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annotate +scheme/LaplaceCurvilinear.m @ 743:f4595f14d696 feature/utux2D

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Change schemes to work for special coefficients.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 21 May 2018 23:11:34 -0700
parents 07f8311374c6
children 14b093a344eb
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450
8d455e49364f Copy Wave2dCurve to new scheme LaplaceCurvilinear
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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
27
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40 lambda
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41
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42 interpolation_type
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43 end
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44
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45 methods
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46 % Implements a*div(b*grad(u)) as a SBP scheme
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47 % 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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48
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49 function obj = LaplaceCurvilinear(g ,order, a, b, opSet, interpolation_type)
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50 default_arg('opSet',@sbp.D2Variable);
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51 default_arg('a', 1);
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52 default_arg('b', 1);
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53 default_arg('interpolation_type','AWW');
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54
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55 if b ~=1
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56 error('Not implemented yet')
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57 end
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58
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59 % assert(isa(g, 'grid.Curvilinear'))
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60 if isa(a, 'function_handle')
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61 a = grid.evalOn(g, a);
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62 a = spdiag(a);
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63 end
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64
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65 m = g.size();
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66 m_u = m(1);
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67 m_v = m(2);
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68 m_tot = g.N();
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69
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70 h = g.scaling();
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71 h_u = h(1);
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72 h_v = h(2);
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73
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74
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75 % 1D operators
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76 ops_u = opSet(m_u, {0, 1}, order);
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77 ops_v = opSet(m_v, {0, 1}, order);
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78
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79 I_u = speye(m_u);
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80 I_v = speye(m_v);
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81
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82 D1_u = ops_u.D1;
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83 D2_u = ops_u.D2;
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84 H_u = ops_u.H;
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85 Hi_u = ops_u.HI;
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86 e_l_u = ops_u.e_l;
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87 e_r_u = ops_u.e_r;
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88 d1_l_u = ops_u.d1_l;
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89 d1_r_u = ops_u.d1_r;
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91 D1_v = ops_v.D1;
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92 D2_v = ops_v.D2;
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93 H_v = ops_v.H;
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94 Hi_v = ops_v.HI;
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95 e_l_v = ops_v.e_l;
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96 e_r_v = ops_v.e_r;
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97 d1_l_v = ops_v.d1_l;
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98 d1_r_v = ops_v.d1_r;
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99
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100
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101 % Logical operators
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102 Du = kr(D1_u,I_v);
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103 Dv = kr(I_u,D1_v);
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104 obj.Hu = kr(H_u,I_v);
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105 obj.Hv = kr(I_u,H_v);
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106 obj.Hiu = kr(Hi_u,I_v);
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107 obj.Hiv = kr(I_u,Hi_v);
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108
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109 e_w = kr(e_l_u,I_v);
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110 e_e = kr(e_r_u,I_v);
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111 e_s = kr(I_u,e_l_v);
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112 e_n = kr(I_u,e_r_v);
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113 obj.du_w = kr(d1_l_u,I_v);
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114 obj.dv_w = (e_w'*Dv)';
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115 obj.du_e = kr(d1_r_u,I_v);
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116 obj.dv_e = (e_e'*Dv)';
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117 obj.du_s = (e_s'*Du)';
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118 obj.dv_s = kr(I_u,d1_l_v);
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119 obj.du_n = (e_n'*Du)';
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120 obj.dv_n = kr(I_u,d1_r_v);
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121
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122
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123 % Metric coefficients
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124 coords = g.points();
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125 x = coords(:,1);
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126 y = coords(:,2);
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127
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128 x_u = Du*x;
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129 x_v = Dv*x;
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130 y_u = Du*y;
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131 y_v = Dv*y;
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132
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133 J = x_u.*y_v - x_v.*y_u;
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134 a11 = 1./J .* (x_v.^2 + y_v.^2);
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135 a12 = -1./J .* (x_u.*x_v + y_u.*y_v);
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136 a22 = 1./J .* (x_u.^2 + y_u.^2);
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137 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
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138
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139 obj.x_u = x_u;
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140 obj.x_v = x_v;
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141 obj.y_u = y_u;
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142 obj.y_v = y_v;
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143
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144
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145 % Assemble full operators
551
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146 L_12 = spdiag(a12);
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147 Duv = Du*L_12*Dv;
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148 Dvu = Dv*L_12*Du;
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149
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150 Duu = sparse(m_tot);
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151 Dvv = sparse(m_tot);
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152 ind = grid.funcToMatrix(g, 1:m_tot);
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153
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154 for i = 1:m_v
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155 D = D2_u(a11(ind(:,i)));
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156 p = ind(:,i);
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157 Duu(p,p) = D;
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158 end
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159
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160 for i = 1:m_u
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161 D = D2_v(a22(ind(i,:)));
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162 p = ind(i,:);
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163 Dvv(p,p) = D;
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164 end
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165
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166
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167 % Physical operators
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168 obj.J = spdiag(J);
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169 obj.Ji = spdiag(1./J);
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170
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171 obj.D = obj.Ji*a*(Duu + Duv + Dvu + Dvv);
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172 obj.H = obj.J*kr(H_u,H_v);
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173 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
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174
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175 obj.e_w = e_w;
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176 obj.e_e = e_e;
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177 obj.e_s = e_s;
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178 obj.e_n = e_n;
376
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179
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180 %% normal derivatives
