annotate +scheme/Hypsyst3dCurve.m @ 351:7cc3d5bd3692 feature/hypsyst

Curve linear code in 3D converges for manufactures solution
author Ylva Rydin <ylva.rydin@telia.com>
date Thu, 03 Nov 2016 22:03:09 +0100
parents 5d5652fe826a
children dbac99d2c318
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1 classdef Hypsyst3dCurve < 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, Z% Values of x and y for each grid point
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7 Yx, Zx, Xy, Zy, Xz, Yz %Grid values for boundary surfaces
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8
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9 xi,eta,zeta
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10 Xi, Eta, Zeta
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11
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12 Eta_xi, Zeta_xi, Xi_eta, Zeta_eta, Xi_zeta, Eta_zeta
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14 X_xi, X_eta, X_zeta,Y_xi,Y_eta,Y_zeta,Z_xi,Z_eta,Z_zeta
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15 Aev
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16
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17 metric_terms
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18
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19 order % Order accuracy for the approximation
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20
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21 D % non-stabalized scheme operator
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22 Aevaluated, Bevaluated, Cevaluated, Eevaluated
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23 Ahat, Bhat, Chat, E
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24 A,B,C
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25
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26 J, Ji
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27
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28 H % Discrete norm
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29 % Norms in the x, y and z directions
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30 Hxii,Hetai,Hzetai, Hzi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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31 I_xi,I_eta,I_zeta, I_N,onesN
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32 e_w, e_e, e_s, e_n, e_b, e_t
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33 index_w, index_e,index_s,index_n, index_b, index_t
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34 params %parameters for the coeficient matrice
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35 end
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38 methods
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39 function obj = Hypsyst3dCurve(m, order, A, B,C, E, params,ti)
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40 xilim ={0 1};
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41 etalim = {0 1};
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42 zetalim = {0 1};
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43
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44 if length(m) == 1
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45 m = [m m m];
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46 end
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47 m_xi = m(1);
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48 m_eta = m(2);
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49 m_zeta=m(3);
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50 m_tot=m_xi*m_eta*m_zeta;
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51 obj.params = params;
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52 obj.n = length(A(obj,0,0,0));
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53
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54 obj.m=m;
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55
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56 obj.order=order;
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57 obj.onesN=ones(obj.n);
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58 ops_xi = sbp.D2Standard(m_xi,xilim,order);
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59 ops_eta = sbp.D2Standard(m_eta,etalim,order);
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60 ops_zeta = sbp.D2Standard(m_zeta,zetalim,order);
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61
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62 obj.xi = ops_xi.x;
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63 obj.eta = ops_eta.x;
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64 obj.zeta = ops_zeta.x;
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65
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66 obj.Xi = kr(obj.xi,ones(m_eta,1),ones(m_zeta,1));%% Que pasa?
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67 obj.Eta = kr(ones(m_xi,1),obj.eta,ones(m_zeta,1));
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68 obj.Zeta = kr(ones(m_xi,1),ones(m_eta,1),obj.zeta);
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69
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70 obj.Eta_xi=kr(obj.eta,ones(m_xi,1));
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71 obj.Zeta_xi=kr(ones(m_eta,1),obj.zeta);
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72
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73 obj.Xi_eta=kr(obj.xi,ones(m_zeta,1));
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74 obj.Zeta_eta=kr(ones(m_xi,1),obj.zeta);
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75
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76 obj.Xi_zeta=kr(obj.xi,ones(m_eta,1));
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77 obj.Eta_zeta=kr(ones(m_zeta,1),obj.eta);
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78
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79 [X,Y,Z] = ti.map(obj.Xi,obj.Eta,obj.Zeta);
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80 obj.X=X;
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81 obj.Y=Y;
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82 obj.Z=Z;
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83
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84 I_n = eye(obj.n);
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85 I_xi = speye(m_xi);
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86 obj.I_xi = I_xi;
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87 I_eta = speye(m_eta);
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88 obj.I_eta = I_eta;
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89 I_zeta = speye(m_zeta);
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90 obj.I_zeta = I_zeta;
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91
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92
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93 O_xi=ones(m_xi,1);
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94 O_eta=ones(m_eta,1);
