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annotate +scheme/Hypsyst2dCurve.m @ 417:effd75b113ba feature/better_map

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Add tests and fix a bunch of bugs.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 02 Feb 2017 20:49:06 +0100
parents 9d1fc984f40d
children 459eeb99130f
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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 % Jacobaian and inverse Jacobian
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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 Hxii,Hetai % Kroneckerd norms in xi and eta.
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22 I_xi,I_eta, I_N, onesN
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23 e_w, e_e, e_s, e_n
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24 index_w, index_e,index_s,index_n
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25 params % Parameters for the coeficient matrice
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26 end
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29 methods
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30 % Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Eu
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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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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 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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44 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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45 obj.E=@(params,x,y,~,~)E(params,x,y);
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46
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47 m_xi = m(1);
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48 m_eta = m(2);
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49 m_tot=m_xi*m_eta;
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51 ops_xi = sbp.D2Standard(m_xi,xilim,order);
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52 ops_eta = sbp.D2Standard(m_eta,etalim,order);
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53
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54 obj.xi = ops_xi.x;
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55 obj.eta = ops_eta.x;
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57 obj.Xi = kr(obj.xi,ones(m_eta,1));
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58 obj.Eta = kr(ones(m_xi,1),obj.eta);
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59
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60 obj.n = length(A(obj.params,0,0));
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61 obj.onesN=ones(obj.n);
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62
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63 obj.index_w=1:m_eta;
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64 obj.index_e=(m_tot-m_e
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65
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66 metric_termsta+1):m_tot;
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67 obj.index_s=1:m_eta:(m_tot-m_eta+1);
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68 obj.index_n=(m_eta):m_eta:m_tot;
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70 I_n = eye(obj.n);
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71 I_xi = speye(m_xi);
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72 obj.I_xi = I_xi;
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73 I_eta = speye(m_eta);
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74 obj.I_eta = I_eta;
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76 D1_xi = kr(I_n, ops_xi.D1, I_eta);
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77 obj.Hxii = kr(I_n, ops_xi.HI, I_eta);
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78 D1_eta = kr(I_n, I_xi, ops_eta.D1);
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79 obj.Hetai = kr(I_n, I_xi, ops_eta.HI);
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80
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81 obj.e_w = kr(I_n, ops_xi.e_l, I_eta);
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82 obj.e_e = kr(I_n, ops_xi.e_r, I_eta);
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83 obj.e_s = kr(I_n, I_xi, ops_eta.e_l);
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84 obj.e_n = kr(I_n, I_xi,
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85
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86 metric_termsops_eta.e_r);
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87
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88 [X,Y] = ti.map(obj.xi,obj.eta);
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89
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90 [x_xi,x_eta] = gridDerivatives(X,ops_xi.D1,ops_eta.D1);
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91 [y_xi,y_eta] = gridDerivatives(Y,ops_xi.D1, ops_eta.D1);
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93 obj.X = reshape(X,m_tot,1);
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94 obj.Y = reshape(Y,m_tot,1);
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95 obj.X_xi = reshape(x_xi,m_tot,1);
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96 obj.Y_xi = reshape(y_xi,m_tot,1);
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97 obj.X_eta = reshape(x_eta,m_tot,1);
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98 obj.Y_eta = reshape(y_eta,m_tot,1);
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99
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100 Ahat_evaluated = obj.evaluateCoefficientMatrix(obj.Ahat, obj.X, obj.Y,obj.X_eta,obj.Y_eta);
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101 Bhat_evaluated = obj.evaluateCoefficientMatrix(obj.Bhat, obj.X, obj.Y,obj.X_xi,obj.Y_xi);
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102 E_evaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,[],[]);
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103
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104 obj.m = m;
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105 obj.h = [ops_xi.h ops_eta.h];
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106 obj.order = order;
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107 obj.J = obj.X_xi.*obj.Y_eta - obj.X_eta.*obj.Y_xi;
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108 obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot));
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109
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110 obj.D = obj.Ji*(-Ahat_evaluated*D1_xi-Bhat_evaluated*D1_eta)-E_evaluated;
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111
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112 end
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114 % Closure functions return the opertors applied to the own doamin to close the boundary
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115 % 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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116 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w',General boundary conditions'n','s'.
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117 % type is a string specifying the type of boundary condition if there are several.
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118 % data is a function returning the data that should be applied at the boundary.