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181 I_w = ind(1,:);
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182 I_e = ind(end,:);
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183 I_s = ind(:,1);
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184 I_n = ind(:,end);
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185
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186 a11_w = spdiag(a11(I_w));
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187 a12_w = spdiag(a12(I_w));
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188 a11_e = spdiag(a11(I_e));
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189 a12_e = spdiag(a12(I_e));
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190 a22_s = spdiag(a22(I_s));
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191 a12_s = spdiag(a12(I_s));
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192 a22_n = spdiag(a22(I_n));
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193 a12_n = spdiag(a12(I_n));
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194
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195 s_w = sqrt((e_w'*x_v).^2 + (e_w'*y_v).^2);
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196 s_e = sqrt((e_e'*x_v).^2 + (e_e'*y_v).^2);
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197 s_s = sqrt((e_s'*x_u).^2 + (e_s'*y_u).^2);
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198 s_n = sqrt((e_n'*x_u).^2 + (e_n'*y_u).^2);
562
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199
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200 obj.d_w = -1*(spdiag(1./s_w)*(a11_w*obj.du_w' + a12_w*obj.dv_w'))';
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201 obj.d_e = (spdiag(1./s_e)*(a11_e*obj.du_e' + a12_e*obj.dv_e'))';
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202 obj.d_s = -1*(spdiag(1./s_s)*(a22_s*obj.dv_s' + a12_s*obj.du_s'))';
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203 obj.d_n = (spdiag(1./s_n)*(a22_n*obj.dv_n' + a12_n*obj.du_n'))';
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204
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205 obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv;
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206 obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv;
384
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207
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208 %% Boundary inner products
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209 obj.H_w = H_v*spdiag(s_w);
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210 obj.H_e = H_v*spdiag(s_e);
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211 obj.H_s = H_u*spdiag(s_s);
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212 obj.H_n = H_u*spdiag(s_n);
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213
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214 % Misc.
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215 obj.m = m;
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216 obj.h = [h_u h_v];
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217 obj.order = order;
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218 obj.grid = g;
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219 obj.interpolation_type = interpolation_type;
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220
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221 obj.a = a;
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222 obj.b = b;
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223 obj.a11 = a11;
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224 obj.a12 = a12;
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225 obj.a22 = a22;
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226 obj.lambda = lambda;
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227
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228 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
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229 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
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230 end
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231
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232
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233 % Closure functions return the opertors applied to the own doamin to close the boundary
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234 % 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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235 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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236 % type is a string specifying the type of boundary condition if there are several.
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237 % data is a function returning the data that should be applied at the boundary.
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238 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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239 % neighbour_boundary is a string specifying which boundary to interface to.
347
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240 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
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241 default_arg('type','neumann');
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242 default_arg('parameter', []);
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243
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244 [e, d, gamm, H_b, ~] = obj.get_boundary_ops(boundary);
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245 switch type
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246 % Dirichlet boundary condition
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247 case {'D','d','dirichlet'}
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248 tuning = 1.2;
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249 % tuning = 20.2;
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250
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251 b1 = gamm*obj.lambda./obj.a11.^2;
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252 b2 = gamm*obj.lambda./obj.a22.^2;
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253
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254 tau1 = tuning * spdiag(-1./b1 - 1./b2);
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255 tau2 = 1;
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256
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257 tau = (tau1*e + tau2*d)*H_b;
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258
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259 closure = obj.a*obj.Hi*tau*e';
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260 penalty = -obj.a*obj.Hi*tau;
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261
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262
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263 % Neumann boundary condition
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264 case {'N','n','neumann'}
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265 tau1 = -1;
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266 tau2 = 0;
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267 tau = (tau1*e + tau2*d)*H_b;
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268
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269 closure = obj.a*obj.Hi*tau*d';
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270 penalty = -obj.a*obj.Hi*tau;
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271
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272
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273 % Unknown, boundary condition
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274 otherwise
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275 error('No such boundary condition: type = %s',type);
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276 end
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277 end
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278
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279 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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280
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281 [e_u, d_u, gamm_u, H_b_u, I_u] = obj.get_boundary_ops(boundary);
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282 [e_v, d_v, gamm_v, H_b_v, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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283 Hi = obj.Hi;
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284 a = obj.a;
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285
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286 m_u = length(H_b_u);
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287 m_v = length(H_b_v);
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288
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289 grid_ratio = m_u/m_v;
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290 if grid_ratio ~= 1
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291
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292 [ms, index] = sort([m_u, m_v]);
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293 orders = [obj.order, neighbour_scheme.order];
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diff changeset
294 orders = orders(index);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
295
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
296 switch obj.interpolation_type
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
297 case 'MC'
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
298 interpOpSet = sbp.InterpMC(ms(1),ms(2),orders(1),orders(2));
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
299 if grid_ratio < 1
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
300 I_v2u_good = interpOpSet.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
301 I_v2u_bad = interpOpSet.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
302 I_u2v_good = interpOpSet.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
303 I_u2v_bad = interpOpSet.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
304 elseif grid_ratio > 1
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
305 I_v2u_good = interpOpSet.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
306 I_v2u_bad = interpOpSet.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
307 I_u2v_good = interpOpSet.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
308 I_u2v_bad = interpOpSet.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
309 end
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
310 case 'AWW'
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
311 %String 'C2F' indicates that ICF2 is more accurate.