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95 O_zeta=ones(m_zeta,1);
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96
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97 D1_xi = kr(ops_xi.D1, I_eta,I_zeta);
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98 obj.Hxii = kr(I_n, ops_xi.HI, I_eta,I_zeta);
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99 D1_eta = kr(I_xi, ops_eta.D1,I_zeta);
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100 obj.Hetai = kr(I_n, I_xi, ops_eta.HI,I_zeta);
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101 D1_zeta = kr(I_xi, I_eta,ops_zeta.D1);
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102 obj.Hzetai = kr(I_n, I_xi,I_eta, ops_zeta.HI);
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103 obj.h=[ops_xi.h ops_eta.h ops_zeta.h];
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104
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105 obj.e_w = kr(I_n, ops_xi.e_l, I_eta,I_zeta);
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106 obj.e_e = kr(I_n, ops_xi.e_r, I_eta,I_zeta);
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107 obj.e_s = kr(I_n, I_xi, ops_eta.e_l,I_zeta);
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108 obj.e_n = kr(I_n, I_xi, ops_eta.e_r,I_zeta);
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109 obj.e_b = kr(I_n, I_xi, I_eta, ops_zeta.e_l);
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110 obj.e_t = kr(I_n, I_xi, I_eta, ops_zeta.e_r);
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111
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112 obj.A=A;
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113 obj.B=B;
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114 obj.C=C;
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115
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116 obj.X_xi=D1_xi*X;
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117 obj.X_eta=D1_eta*X;
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118 obj.X_zeta=D1_zeta*X;
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119 obj.Y_xi=D1_xi*Y;
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120 obj.Y_eta=D1_eta*Y;
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121 obj.Y_zeta=D1_zeta*Y;
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122 obj.Z_xi=D1_xi*Z;
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123 obj.Z_eta=D1_eta*Z;
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124 obj.Z_zeta=D1_zeta*Z;
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125
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126 D1_xi=kr(I_n,D1_xi);
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127 D1_eta=kr(I_n,D1_eta);
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128 D1_zeta=kr(I_n,D1_zeta);
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129
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130 obj.index_w=(kr(ops_xi.e_l, O_eta,O_zeta)==1);
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131 obj.index_e=(kr(ops_xi.e_r, O_eta,O_zeta)==1);
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132 obj.index_s=(kr(O_xi, ops_eta.e_l,O_zeta)==1);
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133 obj.index_n=(kr(O_xi, ops_eta.e_r,O_zeta)==1);
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134 obj.index_b=(kr(O_xi, O_eta, ops_zeta.e_l)==1);
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135 obj.index_t=(kr(O_xi, O_eta, ops_zeta.e_r)==1);
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136
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137
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138 obj.Ahat=@transform_coefficient_matrix;
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139 obj.Bhat=@transform_coefficient_matrix;
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140 obj.Chat=@transform_coefficient_matrix;
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141 obj.E=@(obj,x,y,z,~,~,~,~,~,~)E(obj,x,y,z);
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142
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143 obj.Aevaluated = obj.evaluateCoefficientMatrix(obj.Ahat,obj.X, obj.Y,obj.Z, obj.X_eta,obj.X_zeta,obj.Y_eta,obj.Y_zeta,obj.Z_eta,obj.Z_zeta);
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144 obj.Bevaluated = obj.evaluateCoefficientMatrix(obj.Bhat,obj.X, obj.Y,obj.Z, obj.X_zeta,obj.X_xi,obj.Y_zeta,obj.Y_xi,obj.Z_zeta,obj.Z_xi);
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145 obj.Cevaluated = obj.evaluateCoefficientMatrix(obj.Chat,obj.X,obj.Y,obj.Z, obj.X_xi,obj.X_eta,obj.Y_xi,obj.Y_eta,obj.Z_xi,obj.Z_eta);
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146 obj.Eevaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,obj.Z,[],[],[],[],[],[]);
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147
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148 obj.J=obj.X_xi.*obj.Y_eta.*obj.Z_zeta...
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149 +obj.X_zeta.*obj.Y_xi.*obj.Z_eta...
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150 +obj.X_eta.*obj.Y_zeta.*obj.Z_xi...
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151 -obj.X_xi.*obj.Y_zeta.*obj.Z_eta...
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152 -obj.X_eta.*obj.Y_xi.*obj.Z_zeta...
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153 -obj.X_zeta.*obj.Y_eta.*obj.Z_xi;
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154
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155 obj.Ji =kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot));
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156
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157 obj.D=obj.Ji*(-obj.Aevaluated*D1_xi-obj.Bevaluated*D1_eta -obj.Cevaluated*D1_zeta)-obj.Eevaluated;
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158 end
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159
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160 function [ret]=transform_coefficient_matrix(obj,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)
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161 ret=obj.A(obj,x,y,z).*(y_1.*z_2-z_1.*y_2);
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162 ret=ret+obj.B(obj,x,y,z).*(x_2.*z_1-x_1.*z_2);
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163 ret=ret+obj.C(obj,x,y,z).*(x_1.*y_2-x_2.*y_1);
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164 end
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165
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166
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167 % Closure functions return the opertors applied to the own doamin to close the boundary
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168 % 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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169 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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170 % type is a string specifying the type of boundary condition if there are several.
