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annotate +scheme/LaplaceCurvilinear.m @ 989:e41c93d7ab08 feature/timesteppers

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Merge with default
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 09 Jan 2019 08:56:42 +0100
parents 706d1c2b4199
children a0b3161e44f3
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450
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1 classdef LaplaceCurvilinear < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5
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6 grid
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7
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8 order % Order accuracy for the approximation
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9
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10 a,b % Parameters of the operator
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11
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12
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13 % Inner products and operators for physical coordinates
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14 D % Laplace operator
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15 H, Hi % Inner product
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16 e_w, e_e, e_s, e_n
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17 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
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18 H_w, H_e, H_s, H_n % Boundary inner products
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19 Dx, Dy % Physical derivatives
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20 M % Gradient inner product
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21
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22 % Metric coefficients
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23 J, Ji
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24 a11, a12, a22
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25 x_u
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26 x_v
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27 y_u
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28 y_v
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29
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30 % Inner product and operators for logical coordinates
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31 H_u, H_v % Norms in the x and y directions
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32 Hi_u, Hi_v
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33 Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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34 Hiu, Hiv
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35 du_w, dv_w
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36 du_e, dv_e
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37 du_s, dv_s
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38 du_n, dv_n
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39 gamm_u, gamm_v
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40 lambda
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41
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42 end
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43
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44 methods
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45 % Implements a*div(b*grad(u)) as a SBP scheme
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46 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
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47
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48 function obj = LaplaceCurvilinear(g ,order, a, b, opSet)
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49 default_arg('opSet',@sbp.D2Variable);
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50 default_arg('a', 1);
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51 default_arg('b', 1);
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52
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53 if b ~=1
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54 error('Not implemented yet')
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55 end
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56
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57 % assert(isa(g, 'grid.Curvilinear'))
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58 if isa(a, 'function_handle')
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59 a = grid.evalOn(g, a);
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60 a = spdiag(a);
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61 end
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63 m = g.size();
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64 m_u = m(1);
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65 m_v = m(2);
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66 m_tot = g.N();
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67
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68 h = g.scaling();
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69 h_u = h(1);
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70 h_v = h(2);
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71
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72
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73 % 1D operators
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74 ops_u = opSet(m_u, {0, 1}, order);
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75 ops_v = opSet(m_v, {0, 1}, order);
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76
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77 I_u = speye(m_u);
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78 I_v = speye(m_v);
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79
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80 D1_u = ops_u.D1;
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81 D2_u = ops_u.D2;
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82 H_u = ops_u.H;
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83 Hi_u = ops_u.HI;
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84 e_l_u = ops_u.e_l;
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85 e_r_u = ops_u.e_r;
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86 d1_l_u = ops_u.d1_l;
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87 d1_r_u = ops_u.d1_r;
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88
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89 D1_v = ops_v.D1;
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90 D2_v = ops_v.D2;
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91 H_v = ops_v.H;
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92 Hi_v = ops_v.HI;
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93 e_l_v = ops_v.e_l;
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94 e_r_v = ops_v.e_r;
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95 d1_l_v = ops_v.d1_l;
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96 d1_r_v = ops_v.d1_r;
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97
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98
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99 % Logical operators
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100 Du = kr(D1_u,I_v);
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101 Dv = kr(I_u,D1_v);
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102 obj.Hu = kr(H_u,I_v);
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103 obj.Hv = kr(I_u,H_v);
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104 obj.Hiu = kr(Hi_u,I_v);
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105 obj.Hiv = kr(I_u,Hi_v);
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106
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107 e_w = kr(e_l_u,I_v);
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108 e_e = kr(e_r_u,I_v);
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109 e_s = kr(I_u,e_l_v);
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110 e_n = kr(I_u,e_r_v);
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111 obj.du_w = kr(d1_l_u,I_v);
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112 obj.dv_w = (e_w'*Dv)';
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113 obj.du_e = kr(d1_r_u,I_v);
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114 obj.dv_e = (e_e'*Dv)';
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115 obj.du_s = (e_s'*Du)';
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116 obj.dv_s = kr(I_u,d1_l_v);
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117 obj.du_n = (e_n'*Du)';
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118 obj.dv_n = kr(I_u,d1_r_v);
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119
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120
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121 % Metric coefficients
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122 coords = g.points();
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123 x = coords(:,1);
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124 y = coords(:,2);
