Mercurial > repos > public > sbplib
annotate +scheme/Hypsyst2dCurve.m @ 300:32f3ee81bc37 feature/hypsyst
A commit before i destroy everything
author | Ylva Rydin <ylva.rydin@telia.com> |
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date | Tue, 04 Oct 2016 16:25:38 +0200 |
parents | 4d8d6eb0c116 |
children | d9860ebc3148 |
rev | line source |
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1 classdef Hypsyst2dCurve < 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 % Values of x and y for each grid point |
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7 |
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8 J, Ji |
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9 xi,eta |
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10 Xi,Eta |
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11 |
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12 A,B |
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13 X_eta, Y_eta |
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14 X_xi,Y_xi |
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15 order % Order accuracy for the approximation |
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16 |
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17 D % non-stabalized scheme operator |
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18 Ahat, Bhat, E |
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19 |
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20 H % Discrete norm |
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21 % Norms in the x and y directions |
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22 Hxii,Hetai % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. |
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23 I_xi,I_eta, I_N, onesN |
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24 e_w, e_e, e_s, e_n |
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25 index_w, index_e,index_s,index_n |
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26 params %parameters for the coeficient matrice |
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27 end |
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28 |
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29 |
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30 methods |
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31 function obj = Hypsyst2dCurve(m, order, A, B, E, params, ti) |
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32 default_arg('E', []) |
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33 xilim = {0 1}; |
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34 etalim = {0 1}; |
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35 |
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36 if length(m) == 1 |
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37 m = [m m]; |
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38 end |
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39 obj.params = params; |
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40 obj.A=A; |
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41 obj.B=B; |
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42 |
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43 |
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44 obj.Ahat=@(params,x,y,x_eta,y_eta)(A(params,x,y).*y_eta-B(params,x,y).*x_eta); |
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45 obj.Bhat=@(params,x,y,x_xi,y_xi)(B(params,x,y).*x_xi-A(params,x,y).*y_xi); |
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46 obj.E=@(params,x,y,~,~)E(params,x,y); |
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47 |
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48 m_xi = m(1); |
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49 m_eta = m(2); |
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50 m_tot=m_xi*m_eta; |
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51 |
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52 ops_xi = sbp.D2Standard(m_xi,xilim,order); |
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53 ops_eta = sbp.D2Standard(m_eta,etalim,order); |
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54 |
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55 obj.xi = ops_xi.x; |
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56 obj.eta = ops_eta.x; |
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57 |
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58 obj.Xi = kr(obj.xi,ones(m_eta,1)); |
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59 obj.Eta = kr(ones(m_xi,1),obj.eta); |
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60 |
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61 obj.n = length(A(obj.params,0,0)); |
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62 obj.onesN=ones(obj.n); |
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63 |
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64 obj.index_w=1:m_xi; |
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65 obj.index_e=(m_tot-m_xi+1):m_tot; |
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66 obj.index_s=1:m_xi:(m_tot-m_xi+1); |
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67 obj.index_n=(m_xi):m_xi:m_tot; |
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68 |
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69 I_n = eye(obj.n); |
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70 I_xi = speye(m_xi); |
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71 obj.I_xi = I_xi; |
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72 I_eta = speye(m_eta); |
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73 obj.I_eta = I_eta; |
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74 |
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75 D1_xi = kr(I_n, ops_xi.D1, I_eta); |
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76 obj.Hxii = kr(I_n, ops_xi.HI, I_eta); |
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77 D1_eta = kr(I_n, I_xi, ops_eta.D1); |
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78 obj.Hetai = kr(I_n, I_xi, ops_eta.HI); |
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79 |
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80 obj.e_w = kr(I_n, ops_xi.e_l, I_eta); |
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81 obj.e_e = kr(I_n, ops_xi.e_r, I_eta); |
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82 obj.e_s = kr(I_n, I_xi, ops_eta.e_l); |
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83 obj.e_n = kr(I_n, I_xi, ops_eta.e_r); |
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84 |
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85 [X,Y] = ti.map(obj.xi,obj.eta); |
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86 |
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87 [x_xi,x_eta] = gridDerivatives(X,ops_xi.D1,ops_eta.D1); |
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88 [y_xi,y_eta] = gridDerivatives(Y,ops_xi.D1, ops_eta.D1); |
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89 |
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90 obj.X=reshape(X,m_tot,1); |
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91 obj.Y=reshape(Y,m_tot,1); |
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92 obj.X_xi=reshape(x_xi,m_tot,1); |
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93 obj.Y_xi=reshape(y_xi,m_tot,1); |
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94 obj.X_eta=reshape(x_eta,m_tot,1); |
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95 obj.Y_eta=reshape(y_eta,m_tot,1); |
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96 |
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97 Ahat_evaluated = obj.evaluateCoefficientMatrix(obj.Ahat, obj.X, obj.Y,obj.X_eta,obj.Y_eta); |
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98 Bhat_evaluated = obj.evaluateCoefficientMatrix(obj.Bhat, obj.X, obj.Y,obj.X_xi,obj.Y_xi); |
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99 E_evaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,[],[]); |
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100 |
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101 obj.m=m; |
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102 obj.h=[ops_xi.h ops_eta.h]; |
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103 obj.order=order; |
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104 obj.J=obj.X_xi.*obj.Y_eta - obj.X_eta.*obj.Y_xi; |
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105 obj.Ji =kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot)); |
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106 |
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107 obj.D=obj.Ji*(-Ahat_evaluated*D1_xi-Bhat_evaluated*D1_eta)-E_evaluated; |
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108 |
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109 end |
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110 |
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111 % Closure functions return the opertors applied to the own doamin to close the boundary |