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171 % data is a function returning the data that should be applied at the boundary.
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172 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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173 default_arg('type','char');
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174 BM=boundary_matrices(obj,boundary);
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175
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176 switch type
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177 case{'c','char'}
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178 [closure,penalty]=boundary_condition_char(obj,BM);
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179 case{'general'}
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180 [closure,penalty]=boundary_condition_general(obj,BM,boundary,L);
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181 otherwise
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182 error('No such boundary condition')
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183 end
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184 end
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185
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186 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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187 error('An interface function does not exist yet');
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188 end
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189
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190 function N = size(obj)
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191 N = obj.m;
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192 end
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193
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194 function [ret] = evaluateCoefficientMatrix(obj,mat, X, Y, Z , x_1 , x_2 , y_1 , y_2 , z_1 , z_2)
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195 params=obj.params;
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196 side=max(length(X),length(Y));
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197 if isa(mat,'function_handle')
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198 [rows,cols]=size(mat(obj,0,0,0,0,0,0,0,0,0));
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199 x_1=kr(obj.onesN,x_1);
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200 x_2=kr(obj.onesN,x_2);
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201 y_1=kr(obj.onesN,y_1);
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202 y_2=kr(obj.onesN,y_2);
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203 z_1=kr(obj.onesN,z_1);
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204 z_2=kr(obj.onesN,z_2);
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205 matVec=mat(obj,X',Y',Z',x_1',x_2',y_1',y_2',z_1',z_2');
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206 matVec=sparse(matVec);
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207 else
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208 matVec=mat;
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209 [rows,cols]=size(matVec);
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210 side=max(length(X),length(Y));
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211 cols=cols/side;
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212 end
351
7cc3d5bd3692 Curve linear code in 3D converges for manufactures solution
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213 ret=cell(rows,cols);
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214
350
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215
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216 for ii=1:rows
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217 for jj=1:cols
351
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218 ret{ii,jj}=diag(matVec(ii,(jj-1)*side+1:jj*side));
350
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219 end
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220 end
351
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221
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222 ret=cell2mat(ret);
350
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223 end
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224
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225
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226 function [BM]=boundary_matrices(obj,boundary)
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227 params=obj.params;
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228 BM.boundary=boundary;
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229 switch boundary
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230 case {'w','W','west'}
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231 BM.e_=obj.e_w;
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232 mat=obj.Ahat;
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233 BM.boundpos='l';
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234 BM.Hi=obj.Hxii;
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235 BM.index=obj.index_w;
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236 BM.x_1=obj.X_eta(BM.index);
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237 BM.x_2=obj.X_zeta(BM.index);
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238 BM.y_1=obj.Y_eta(BM.index);
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239 BM.y_2=obj.Y_zeta(BM.index);
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240 BM.z_1=obj.Z_eta(BM.index);
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241 BM.z_2=obj.Z_zeta(BM.index);
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242 case {'e','E','east'}
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243 BM.e_=obj.e_e;
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244 mat=obj.Ahat;
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245 BM.boundpos='r';
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246 BM.Hi=obj.Hxii;
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247 BM.index=obj.index_e;
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248 BM.x_1=obj.X_eta(BM.index);
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249 BM.x_2=obj.X_zeta(BM.index);
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250 BM.y_1=obj.Y_eta(BM.index);
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251 BM.y_2=obj.Y_zeta(BM.index);
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252 BM.z_1=obj.Z_eta(BM.index);
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253 BM.z_2=obj.Z_zeta(BM.index);
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254 case {'s','S','south'}
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255 BM.e_=obj.e_s;
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256 mat=obj.Bhat;
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257 BM.boundpos='l';
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258 BM.Hi=obj.Hetai;
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259 BM.index=obj.index_s;
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260 BM.x_1=obj.X_zeta(BM.index);
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261 BM.x_2=obj.X_xi(BM.index);
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262 BM.y_1=obj.Y_zeta(BM.index);
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263 BM.y_2=obj.Y_xi(BM.index);
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264 BM.z_1=obj.Z_zeta(BM.index);
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265 BM.z_2=obj.Z_xi(BM.index);
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266 case {'n','N','north'}
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267 BM.e_=obj.e_n;
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268 mat=obj.Bhat;
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269 BM.boundpos='r';
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270 BM.Hi=obj.Hetai;
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271 BM.index=obj.index_n;
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272 BM.x_1=obj.X_zeta(BM.index);
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273 BM.x_2=obj.X_xi(BM.index);
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274 BM.y_1=obj.Y_zeta(BM.index);
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275 BM.y_2=obj.Y_xi(BM.index);
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276 BM.z_1=obj.Z_zeta(BM.index);
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277 BM.z_2=obj.Z_xi(BM.index);