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125
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126 x_u = Du*x;
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127 x_v = Dv*x;
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128 y_u = Du*y;
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129 y_v = Dv*y;
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130
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131 J = x_u.*y_v - x_v.*y_u;
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132 a11 = 1./J .* (x_v.^2 + y_v.^2);
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133 a12 = -1./J .* (x_u.*x_v + y_u.*y_v);
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134 a22 = 1./J .* (x_u.^2 + y_u.^2);
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135 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
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136
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137 obj.x_u = x_u;
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138 obj.x_v = x_v;
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139 obj.y_u = y_u;
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140 obj.y_v = y_v;
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141
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142
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143 % Assemble full operators
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144 L_12 = spdiag(a12);
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145 Duv = Du*L_12*Dv;
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146 Dvu = Dv*L_12*Du;
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147
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148 Duu = sparse(m_tot);
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149 Dvv = sparse(m_tot);
337
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diff changeset
150 ind = grid.funcToMatrix(g, 1:m_tot);
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151
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152 for i = 1:m_v
337
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diff changeset
153 D = D2_u(a11(ind(:,i)));
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154 p = ind(:,i);
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155 Duu(p,p) = D;
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156 end
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157
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158 for i = 1:m_u
337
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diff changeset
159 D = D2_v(a22(ind(i,:)));
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160 p = ind(i,:);
0
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161 Dvv(p,p) = D;
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162 end
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163
553
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164
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165 % Physical operators
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166 obj.J = spdiag(J);
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167 obj.Ji = spdiag(1./J);
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168
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169 obj.D = obj.Ji*a*(Duu + Duv + Dvu + Dvv);
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170 obj.H = obj.J*kr(H_u,H_v);
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171 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
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172
553
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173 obj.e_w = e_w;
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parents: 552
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174 obj.e_e = e_e;
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175 obj.e_s = e_s;
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176 obj.e_n = e_n;
376
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parents: 371
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177
557
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178 %% normal derivatives
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179 I_w = ind(1,:);
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180 I_e = ind(end,:);
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181 I_s = ind(:,1);
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182 I_n = ind(:,end);
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183
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184 a11_w = spdiag(a11(I_w));
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185 a12_w = spdiag(a12(I_w));
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186 a11_e = spdiag(a11(I_e));
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187 a12_e = spdiag(a12(I_e));
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188 a22_s = spdiag(a22(I_s));
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189 a12_s = spdiag(a12(I_s));
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190 a22_n = spdiag(a22(I_n));
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191 a12_n = spdiag(a12(I_n));
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192
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193 s_w = sqrt((e_w'*x_v).^2 + (e_w'*y_v).^2);
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194 s_e = sqrt((e_e'*x_v).^2 + (e_e'*y_v).^2);
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195 s_s = sqrt((e_s'*x_u).^2 + (e_s'*y_u).^2);
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196 s_n = sqrt((e_n'*x_u).^2 + (e_n'*y_u).^2);
562
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197
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198 obj.d_w = -1*(spdiag(1./s_w)*(a11_w*obj.du_w' + a12_w*obj.dv_w'))';
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199 obj.d_e = (spdiag(1./s_e)*(a11_e*obj.du_e' + a12_e*obj.dv_e'))';
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200 obj.d_s = -1*(spdiag(1./s_s)*(a22_s*obj.dv_s' + a12_s*obj.du_s'))';
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201 obj.d_n = (spdiag(1./s_n)*(a22_n*obj.dv_n' + a12_n*obj.du_n'))';
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202
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203 obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv;
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204 obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv;
384
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205
562
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206 %% Boundary inner products
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207 obj.H_w = H_v*spdiag(s_w);
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208 obj.H_e = H_v*spdiag(s_e);
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209 obj.H_s = H_u*spdiag(s_s);
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210 obj.H_n = H_u*spdiag(s_n);
553
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211
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212 % Misc.
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213 obj.m = m;
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214 obj.h = [h_u h_v];
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215 obj.order = order;
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216 obj.grid = g;
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217
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218 obj.a = a;
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219 obj.b = b;
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220 obj.a11 = a11;
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221 obj.a12 = a12;
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222 obj.a22 = a22;
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diff changeset
223 obj.lambda = lambda;
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224
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225 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
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226 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
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227 end
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228
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229
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230 % Closure functions return the opertors applied to the own doamin to close the boundary
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231 % 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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232 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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233 % type is a string specifying the type of boundary condition if there are several.
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234 % data is a function returning the data that should be applied at the boundary.
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235 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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236 % neighbour_boundary is a string specifying which boundary to interface to.
