Mercurial > repos > public > sbplib
annotate +scheme/Hypsyst3dCurve.m @ 350:5d5652fe826a feature/hypsyst
A commit before I try resolving the performance issues
author | Ylva Rydin <ylva.rydin@telia.com> |
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date | Wed, 02 Nov 2016 00:02:01 +0100 |
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children | 7cc3d5bd3692 |
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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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13 |
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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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36 |
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37 |
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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 |
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213 ret=kron(ones(rows,cols),speye(side)); |
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214 |
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215 for ii=1:rows |
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216 for jj=1:cols |
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217 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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218 end |
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219 end |
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220 end |
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221 |
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222 |
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223 function [BM]=boundary_matrices(obj,boundary) |
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224 params=obj.params; |
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225 BM.boundary=boundary; |
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226 switch boundary |
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227 case {'w','W','west'} |
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228 BM.e_=obj.e_w; |
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229 mat=obj.Ahat; |
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230 BM.boundpos='l'; |
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231 BM.Hi=obj.Hxii; |
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232 BM.index=obj.index_w; |
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233 BM.x_1=obj.X_eta(BM.index); |
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234 BM.x_2=obj.X_zeta(BM.index); |
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235 BM.y_1=obj.Y_eta(BM.index); |
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236 BM.y_2=obj.Y_zeta(BM.index); |
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237 BM.z_1=obj.Z_eta(BM.index); |
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238 BM.z_2=obj.Z_zeta(BM.index); |
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239 case {'e','E','east'} |
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240 BM.e_=obj.e_e; |
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241 mat=obj.Ahat; |
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242 BM.boundpos='r'; |
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243 BM.Hi=obj.Hxii; |
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244 BM.index=obj.index_e; |
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245 BM.x_1=obj.X_eta(BM.index); |
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246 BM.x_2=obj.X_zeta(BM.index); |
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247 BM.y_1=obj.Y_eta(BM.index); |
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248 BM.y_2=obj.Y_zeta(BM.index); |
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249 BM.z_1=obj.Z_eta(BM.index); |
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250 BM.z_2=obj.Z_zeta(BM.index); |
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251 case {'s','S','south'} |
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252 BM.e_=obj.e_s; |
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253 mat=obj.Bhat; |
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254 BM.boundpos='l'; |
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255 BM.Hi=obj.Hetai; |
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256 BM.index=obj.index_s; |
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257 BM.x_1=obj.X_zeta(BM.index); |
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258 BM.x_2=obj.X_xi(BM.index); |
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259 BM.y_1=obj.Y_zeta(BM.index); |
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260 BM.y_2=obj.Y_xi(BM.index); |
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261 BM.z_1=obj.Z_zeta(BM.index); |
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262 BM.z_2=obj.Z_xi(BM.index); |
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263 case {'n','N','north'} |
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264 BM.e_=obj.e_n; |
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265 mat=obj.Bhat; |
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266 BM.boundpos='r'; |
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267 BM.Hi=obj.Hetai; |
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268 BM.index=obj.index_n; |
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269 BM.x_1=obj.X_zeta(BM.index); |
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270 BM.x_2=obj.X_xi(BM.index); |
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271 BM.y_1=obj.Y_zeta(BM.index); |
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272 BM.y_2=obj.Y_xi(BM.index); |
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273 BM.z_1=obj.Z_zeta(BM.index); |
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274 BM.z_2=obj.Z_xi(BM.index); |
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275 case{'b','B','Bottom'} |
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276 BM.e_=obj.e_b; |
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277 mat=obj.Chat; |
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278 BM.boundpos='l'; |
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279 BM.Hi=obj.Hzetai; |
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280 BM.index=obj.index_b; |
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281 BM.x_1=obj.X_xi(BM.index); |
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282 BM.x_2=obj.X_eta(BM.index); |
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283 BM.y_1=obj.Y_xi(BM.index); |
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284 BM.y_2=obj.Y_eta(BM.index); |
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285 BM.z_1=obj.Z_xi(BM.index); |
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286 BM.z_2=obj.Z_eta(BM.index); |
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287 case{'t','T','Top'} |
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288 BM.e_=obj.e_t; |
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289 mat=obj.Chat; |
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290 BM.boundpos='r'; |
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291 BM.Hi=obj.Hzetai; |
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292 BM.index=obj.index_t; |
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293 BM.x_1=obj.X_xi(BM.index); |
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294 BM.x_2=obj.X_eta(BM.index); |
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295 BM.y_1=obj.Y_xi(BM.index); |
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296 BM.y_2=obj.Y_eta(BM.index); |