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278 case{'b','B','Bottom'}
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279 BM.e_=obj.e_b;
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280 mat=obj.Chat;
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281 BM.boundpos='l';
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282 BM.Hi=obj.Hzetai;
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283 BM.index=obj.index_b;
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284 BM.x_1=obj.X_xi(BM.index);
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285 BM.x_2=obj.X_eta(BM.index);
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286 BM.y_1=obj.Y_xi(BM.index);
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287 BM.y_2=obj.Y_eta(BM.index);
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288 BM.z_1=obj.Z_xi(BM.index);
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289 BM.z_2=obj.Z_eta(BM.index);
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290 case{'t','T','Top'}
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291 BM.e_=obj.e_t;
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292 mat=obj.Chat;
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293 BM.boundpos='r';
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294 BM.Hi=obj.Hzetai;
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295 BM.index=obj.index_t;
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296 BM.x_1=obj.X_xi(BM.index);
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297 BM.x_2=obj.X_eta(BM.index);
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298 BM.y_1=obj.Y_xi(BM.index);
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299 BM.y_2=obj.Y_eta(BM.index);
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300 BM.z_1=obj.Z_xi(BM.index);
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301 BM.z_2=obj.Z_eta(BM.index);
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302 end
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303 [BM.V,BM.Vi,BM.D,signVec]=obj.matrixDiag(mat,obj.X(BM.index),obj.Y(BM.index),obj.Z(BM.index),...
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304 BM.x_1,BM.x_2,BM.y_1,BM.y_2,BM.z_1,BM.z_2);
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305 BM.side=sum(BM.index);
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306 BM.pos=signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3);
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307 end
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308
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diff changeset
309
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310 function [closure, penalty]=boundary_condition_char(obj,BM)
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311 side = BM.side;
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312 pos = BM.pos;
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313 neg = BM.neg;
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314 zeroval=BM.zeroval;
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315 V = BM.V;
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316 Vi = BM.Vi;
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317 Hi=BM.Hi;
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318 D=BM.D;
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319 e_=BM.e_;
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diff changeset
320
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321 switch BM.boundpos
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322 case {'l'}
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323 tau=sparse(obj.n*side,pos);
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324 Vi_plus=Vi(1:pos,:);
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325 tau(1:pos,:)=-abs(D(1:pos,1:pos));
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diff changeset
326 closure=Hi*e_*V*tau*Vi_plus*e_';
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327 penalty=-Hi*e_*V*tau*Vi_plus;
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
328 case {'r'}
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329 tau=sparse(obj.n*side,neg);
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Ylva Rydin <ylva.rydin@telia.com>
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330 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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331 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:);
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diff changeset
332 closure=Hi*e_*V*tau*Vi_minus*e_';
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333 penalty=-Hi*e_*V*tau*Vi_minus;
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334 end
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Ylva Rydin <ylva.rydin@telia.com>
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335 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
336
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parents:
diff changeset
337
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diff changeset
338 function [closure,penalty]=boundary_condition_general(obj,BM,boundary,L)
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diff changeset
339 side = BM.side;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
340 pos = BM.pos;
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Ylva Rydin <ylva.rydin@telia.com>
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341 neg = BM.neg;
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Ylva Rydin <ylva.rydin@telia.com>
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342 zeroval=BM.zeroval;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
343 V = BM.V;
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
344 Vi = BM.Vi;
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Ylva Rydin <ylva.rydin@telia.com>
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345 Hi=BM.Hi;
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Ylva Rydin <ylva.rydin@telia.com>
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346 D=BM.D;
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diff changeset
347 e_=BM.e_;
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Ylva Rydin <ylva.rydin@telia.com>
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348 index=BM.index;
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349
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diff changeset
350 switch BM.boundary
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351 case{'b','B','bottom'}
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
352 Ji_vec=diag(obj.Ji);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
353 Ji=diag(Ji_vec(index));
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Ylva Rydin <ylva.rydin@telia.com>
parents:
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354 Zeta_x=Ji*(obj.Y_xi(index).*obj.Z_eta(index)-obj.Z_xi(index).*obj.Y_eta(index));
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355 Zeta_y=Ji*(obj.X_eta(index).*obj.Z_xi(index)-obj.X_xi(index).*obj.Z_eta(index));
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356 Zeta_z=Ji*(obj.X_xi(index).*obj.Y_eta(index)-obj.Y_xi(index).*obj.X_eta(index));
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diff changeset
357
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358 L=obj.evaluateCoefficientMatrix(L,Zeta_x,Zeta_y,Zeta_z,[],[],[],[],[],[]);
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359 end
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parents:
diff changeset
360
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
361 switch BM.boundpos
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362 case {'l'}
5d5652fe826a A commit before I try resolving the performance issues
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363 tau=sparse(obj.n*side,pos);
5d5652fe826a A commit before I try resolving the performance issues
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diff changeset
364 Vi_plus=Vi(1:pos,:);
5d5652fe826a A commit before I try resolving the performance issues
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
365 Vi_minus=Vi(pos+zeroval+1:obj.n*side,:);
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diff changeset
366 V_plus=V(:,1:pos);
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367 V_minus=V(:,(pos+zeroval)+1:obj.n*side);
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parents:
diff changeset
368
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369 tau(1:pos,:)=-abs(D(1:pos,1:pos));