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119 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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120 default_arg('type','char');
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121 switch type
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122 case{'c','char'}
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123 [closure,penalty] = boundary_condition_char(obj,boundary);
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124 case{'general'}
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125 [closure,penalty] = boundary_condition_general(obj,boundary,L);
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126 otherwise
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127 error('No such boundary condition')
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128 end
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129 end
369
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diff changeset
130
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diff changeset
131 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundaryGeneral boundary conditions)
298
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132 error('An interface function does not exist yet');
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133 end
369
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diff changeset
134
298
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135 function N = size(obj)
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136 N = obj.m;
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137 end
369
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diff changeset
138
298
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139 function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y,x_,y_)
369
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140 params = obj.params;
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141
298
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142 if isa(mat,'function_handle')
369
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143 [rows,cols] = size(mat(params,0,0,0,0));
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144 x_ = kr(obj.onesN,x_);
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145 y_ = kr(obj.onesN,y_);
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diff changeset
146 matVec = mat(params,X',Y',x_',y_');
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147 matVec = sparse(matVec);
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148 side = max(length(X),length(Y));
298
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149 else
369
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150 matVec = mat;
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151 [rows,cols] = size(matVec);
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152 side = max(length(X),length(Y));
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153 cols = cols/side;
298
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154 end
369
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diff changeset
155
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156 ret = cell(rows,cols);
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157 for ii = 1:rows
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158 for jj = 1:cols
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159 ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side));
298
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160 end
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161 end
369
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diff changeset
162 ret = cell2mat(ret);
298
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163 end
369
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diff changeset
164
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diff changeset
165 %Characteristic boundary conditions
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diff changeset
166 function [closure, penalty] = boundary_condition_char(obj,boundary)
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167 params = obj.params;
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diff changeset
168 X = obj.X;
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169 Y = obj.Y;
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diff changeset
170 xi = obj.xi;
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171 eta = obj.eta;
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diff changeset
172
298
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173 switch boundary
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174 case {'w','W','west'}
369
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175 e_ = obj.e_w;
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176 mat = obj.Ahat;
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177 boundPos = 'l';
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178 Hi = obj.Hxii;
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diff changeset
179 [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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diff changeset
180 side = max(length(eta));
298
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181 case {'e','E','east'}
369
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diff changeset
182 e_ = obj.e_e;
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diff changeset
183 mat = obj.Ahat;
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diff changeset
184 boundPos = 'r';
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185 Hi = obj.Hxii;
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diff changeset
186 [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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187 side = max(length(eta));
298
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188 case {'s','S','south'}
369
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diff changeset
189 e_ = obj.e_s;
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diff changeset
190 mat = obj.Bhat;
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diff changeset
191 boundPos = 'l';
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diff changeset
192 Hi = obj.Hetai;
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diff changeset
193 [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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diff changeset
194 side = max(length(xi));
298
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195 case {'n','N','north'}
369
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diff changeset
196 e_ = obj.e_n;
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diff changeset
197 mat = obj.Bhat;
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198 boundPos = 'r';
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199 Hi = obj.Hetai;
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diff changeset
200 [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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diff changeset
201 side = max(length(xi));
298
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202 end
369
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diff changeset
203
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diff changeset
204 pos = signVec(1);
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diff changeset
205 zeroval = signVec(2);
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diff changeset
206 neg = signVec(3);
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diff changeset
207
298
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208 switch boundPos
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209 case {'l'}
369
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diff changeset
210 tau = sparse(obj.n*side,pos);
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diff changeset
211 Vi_plus = Vi(1:pos,:);
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diff changeset
212 tau(1:pos,:) = -abs(D(1:pos,1:pos));
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diff changeset
213 closure = Hi*e_*V*tau*Vi_plus*e_';