347
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237 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
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238 default_arg('type','neumann');
347
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239 default_arg('parameter', []);
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240
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241 [e, d, gamm, H_b, ~] = obj.get_boundary_ops(boundary);
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242 switch type
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243 % Dirichlet boundary condition
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244 case {'D','d','dirichlet'}
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245 tuning = 1.2;
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246 % tuning = 20.2;
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247
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diff changeset
248 b1 = gamm*obj.lambda./obj.a11.^2;
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diff changeset
249 b2 = gamm*obj.lambda./obj.a22.^2;
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250
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diff changeset
251 tau1 = tuning * spdiag(-1./b1 - 1./b2);
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252 tau2 = 1;
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253
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diff changeset
254 tau = (tau1*e + tau2*d)*H_b;
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255
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256 closure = obj.a*obj.Hi*tau*e';
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parents: 565
diff changeset
257 penalty = -obj.a*obj.Hi*tau;
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258
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259
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260 % Neumann boundary condition
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261 case {'N','n','neumann'}
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262 tau1 = -1;
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263 tau2 = 0;
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264 tau = (tau1*e + tau2*d)*H_b;
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265
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266 closure = obj.a*obj.Hi*tau*d';
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267 penalty = -obj.a*obj.Hi*tau;
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268
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269
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270 % Unknown, boundary condition
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271 otherwise
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272 error('No such boundary condition: type = %s',type);
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273 end
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274 end
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275
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276 % type Struct that specifies the interface coupling.
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277 % Fields:
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278 % -- tuning: penalty strength, defaults to 1.2
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diff changeset
279 % -- interpolation: type of interpolation, default 'none'
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diff changeset
280 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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parents: 925
diff changeset
281
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diff changeset
282 defaultType.tuning = 1.2;
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diff changeset
283 defaultType.interpolation = 'none';
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284 default_struct('type', defaultType);
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parents: 925
diff changeset
285
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286 switch type.interpolation
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parents: 925
diff changeset
287 case {'none', ''}
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parents: 938
diff changeset
288 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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parents: 925
diff changeset
289 case {'op','OP'}
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diff changeset
290 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
291 otherwise
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
292 error('Unknown type of interpolation: %s ', type.interpolation);
904
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
293 end
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
294 end
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
295
928
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
296 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
297 tuning = type.tuning;
904
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
298
906
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
299 % u denotes the solution in the own domain
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
300 % v denotes the solution in the neighbour domain
904
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
301 [e_u, d_u, gamm_u, H_b_u, I_u] = obj.get_boundary_ops(boundary);
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
302 [e_v, d_v, gamm_v, H_b_v, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
303
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
304 u = obj;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
305 v = neighbour_scheme;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
306
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
307 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
308 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
309 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
310 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
311
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
312 tau1 = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v);
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
313 tau1 = tuning * spdiag(tau1);
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
314 tau2 = 1/2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
315
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
316 sig1 = -1/2;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
317 sig2 = 0;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
318
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
319 tau = (e_u*tau1 + tau2*d_u)*H_b_u;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
320 sig = (sig1*e_u + sig2*d_u)*H_b_u;
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
321
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
322 closure = obj.a*obj.Hi*( tau*e_u' + sig*d_u');
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
323 penalty = obj.a*obj.Hi*(-tau*e_v' + sig*d_v');
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
324 end
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
325
928
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
326 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
904
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
327
921
19c05eefc8c6 Add warning that interfaceNonConforming in LaplaceCurve only works for Cartesian grids.
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
328 % TODO: Make this work for curvilinear grids
19c05eefc8c6 Add warning that interfaceNonConforming in LaplaceCurve only works for Cartesian grids.
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
329 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
19c05eefc8c6 Add warning that interfaceNonConforming in LaplaceCurve only works for Cartesian grids.
