_y = m(2);
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34
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35 obj.matrices=matrices;
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36
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37 ops_x = sbp.D2Standard(m_x,xlim,order);
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38 ops_y = sbp.D2Standard(m_y,ylim,order);
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39
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40 obj.x=ops_x.x;
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41 obj.y=ops_y.x;
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43 obj.X = kr(obj.x,ones(m_y,1));
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44 obj.Y = kr(ones(m_x,1),obj.y);
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45
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46 I_x = speye(m_x); obj.I_x=I_x;
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47 I_y = speye(m_y); obj.I_y=I_y;
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48
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49 I_n= eye(4);
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51
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52 D1_x = kr(kr(I_n,ops_x.D1),I_y);
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53 obj.Hxi= kr(kr(I_n,ops_x.HI),I_y);
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54 D1_y=kr(I_n,kr(I_x,ops_y.D1));
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55 obj.Hyi=kr(I_n,kr(I_x,ops_y.HI));
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56
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57 obj.e_w=kr(I_n,kr(ops_x.e_l,I_y));
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58 obj.e_e=kr(I_n,kr(ops_x.e_r,I_y));
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59 obj.e_s=kr(I_n,kr(I_x,ops_y.e_l));
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60 obj.e_n=kr(I_n,kr(I_x,ops_y.e_r));
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61
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62 obj.m=m;
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63 obj.h=[ops_x.h ops_y.h];
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64 obj.order=order;
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65 obj.params=params;
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66
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67 obj.A=obj.matrixBuild(matrices.A);
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68 obj.B=obj.matrixBuild(matrices.B);
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69 obj.E=obj.matrixBuild(matrices.E);
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72 obj.D=-obj.A*D1_x-obj.B*D1_y-obj.E;
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74 end
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75 % Closure functions return the opertors applied to the own doamin to close the boundary
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76 % 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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77 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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78 % type is a string specifying the type of boundary condition if there are several.
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79 % data is a function returning the data that should be applied at the boundary.
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80 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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81 % neighbour_boundary is a string specifying which boundary to interface to.
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82 function [closure, penalty] = boundary_condition(obj,boundary,type)
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83 default_arg('type','neumann');
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84 default_arg('data',0);
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85
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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{'wall'}
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90 [closure,penalty]=GetBoundarydata_wall(obj,boundary);
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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 %extra info for coordinate transfomration mult my y_ny and
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106 %x,ny osv...
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107 params=obj.params;
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108 X=obj.X;
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109 Y=obj.Y;
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110
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111 if isa(mat,'function_handle')
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112 [rows,cols]=size(mat(params,0,0));
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113 matVec=mat(params,X',Y');
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114 matVec=sparse(matVec);
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115 side=max(length(X),length(Y));
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116 else
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117 matVec=mat;
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118 [rows,cols]=size(matVec);
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119 side=max(length(x),length(y));
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120 cols=cols/side;
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121 end
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122
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123
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124 ret=kron(ones(rows,cols),speye(side));
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125
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126 for ii=1:rows
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127 for jj=1:cols
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diff changeset
128 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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diff changeset
129 end
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diff changeset
130 end
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diff changeset
131
291
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diff changeset
132 end
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diff changeset
133
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diff changeset
134
292
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diff changeset
135 function [closure, penalty]=GetBoundarydata_char(obj,boundary)
291
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diff changeset
136 params=obj.params;
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diff changeset
137 x=obj.x;
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diff changeset
138 y=obj.y;
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diff changeset
139
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diff changeset
140 side=max(length(x),length(y));
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diff changeset
141
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diff changeset
142 switch boundary
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diff changeset
143 case {'w','W','west'}
292
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diff changeset
144 e_=obj.e_w;
291
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diff changeset
145 mat=obj.matrices.A;
292
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diff changeset
146 boundPos='l';
291
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diff changeset
147 Hi=obj.Hxi;
292
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diff changeset
148 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
291
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diff changeset
149 case {'e','E','east'}
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diff changeset
150 e_=obj.e_e;
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diff changeset
151 mat=obj.matrices.A;
292
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diff changeset
152 boundPos='r';
291
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diff changeset
153 Hi=obj.Hxi;
292
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diff changeset
154 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
291
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diff changeset
155 case {'s','S','south'}
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diff changeset
156 e_=obj.e_s;
292
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diff changeset
157 mat=obj.matrices.B;
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diff changeset
158 boundPos='l';
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diff changeset
159 Hi=obj.Hxi;
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diff changeset
160 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
291
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diff changeset
161 case {'n','N','north'}
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162 e_=obj.e_n;
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diff changeset
163 mat=obj.matrices.B;
292
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diff changeset
164 boundPos='r';
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diff changeset
165 Hi=obj.Hxi;
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diff changeset
166 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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diff changeset
167 end
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diff changeset
168
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diff changeset
169 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
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diff changeset
170
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diff changeset
171 switch boundPos
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diff changeset
172 case {'l'}
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diff changeset
173 tau=sparse(4*side,pos*side);
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diff changeset
174 Vi_plus=Vi(1:pos*side,:);
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diff changeset
175 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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diff changeset
176 closure=Hi*e_*V*tau*Vi_plus*e_';
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diff changeset
177 penalty=-Hi*e_*V*tau*Vi_plus;
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diff changeset
178
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diff changeset
179 case {'r'}
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diff changeset
180 tau=sparse(4*side,neg*side);
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diff changeset
181 tau((pos+zeroval)*side+1:4*side,:)=-abs(D((pos+zeroval)*side+1:4*side,(pos+zeroval)*side+1:4*side));
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diff changeset
182 Vi_minus=Vi((pos+zeroval)*side+1:4*side,:);
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diff changeset
183 closure=Hi*e_*V*tau*Vi_minus*e_';
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diff changeset
184 penalty=-Hi*e_*V*tau*Vi_minus;
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diff changeset
185
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diff changeset
186 end
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187 end
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diff changeset
188
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diff changeset
189 function [closure, penalty]=GetBoundarydata_wall(obj,boundary)