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diff changeset
214 penalty = -Hi*e_*V*tau*Vi_plus;
298
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215 case {'r'}
369
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diff changeset
216 tau = sparse(obj.n*side,neg);
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diff changeset
217 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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diff changeset
218 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
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diff changeset
219 closure = Hi*e_*V*tau*Vi_minus*e_';
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diff changeset
220 penalty = -Hi*e_*V*tau*Vi_minus;
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diff changeset
221 end
298
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diff changeset
222 end
369
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diff changeset
223
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diff changeset
224
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diff changeset
225 % General boundary condition in the form Lu=g(x)
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diff changeset
226 function [closure,penalty] = boundary_condition_general(obj,boundary,L)
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diff changeset
227 params = obj.params;
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diff changeset
228 X = obj.X;
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diff changeset
229 Y = obj.Y;
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diff changeset
230 xi = obj.xi;
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diff changeset
231 eta = obj.eta;
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diff changeset
232
298
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diff changeset
233 switch boundary
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diff changeset
234 case {'w','W','west'}
369
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diff changeset
235 e_ = obj.e_w;
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diff changeset
236 mat = obj.Ahat;
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diff changeset
237 boundPos = 'l';
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diff changeset
238 Hi = obj.Hxii;
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diff changeset
239 [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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diff changeset
240
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parents: 352
diff changeset
241 Ji_vec = diag(obj.Ji);
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parents: 352
diff changeset
242 Ji = diag(Ji_vec(obj.index_w));
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parents: 352
diff changeset
243 xi_x = Ji*obj.Y_eta(obj.index_w);
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parents: 352
diff changeset
244 xi_y = -Ji*obj.X_eta(obj.index_w);
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parents: 352
diff changeset
245 L = obj.evaluateCoefficientMatrix(L,xi_x,xi_y,[],[]);
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parents: 352
diff changeset
246 side = max(length(eta));
298
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diff changeset
247 case {'e','E','east'}
369
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diff changeset
248 e_ = obj.e_e;
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diff changeset
249 mat = obj.Ahat;
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diff changeset
250 boundPos = 'r';
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parents: 352
diff changeset
251 Hi = obj.Hxii;
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parents: 352
diff changeset
252 [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));
301
d9860ebc3148 HypsystCurve2D Seems to work (Converges with MMS)
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parents: 300
diff changeset
253
369
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diff changeset
254 Ji_vec = diag(obj.Ji);
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diff changeset
255 Ji = diag(Ji_vec(obj.index_e));
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diff changeset
256 xi_x = Ji*obj.Y_eta(obj.index_e);
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diff changeset
257 xi_y = -Ji*obj.X_eta(obj.index_e);
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diff changeset
258 L = obj.evaluateCoefficientMatrix(L,-xi_x,-xi_y,[],[]);
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diff changeset
259 side = max(length(eta));
298
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260 case {'s','S','south'}
369
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diff changeset
261 e_ = obj.e_s;
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diff changeset
262 mat = obj.Bhat;
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diff changeset
263 boundPos = 'l';
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diff changeset
264 Hi = obj.Hetai;
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diff changeset
265 [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));
301
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diff changeset
266
369
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diff changeset
267 Ji_vec = diag(obj.Ji);
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diff changeset
268 Ji = diag(Ji_vec(obj.index_s));
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diff changeset
269 eta_x = Ji*obj.Y_xi(obj.index_s);
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diff changeset
270 eta_y = -Ji*obj.X_xi(obj.index_s);
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diff changeset
271 L = obj.evaluateCoefficientMatrix(L,eta_x,eta_y,[],[]);
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diff changeset
272 side = max(length(xi));
298
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273 case {'n','N','north'}
369
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diff changeset
274 e_ = obj.e_n;
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diff changeset
275 mat = obj.Bhat;
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276 boundPos = 'r';
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277 Hi = obj.Hetai;
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diff changeset
278 [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));
301
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diff changeset
279
369
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diff changeset
280 Ji_vec = diag(obj.Ji);
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diff changeset
281 Ji = diag(Ji_vec(obj.index_n));
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diff changeset
282 eta_x = Ji*obj.Y_xi(obj.index_n);
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diff changeset
283 eta_y = -Ji*obj.X_xi(obj.index_n);
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diff changeset
284 L = obj.evaluateCoefficientMatrix(L,-eta_x,-eta_y,[],[]);
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diff changeset
285 side = max(length(xi));
298
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286 end
369
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diff changeset
287
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diff changeset
288 pos = signVec(1);
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diff changeset
289 zeroval = signVec(2);
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diff changeset
290 neg = signVec(3);
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diff changeset
291
298
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292 switch boundPos
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diff changeset
293 case {'l'}
369
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diff changeset
294 tau = sparse(obj.n*side,pos);
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diff changeset
295 Vi_plus = Vi(1:pos,:);
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diff changeset
296 Vi_minus = Vi(pos+1:obj.n*side,:);