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
330
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
331 % User can request special interpolation operators by specifying type.interpOpSet
928
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
332 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
333 interpOpSet = type.interpOpSet;
1c61d8fa9903 Replace opts by type everywhere
Martin Almquist <malmquist@stanford.edu>
parents: 927
diff changeset
334 tuning = type.tuning;
904
14b093a344eb Outline new interface method in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
335
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
336
906
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
337 % u denotes the solution in the own domain
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
338 % v denotes the solution in the neighbour domain
938
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
339 [e_u, d_u, gamm_u, H_b_u, I_u] = obj.get_boundary_ops(boundary);
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
340 [e_v, d_v, gamm_v, H_b_v, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
341
938
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
342 % Find the number of grid points along the interface
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
343 m_u = size(e_u, 2);
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
344 m_v = size(e_v, 2);
922
1d91c2a8aada Refactor LaplCurv.interfaceNonConf. Add method for interpolation operator generation in LaplCurv
Martin Almquist <malmquist@stanford.edu>
parents: 921
diff changeset
345
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
346 Hi = obj.Hi;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
347 a = obj.a;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
348
5
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
349 u = obj;
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
350 v = neighbour_scheme;
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
351
85
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
352 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
353 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
354 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
355 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
5
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
356
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
357 tau_u = -1./(4*b1_u) -1./(4*b2_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
358 tau_v = -1./(4*b1_v) -1./(4*b2_v);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
359
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
360 tau_u = tuning * spdiag(tau_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
361 tau_v = tuning * spdiag(tau_v);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
362 beta_u = tau_v;
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
363
922
1d91c2a8aada Refactor LaplCurv.interfaceNonConf. Add method for interpolation operator generation in LaplCurv
Martin Almquist <malmquist@stanford.edu>
parents: 921
diff changeset
364 % Build interpolation operators
938
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
365 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
366 Iu2v = intOps.Iu2v;
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
367 Iv2u = intOps.Iv2u;
922
1d91c2a8aada Refactor LaplCurv.interfaceNonConf. Add method for interpolation operator generation in LaplCurv
Martin Almquist <malmquist@stanford.edu>
parents: 921
diff changeset
368
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
369 closure = a*Hi*e_u*tau_u*H_b_u*e_u' + ...
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
370 a*Hi*e_u*H_b_u*Iv2u.bad*beta_u*Iu2v.good*e_u' + ...
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
371 a*1/2*Hi*d_u*H_b_u*e_u' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
372 -a*1/2*Hi*e_u*H_b_u*d_u';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
373
927
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
374 penalty = -a*Hi*e_u*tau_u*H_b_u*Iv2u.good*e_v' + ...
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
375 -a*Hi*e_u*H_b_u*Iv2u.bad*beta_u*e_v' + ...
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
376 -a*1/2*Hi*d_u*H_b_u*Iv2u.good*e_v' + ...
4291731570bb Rename AWW OP. Make Interpolation operator classes take grid points as arguments. Remove LaplCurv.interpolationOperators. Introduce default struct in LaplCurv.interface.
Martin Almquist <malmquist@stanford.edu>
parents: 925
diff changeset
377 -a*1/2*Hi*e_u*H_b_u*Iv2u.bad*d_v';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
378
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
379 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
380
906
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
381 % Returns the boundary ops and sign for the boundary specified by the string boundary.
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
382 % The right boundary is considered the positive boundary
85
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
383 %
906
0499239496cf Remove property interpolation_type in LaplaceCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 904
diff changeset
384 % I -- the indices of the boundary points in the grid matrix
938
97291e1bd57c Make LaplCurv send only number of grid points to InterpOpsXX. Remove coordinates from get_boundary_ops method.
Martin Almquist <malmquist@stanford.edu>
parents: 936
diff changeset
385 function [e, d, gamm, H_b, I] = get_boundary_ops(obj, boundary)
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
386 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
85
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
387
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
388 switch boundary
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
389 case 'w'
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
390 e = obj.e_w;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
391 d = obj.d_w;
566
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Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
392 H_b = obj.H_w;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
393 I = ind(1,:);
0
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
394 case 'e'
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
395 e = obj.e_e;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
396 d = obj.d_e;
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
397 H_b = obj.H_e;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
398 I = ind(end,:);
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
399 case 's'
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
400 e = obj.e_s;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
401 d = obj.d_s;
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
402 H_b = obj.H_s;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
403 I = ind(:,1)';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
404 case 'n'
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
405 e = obj.e_n;
561
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Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
406 d = obj.d_n;
566
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Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
407 H_b = obj.H_n;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
408 I = ind(:,end)';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
409 otherwise
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
410 error('No such boundary: boundary = %s',boundary);
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
411 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
412
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
413 switch boundary
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
414 case {'w','e'}
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
415 gamm = obj.gamm_u;
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
416 case {'s','n'}
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parents:
diff changeset
417 gamm = obj.gamm_v;
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Jonatan Werpers <jonatan@werpers.com>
parents:
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418 end
922
1d91c2a8aada Refactor LaplCurv.interfaceNonConf. Add method for interpolation operator generation in LaplCurv
Martin Almquist <malmquist@stanford.edu>
parents: 921
diff changeset
419 end
1d91c2a8aada Refactor LaplCurv.interfaceNonConf. Add method for interpolation operator generation in LaplCurv
Martin Almquist <malmquist@stanford.edu>
parents: 921
diff changeset
420
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
421 function N = size(obj)
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
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422 N = prod(obj.m);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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423 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
424 end
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
425 end