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diff changeset
190 switch boundary
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diff changeset
191 case {'e','w'}
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diff changeset
192 L=[0 1 0 0]';
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diff changeset
193 L=kr(L,obj.I_y);
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diff changeset
194 L=L';
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195 case {'s','n'}
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diff changeset
196 L=[0 0 1 0]';
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diff changeset
197 L=kr(L,obj.I_x);
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diff changeset
198 L=L';
291
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diff changeset
199
292
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200 end
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diff changeset
201 [closure,penalty]=GeneralBoundaryCond(obj,boundary,L);
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diff changeset
202 end
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diff changeset
203
291
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diff changeset
204
292
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diff changeset
205 function [closure,penalty]=GeneralBoundaryCond(obj,boundary,L)
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diff changeset
206 params=obj.params;
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diff changeset
207 x=obj.x;
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diff changeset
208 y=obj.y;
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diff changeset
209
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diff changeset
210 side=max(length(x),length(y));
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diff changeset
211
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diff changeset
212
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diff changeset
213 switch boundary
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diff changeset
214 case {'w','W','west'}
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diff changeset
215 e_=obj.e_w;
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diff changeset
216 mat=obj.matrices.A;
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diff changeset
217 boundPos='l';
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diff changeset
218 Hi=obj.Hxi;
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diff changeset
219 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y);
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diff changeset
220 case {'e','E','east'}
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diff changeset
221 e_=obj.e_e;
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diff changeset
222 mat=obj.matrices.A;
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diff changeset
223 boundPos='r';
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diff changeset
224 Hi=obj.Hxi;
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diff changeset
225 [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y);
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diff changeset
226 case {'s','S','south'}
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diff changeset
227 e_=obj.e_s;
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diff changeset
228 mat=obj.matrices.B;
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diff changeset
229 boundPos='l';
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diff changeset
230 Hi=obj.Hxi;
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diff changeset
231 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1));
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diff changeset
232 case {'n','N','north'}
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diff changeset
233 e_=obj.e_n;
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diff changeset
234 mat=obj.matrices.B;
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diff changeset
235 boundPos='r';
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diff changeset
236 Hi=obj.Hxi;
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diff changeset
237 [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end));
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diff changeset
238 end
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diff changeset
239
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diff changeset
240 pos=signVec(1); zeroval=signVec(2); neg=signVec(3);
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diff changeset
241
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parents: 291
diff changeset
242
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diff changeset
243
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diff changeset
244 switch boundPos
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diff changeset
245 case {'l'}
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diff changeset
246 tau=sparse(4*side,pos*side);
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diff changeset
247 Vi_plus=Vi(1:pos*side,:);
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parents: 291
diff changeset
248 Vi_minus=Vi(pos*side+1:4*side,:);
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diff changeset
249
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diff changeset
250 V_plus=Vi(:,1:pos*side);
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diff changeset
251 V_minus=Vi(:,(pos+zeroval)*side+1:4*side);
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diff changeset
252
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diff changeset
253 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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parents: 291
diff changeset
254 R=-inv(L*V_plus)*(L*V_minus);
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parents: 291
diff changeset
255 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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parents: 291
diff changeset
256 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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parents: 291
diff changeset
257
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parents: 291
diff changeset
258
3d275c5e45b3 Changed how the matrices are built
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parents: 291
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259 case {'r'}
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260 tau=sparse(4*side,neg*side);
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261 tau((pos+zeroval)*side+1:4*side,:)=-abs(D((pos+zeroval)*side+1:4*side,(pos+zeroval)*side+1:4*side));
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262 Vi_plus=Vi(1:pos*side,:);
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263 Vi_minus=Vi((pos+zeroval)*side+1:4*side,:);
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264
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265 V_plus=Vi(:,1:pos*side);
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266 V_minus=Vi(:,(pos+zeroval)*side+1:4*side);
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267 R=-inv(L*V_minus)*(L*V_plus);
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268 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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269 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
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270
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271
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272 end
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273 end
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274
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275
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276 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y)
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277 params=obj.params;
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278 syms xs ys;
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279 [V, D]=eig(mat(params,xs,ys));
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280 xs=1;ys=1;
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281 DD=eval(diag(D));
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282
292
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283 poseig=find(DD>0);
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284 zeroeig=find(DD==0);
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285 negeig=find(DD<0);
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286 syms xs ys
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287 DD=diag(D);
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288
292
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289 D=diag([DD(poseig);DD(zeroeig); DD(negeig)]);
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290 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
291
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291
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292 xs=x; ys=y;
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293
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294
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295 side=max(length(x),length(y));
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296 Dret=zeros(4,side*4);
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297 Vret=zeros(4,side*4);
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298 for ii=1:4
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299 for jj=1:4
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300 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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301 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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302 end
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303 end
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304
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305 D=sparse(Dret);
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306 V=sparse(normc(Vret));
292
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307 V=obj.matrixBuild(V,x,y);
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308 D=obj.matrixBuild(D,x,y);
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309 Vi=inv(V);
292
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310 signVec=[length(poseig),length(zeroeig),length(negeig)];
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311 end
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312
290
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313 end
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314
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315 methods(Static)
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316 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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317 % and bound_v of scheme schm_v.
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318 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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319 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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320 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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321 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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322 end
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323
291
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324
290
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325 end
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326 end