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diff changeset
297 V_plus = V(:,1:pos);
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diff changeset
298 V_minus = V(:,(pos)+1:obj.n*side);
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diff changeset
299
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diff changeset
300 tau(1:pos,:) = -abs(D(1:pos,1:pos));
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diff changeset
301 R = -inv(L*V_plus)*(L*V_minus);
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diff changeset
302 closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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diff changeset
303 penalty = -Hi*e_*V*tau*inv(L*V_plus)*L;
298
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diff changeset
304 case {'r'}
369
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diff changeset
305 tau = sparse(obj.n*side,neg);
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diff changeset
306 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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diff changeset
307 Vi_plus = Vi(1:pos,:);
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diff changeset
308 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
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diff changeset
309
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diff changeset
310 V_plus = V(:,1:pos);
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diff changeset
311 V_minus = V(:,(pos+zeroval)+1:obj.n*side);
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diff changeset
312 R = -inv(L*V_minus)*(L*V_plus);
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diff changeset
313 closure = Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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diff changeset
314 penalty = -Hi*e_*V*tau*inv(L*V_minus)*L;
298
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315 end
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316 end
369
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diff changeset
317
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diff changeset
318 % Function that diagonalizes a symbolic matrix A as A=V*D*Vi
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diff changeset
319 % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign
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diff changeset
320 % [d+ ]
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diff changeset
321 % D = [ d0 ]
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diff changeset
322 % [ d-]
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diff changeset
323 % signVec is a vector specifying the number of possitive, zero and negative eigenvalues of D
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diff changeset
324 function [V,Vi, D,signVec] = matrixDiag(obj,mat,x,y,x_,y_)
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diff changeset
325 params = obj.params;
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diff changeset
326 syms xs ys
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diff changeset
327 if(sum(abs(x_)) ~= 0)
298
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diff changeset
328 syms xs_
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diff changeset
329 else
369
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diff changeset
330 xs_ = 0;
298
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331 end
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diff changeset
332
369
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diff changeset
333 if(sum(abs(y_))~= 0)
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 352
diff changeset
334 syms ys_;
298
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diff changeset
335 else
369
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diff changeset
336 ys_ = 0;
298
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diff changeset
337 end
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diff changeset
338
369
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diff changeset
339 [V, D] = eig(mat(params,xs,ys,xs_,ys_));
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parents: 352
diff changeset
340 Vi = inv(V);
298
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diff changeset
341 syms xs ys xs_ ys_
300
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diff changeset
342
369
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diff changeset
343 xs = x;
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diff changeset
344 ys = y;
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diff changeset
345 xs_ = x_;
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parents: 352
diff changeset
346 ys_ = y_;
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diff changeset
347
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diff changeset
348 side = max(length(x),length(y));
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diff changeset
349 Dret = zeros(obj.n,side*obj.n);
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parents: 352
diff changeset
350 Vret = zeros(obj.n,side*obj.n);
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diff changeset
351 Viret = zeros(obj.n,side*obj.n);
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parents: 352
diff changeset
352 for ii = 1:obj.n
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parents: 352
diff changeset
353 for jj = 1:obj.n
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parents: 352
diff changeset
354 Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii));
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parents: 352
diff changeset
355 Vret(jj,(ii-1)*side+1:side*ii) = eval(V(jj,ii));
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parents: 352
diff changeset
356 Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii));
298
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diff changeset
357 end
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diff changeset
358 end
369
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parents: 352
diff changeset
359
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parents: 352
diff changeset
360 D = sparse(Dret);
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parents: 352
diff changeset
361 V = sparse(Vret);
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parents: 352
diff changeset
362 Vi = sparse(Viret);
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parents: 352
diff changeset
363 V = obj.evaluateCoefficientMatrix(V,x,y,x_,y_);
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parents: 352
diff changeset
364 D = obj.evaluateCoefficientMatrix(D,x,y,x_,y_);
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parents: 352
diff changeset
365 Vi = obj.evaluateCoefficientMatrix(Vi,x,y,x_,y_);
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parents: 352
diff changeset
366 DD = diag(D);
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diff changeset
367
369
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parents: 352
diff changeset
368 poseig = (DD>0);
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parents: 352
diff changeset
369 zeroeig = (DD==0);
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parents: 352
diff changeset
370 negeig = (DD<0);
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diff changeset
371
369
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diff changeset
372 D = diag([DD(poseig); DD(zeroeig); DD(negeig)]);
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parents: 352
diff changeset
373 V = [V(:,poseig) V(:,zeroeig) V(:,negeig)];
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parents: 352
diff changeset
374 Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
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parents: 352
diff changeset
375 signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
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diff changeset
376 end
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377 end
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parents:
diff changeset
378 end