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112 % 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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113 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. |
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114 % type is a string specifying the type of boundary condition if there are several. |
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115 % data is a function returning the data that should be applied at the boundary. |
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116 function [closure, penalty] = boundary_condition(obj,boundary,type,L) |
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117 default_arg('type','char'); |
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118 switch type |
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119 case{'c','char'} |
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120 [closure,penalty]=boundary_condition_char(obj,boundary); |
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121 case{'general'} |
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122 [closure,penalty]=boundary_condition_general(obj,boundary,L); |
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123 otherwise |
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124 error('No such boundary condition') |
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125 end |
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126 end |
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127 |
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128 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) |
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129 error('An interface function does not exist yet'); |
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130 end |
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131 |
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132 function N = size(obj) |
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133 N = obj.m; |
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134 end |
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135 |
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136 function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y,x_,y_) |
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137 params=obj.params; |
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138 |
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139 if isa(mat,'function_handle') |
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140 [rows,cols]=size(mat(params,0,0,0,0)); |
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141 x_=kr(x_,obj.onesN); |
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142 y_=kr(y_,obj.onesN); |
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143 matVec=mat(params,X',Y',x_',y_'); |
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144 matVec=sparse(matVec); |
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145 side=max(length(X),length(Y)); |
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146 else |
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147 matVec=mat; |
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148 [rows,cols]=size(matVec); |
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149 side=max(length(X),length(Y)); |
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150 cols=cols/side; |
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151 end |
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152 ret=kron(ones(rows,cols),speye(side)); |
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153 |
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154 for ii=1:rows |
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155 for jj=1:cols |
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156 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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157 end |
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158 end |
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159 end |
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160 |
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161 |
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162 function [closure, penalty]=boundary_condition_char(obj,boundary) |
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163 params=obj.params; |
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164 X=obj.X; Y=obj.Y; |
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165 xi=obj.xi; eta=obj.eta; |
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166 side=max(length(xi),length(eta)); |
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167 |
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168 switch boundary |
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169 case {'w','W','west'} |
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170 e_=obj.e_w; |
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171 mat=obj.Ahat; |
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172 boundPos='l'; |
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173 Hi=obj.Hxii; |
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174 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_w),Y(obj.index_w),obj.X_eta(obj.index_w),obj.Y_eta(obj.index_w)); |
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175 case {'e','E','east'} |
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176 e_=obj.e_e; |
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177 mat=obj.Ahat; |
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178 boundPos='r'; |
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179 Hi=obj.Hxii; |
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180 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_e),Y(obj.index_e),obj.X_eta(obj.index_e),obj.Y_eta(obj.index_e)); |
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181 case {'s','S','south'} |
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182 e_=obj.e_s; |
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183 mat=obj.Bhat; |
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184 boundPos='l'; |
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185 Hi=obj.Hetai; |
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186 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_s),Y(obj.index_s),obj.X_xi(obj.index_s),obj.Y_xi(obj.index_s)); |
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187 case {'n','N','north'} |
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188 e_=obj.e_n; |
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189 mat=obj.Bhat; |
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190 boundPos='r'; |
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191 Hi=obj.Hetai; |
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192 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_n),Y(obj.index_n),obj.X_xi(obj.index_n),obj.Y_xi(obj.index_n)); |
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193 end |
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194 |
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195 pos=signVec(1); zeroval=signVec(2); neg=signVec(3); |
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196 |
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197 switch boundPos |
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198 case {'l'} |
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199 tau=sparse(obj.n*side,pos); |
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200 Vi_plus=Vi(1:pos,:); |
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201 tau(1:pos,:)=-abs(D(1:pos,1:pos)); |
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202 closure=Hi*e_*V*tau*Vi_plus*e_'; |
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203 penalty=-Hi*e_*V*tau*Vi_plus; |
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204 case {'r'} |
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205 tau=sparse(obj.n*side,neg); |
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206 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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207 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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208 closure=Hi*e_*V*tau*Vi_minus*e_'; |
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209 penalty=-Hi*e_*V*tau*Vi_minus; |
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210 end |
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211 end |
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212 |
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213 |
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214 function [closure,penalty]=boundary_condition_general(obj,boundary,L) |
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215 params=obj.params; |
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216 X=obj.X; Y=obj.Y; |
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217 side=max(length(xi),length(eta)); |
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218 |
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219 switch boundary |