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370 R=-inv(L*V_plus)*(L*V_minus);
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371 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
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parents:
diff changeset
372 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
373 case {'r'}
5d5652fe826a A commit before I try resolving the performance issues
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374 tau=sparse(obj.n*side,neg);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
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375 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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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
376 Vi_plus=Vi(1:pos,:);
5d5652fe826a A commit before I try resolving the performance issues
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
377 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:);
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parents:
diff changeset
378
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379 V_plus=V(:,1:pos);
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parents:
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380 V_minus=V(:,(pos+zeroval)+1:obj.n*side);
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381 R=-inv(L*V_minus)*(L*V_plus);
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parents:
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382 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
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parents:
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383 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L;
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384 end
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385 end
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386
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387
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388 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)
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389 params=obj.params;
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390 eps=10^(-10);
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391 if(sum(abs(x_1))>eps)
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392 syms x_1s
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393 else
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394 x_1s=0;
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395 end
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396
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397 if(sum(abs(x_2))>eps)
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398 syms x_2s;
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399 else
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400 x_2s=0;
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401 end
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402
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403
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404 if(sum(abs(y_1))>eps)
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405 syms y_1s
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406 else
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407 y_1s=0;
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408 end
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409
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410 if(sum(abs(y_2))>eps)
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411 syms y_2s;
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412 else
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413 y_2s=0;
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414 end
351
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415
350
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416 if(sum(abs(z_1))>eps)
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417 syms z_1s
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418 else
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419 z_1s=0;
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420 end
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421
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422 if(sum(abs(z_2))>eps)
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423 syms z_2s;
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424 else
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425 z_2s=0;
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426 end
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427
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428 syms xs ys zs
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429 [V, D]=eig(mat(obj,xs,ys,zs,x_1s,x_2s,y_1s,y_2s,z_1s,z_2s));
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430 Vi=inv(V);
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431 % syms x_1s x_2s y_1s y_2s z_1s z_2s
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432 xs=x;
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433 ys=y;
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434 zs=z;
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435 x_1s=x_1;
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436 x_2s=x_2;
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437 y_1s=y_1;
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438 y_2s=y_2;
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439 z_1s=z_1;
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440 z_2s=z_2;
350
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441
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442 side=max(length(x),length(y));
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443 Dret=zeros(obj.n,side*obj.n);
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444 Vret=zeros(obj.n,side*obj.n);
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445 Viret=zeros(obj.n,side*obj.n);
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446
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447 for ii=1:obj.n
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448 for jj=1:obj.n
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449 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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450 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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451 Viret(jj,(ii-1)*side+1:side*ii)=eval(Vi(jj,ii));
350
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452 end
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453 end
351
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diff changeset
454
350
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455 D=sparse(Dret);
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456 V=sparse(Vret);
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457 Vi=sparse(Viret);
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458 V=obj.evaluateCoefficientMatrix(V,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
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459 D=obj.evaluateCoefficientMatrix(D,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
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460 Vi=obj.evaluateCoefficientMatrix(Vi,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
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461 DD=diag(D);
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diff changeset
462
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463 poseig=(DD>0);
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parents:
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464 zeroeig=(DD==0);
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465 negeig=(DD<0);
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parents:
diff changeset
466
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467 D=diag([DD(poseig); DD(zeroeig); DD(negeig)]);
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468 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)];
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469 Vi=[Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
350
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470 signVec=[sum(poseig),sum(zeroeig),sum(negeig)];
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471 end
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parents:
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472 end
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473 end