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297 BM.z_1=obj.Z_xi(BM.index); |
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298 BM.z_2=obj.Z_eta(BM.index); |
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299 end |
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300 [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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301 BM.x_1,BM.x_2,BM.y_1,BM.y_2,BM.z_1,BM.z_2); |
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302 BM.side=sum(BM.index); |
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303 BM.pos=signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3); |
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304 end |
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305 |
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306 |
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307 function [closure, penalty]=boundary_condition_char(obj,BM) |
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308 side = BM.side; |
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309 pos = BM.pos; |
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310 neg = BM.neg; |
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311 zeroval=BM.zeroval; |
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312 V = BM.V; |
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313 Vi = BM.Vi; |
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314 Hi=BM.Hi; |
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315 D=BM.D; |
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316 e_=BM.e_; |
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317 |
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318 switch BM.boundpos |
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319 case {'l'} |
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320 tau=sparse(obj.n*side,pos); |
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321 Vi_plus=Vi(1:pos,:); |
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322 tau(1:pos,:)=-abs(D(1:pos,1:pos)); |
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323 closure=Hi*e_*V*tau*Vi_plus*e_'; |
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324 penalty=-Hi*e_*V*tau*Vi_plus; |
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325 case {'r'} |
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326 tau=sparse(obj.n*side,neg); |
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327 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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328 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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329 closure=Hi*e_*V*tau*Vi_minus*e_'; |
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330 penalty=-Hi*e_*V*tau*Vi_minus; |
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331 end |
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332 end |
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333 |
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334 |
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335 function [closure,penalty]=boundary_condition_general(obj,BM,boundary,L) |
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336 side = BM.side; |
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337 pos = BM.pos; |
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338 neg = BM.neg; |
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339 zeroval=BM.zeroval; |
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340 V = BM.V; |
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341 Vi = BM.Vi; |
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342 Hi=BM.Hi; |
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343 D=BM.D; |
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344 e_=BM.e_; |
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345 index=BM.index; |
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346 |
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347 switch BM.boundary |
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348 case{'b','B','bottom'} |
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349 Ji_vec=diag(obj.Ji); |
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350 Ji=diag(Ji_vec(index)); |
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351 Zeta_x=Ji*(obj.Y_xi(index).*obj.Z_eta(index)-obj.Z_xi(index).*obj.Y_eta(index)); |
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352 Zeta_y=Ji*(obj.X_eta(index).*obj.Z_xi(index)-obj.X_xi(index).*obj.Z_eta(index)); |
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353 Zeta_z=Ji*(obj.X_xi(index).*obj.Y_eta(index)-obj.Y_xi(index).*obj.X_eta(index)); |
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354 |
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355 L=obj.evaluateCoefficientMatrix(L,Zeta_x,Zeta_y,Zeta_z,[],[],[],[],[],[]); |
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356 end |
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357 |
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358 switch BM.boundpos |
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359 case {'l'} |
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360 tau=sparse(obj.n*side,pos); |
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361 Vi_plus=Vi(1:pos,:); |
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362 Vi_minus=Vi(pos+zeroval+1:obj.n*side,:); |
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363 V_plus=V(:,1:pos); |
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364 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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365 |
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366 tau(1:pos,:)=-abs(D(1:pos,1:pos)); |
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367 R=-inv(L*V_plus)*(L*V_minus); |
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368 closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; |
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369 penalty=-Hi*e_*V*tau*inv(L*V_plus)*L; |
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370 case {'r'} |
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371 tau=sparse(obj.n*side,neg); |
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372 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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373 Vi_plus=Vi(1:pos,:); |
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374 Vi_minus=Vi((pos+zeroval)+1:obj.n*side,:); |
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375 |
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376 V_plus=V(:,1:pos); |
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377 V_minus=V(:,(pos+zeroval)+1:obj.n*side); |
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378 R=-inv(L*V_minus)*(L*V_plus); |
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379 closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_'; |
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380 penalty=-Hi*e_*V*tau*inv(L*V_minus)*L; |
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381 end |
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382 end |
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383 |
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384 |
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385 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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386 params=obj.params; |
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387 eps=10^(-10); |