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220 case {'w','W','west'} |
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221 e_=obj.e_w; |
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222 mat=obj.Ahat; |
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223 boundPos='l'; |
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224 Hi=obj.Hxii; |
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225 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_w),Y(obj.index_w),obj.X_eta(obj.index_w),obj.Y_eta(obj.index_w)); |
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226 L=obj.evaluateCoefficientMatrix(L,X(obj.index_w),Y(obj.index_w)); |
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227 case {'e','E','east'} |
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228 e_=obj.e_e; |
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229 mat=obj.Ahat; |
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230 boundPos='r'; |
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231 Hi=obj.Hxii; |
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232 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_e),Y(obj.index_e),obj.X_eta(obj.index_e),obj.Y_eta(obj.index_e)); |
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233 L=obj.evaluateCoefficientMatrix(L,X(obj.index_e),Y(obj.index_e),[],[]); |
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234 case {'s','S','south'} |
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235 e_=obj.e_s; |
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236 mat=obj.Bhat; |
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237 boundPos='l'; |
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238 Hi=obj.Hetai; |
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239 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_s),Y(obj.index_s),obj.X_xi(obj.index_s),obj.Y_xi(obj.index_s)); |
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240 L=obj.evaluateCoefficientMatrix(L,X(obj.index_s),Y(obj.index_s),[],[]); |
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241 case {'n','N','north'} |
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242 e_=obj.e_n; |
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243 mat=obj.Bhat; |
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244 boundPos='r'; |
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245 Hi=obj.Hetai; |
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246 [V,Vi,D,signVec]=obj.matrixDiag(mat,X(obj.index_n),Y(obj.index_n),obj.X_xi(obj.index_n),obj.Y_xi(obj.index_n)); |
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247 L=obj.evaluateCoefficientMatrix(L,X(obj.index_n),Y(obj.index_n)); |
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248 end |
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249 |
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250 pos=signVec(1); zeroval=signVec(2); neg=signVec(3); |
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251 |
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252 switch boundPos |
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253 case {'l'} |
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254 tau=sparse(obj.n*side,pos); |
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255 Vi_plus=Vi(1:pos,:); |
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256 Vi_minus=Vi(pos+1:obj.n*side,:); |
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257 V_plus=V(:,1:pos); |
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258 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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259 |
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260 tau(1:pos*side,:)=-abs(D(1:pos,1:pos)); |
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261 R=-inv(L*V_plus)*(L*V_minus); |
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262 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; |
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263 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L; |
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264 case {'r'} |
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265 tau=sparse(obj.n*side,neg); |
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266 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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267 Vi_plus=Vi(1:pos,:); |
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268 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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269 |
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270 V_plus=V(:,1:pos); |
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271 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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272 R=-inv(L*V_minus)*(L*V_plus); |
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273 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_'; |
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274 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L; |
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275 end |
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276 end |
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277 |
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278 |
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279 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y,x_,y_) |
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280 params=obj.params; |
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281 syms xs ys |
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282 if(sum(abs(x_))~=0) |
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283 syms xs_ |
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284 else |
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285 xs_=0; |
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286 end |
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287 |
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288 if(sum(abs(y_))~=0) |
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289 syms ys_; |
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290 else |
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291 ys_=0; |
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292 end |
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293 |
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294 [V, D]=eig(mat(params,xs,ys,xs_,ys_)); |
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295 syms xs ys xs_ ys_ |
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296 |
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297 xs=x; |
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298 ys=y; |
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299 xs_=x_; |
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300 ys_=y_; |
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301 |
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302 side=max(length(x),length(y)); |
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303 Dret=zeros(obj.n,side*obj.n); |
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304 Vret=zeros(obj.n,side*obj.n); |
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305 for ii=1:obj.n |
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306 for jj=1:obj.n |
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307 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii)); |
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308 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii)); |
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309 end |
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310 end |
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311 |
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312 D=sparse(Dret); |
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313 V=sparse(Vret); |
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314 V=obj.evaluateCoefficientMatrix(V,x,y,x_,y_); |
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315 D=obj.evaluateCoefficientMatrix(D,x,y,x_,y_); |
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316 DD=diag(D); |
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317 |
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318 poseig=(DD>0); |
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319 zeroeig=(DD==0); |
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320 negeig=(DD<0); |
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321 |
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322 D=diag([DD(poseig); DD(zeroeig); DD(negeig)]); |
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323 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)]; |
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324 Vi=inv(V); |
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325 signVec=[sum(poseig),sum(zeroeig),sum(negeig)]; |
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326 end |
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327 |
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328 end |
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329 end |