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388 if(sum(abs(x_1))>eps) |
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389 syms x_1s |
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390 else |
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391 x_1s=0; |
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392 end |
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393 |
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394 if(sum(abs(x_2))>eps) |
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395 syms x_2s; |
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396 else |
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397 x_2s=0; |
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398 end |
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399 |
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400 |
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401 if(sum(abs(y_1))>eps) |
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402 syms y_1s |
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403 else |
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404 y_1s=0; |
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405 end |
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406 |
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407 if(sum(abs(y_2))>eps) |
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408 syms y_2s; |
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409 else |
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410 y_2s=0; |
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411 end |
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412 |
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413 |
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414 if(sum(abs(z_1))>eps) |
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415 syms z_1s |
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416 else |
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417 z_1s=0; |
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418 end |
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419 |
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420 if(sum(abs(z_2))>eps) |
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421 syms z_2s; |
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422 else |
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423 z_2s=0; |
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424 end |
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425 |
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426 syms xs ys zs |
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427 [V, D]=eig(mat(obj,xs,ys,zs,x_1s,x_2s,y_1s,y_2s,z_1s,z_2s)); |
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428 Vi=inv(V); |
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429 |
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430 syms x_1s x_2s y_1s y_2s z_1s z_2s |
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431 % V= matlabFunction(V); |
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432 % D= matlabFunction(D); |
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433 % Vi= matlabFunction(Vi); |
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434 % |
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435 % xs=x; |
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436 % ys=y; |
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437 % zs=z; |
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438 % x_1s=x_1; |
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439 % x_2s=x_2; |
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440 % y_1s=y_1; |
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441 % y_2s=y_2; |
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442 % z_1s=z_1; |
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443 % z_2s=z_2; |
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444 |
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445 side=max(length(x),length(y)); |
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446 Dret=zeros(obj.n,side*obj.n); |
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447 Vret=zeros(obj.n,side*obj.n); |
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448 Viret=zeros(obj.n,side*obj.n); |
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449 |
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450 for ii=1:obj.n |
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451 for jj=1:obj.n |
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452 Dpart=matlabFunction(D(jj,ii),'Vars',[xs ys zs x_1s x_2s y_1s y_2s z_1s z_2s]); |
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453 Vpart=matlabFunction(V(jj,ii),'Vars',[xs ys zs x_1s x_2s y_1s y_2s z_1s z_2s]); |
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454 Vipart=matlabFunction(V(jj,ii),'Vars',[xs ys zs x_1s x_2s y_1s y_2s z_1s z_2s]); |
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455 Dret(jj,(ii-1)*side+1:side*ii)=sparse(Dpart(x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)); |
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456 Vret(jj,(ii-1)*side+1:side*ii)=sparse(Vpart(x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)); |
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457 Viret(jj,(ii-1)*side+1:side*ii)=sparse(Vipart(x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)); |
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458 end |
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459 end |
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460 |
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461 D=sparse(Dret); |
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462 V=sparse(Vret); |
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463 Vi=sparse(Viret); |
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Ylva Rydin <ylva.rydin@telia.com>
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464 V=obj.evaluateCoefficientMatrix(V,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2); |
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Ylva Rydin <ylva.rydin@telia.com>
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465 D=obj.evaluateCoefficientMatrix(D,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2); |
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Ylva Rydin <ylva.rydin@telia.com>
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466 Vi=obj.evaluateCoefficientMatrix(Vi,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2); |
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467 DD=diag(D); |
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Ylva Rydin <ylva.rydin@telia.com>
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468 |
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469 poseig=(DD>0); |
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470 zeroeig=(DD==0); |
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471 negeig=(DD<0); |
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472 |
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473 D=diag([DD(poseig); DD(zeroeig); DD(negeig)]); |
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474 V=[V(:,poseig) V(:,zeroeig) V(:,negeig)]; |
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475 %Vi=inv(V); |
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476 signVec=[sum(poseig),sum(zeroeig),sum(negeig)]; |
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477 end |
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478 end |
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479 end |