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
312 interpOpSetF2C = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'F2C');
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
313 interpOpSetC2F = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'C2F');
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
314 if grid_ratio < 1
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
315 % Local is coarser than neighbour
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
316 I_v2u_good = interpOpSetF2C.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
317 I_v2u_bad = interpOpSetC2F.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
318 I_u2v_good = interpOpSetC2F.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
319 I_u2v_bad = interpOpSetF2C.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
320 elseif grid_ratio > 1
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
321 % Local is finer than neighbour
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
322 I_v2u_good = interpOpSetC2F.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
323 I_v2u_bad = interpOpSetF2C.IC2F;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
324 I_u2v_good = interpOpSetF2C.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
325 I_u2v_bad = interpOpSetC2F.IF2C;
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
326 end
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
327 otherwise
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
328 error(['Interpolation type ' obj.interpolation_type ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
329 ' is not available.' ]);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
330 end
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
331
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
332 else
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
333 % No interpolation required
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
334 I_v2u_good = speye(m_u,m_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
335 I_v2u_bad = speye(m_u,m_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
336 I_u2v_good = speye(m_u,m_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
337 I_u2v_bad = speye(m_u,m_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
338 end
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
339
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
340 % u denotes the solution in the own domain
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
341 % v denotes the solution in the neighbour domain
5
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
342 tuning = 1.2;
27
97a638f91fb8 Added function spdiag(). Fixed a bunch of bugs in the Wave2dCurve scheme.
Jonatan Werpers <jonatan@werpers.com>
parents: 5
diff changeset
343 % tuning = 20.2;
5
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
344 u = obj;
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
345 v = neighbour_scheme;
5f6b0b6a012b First try at interface implementation in WaveCurve2s
Jonatan Werpers <jonatan@werpers.com>
parents: 0
diff changeset
346
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
347 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
348 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
349 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
350 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
351
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
352 tau_u = -1./(4*b1_u) -1./(4*b2_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
353 tau_v = -1./(4*b1_v) -1./(4*b2_v);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
354
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
355 tau_u = tuning * spdiag(tau_u);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
356 tau_v = tuning * spdiag(tau_v);
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
357 beta_u = tau_v;
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
358
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
359 closure = a*Hi*e_u*tau_u*H_b_u*e_u' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
360 a*Hi*e_u*H_b_u*I_v2u_bad*beta_u*I_u2v_good*e_u' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
361 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
362 -a*1/2*Hi*e_u*H_b_u*d_u';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
363
720
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
364 penalty = -a*Hi*e_u*tau_u*H_b_u*I_v2u_good*e_v' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
365 -a*Hi*e_u*H_b_u*I_v2u_bad*beta_u*e_v' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
366 -a*1/2*Hi*d_u*H_b_u*I_v2u_good*e_v' + ...
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
367 -a*1/2*Hi*e_u*H_b_u*I_v2u_bad*d_v';
07f8311374c6 Add interpolation to LaplaceCurveilinear.
Martin Almquist <malmquist@stanford.edu>
parents: 567
diff changeset
368
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
369
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
370 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
371
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
372 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
373 % 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
374 %
643bc513b8b8 Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents: 83
diff changeset
375 % I -- the indecies of the boundary points in the grid matrix
567
33b962620e24 Remove unneeded sign information from get_boundary_ops
Jonatan Werpers <jonatan@werpers.com>
parents: 566
diff changeset
376 function [e, d, gamm, H_b, I] = get_boundary_ops(obj, 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
377
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
378 % gridMatrix = zeros(obj.m(2),obj.m(1));
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
379 % gridMatrix(:) = 1:numel(gridMatrix);
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
380
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
381 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
382
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
383 switch boundary
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
384 case 'w'
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
385 e = obj.e_w;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
386 d = obj.d_w;
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
387 H_b = obj.H_w;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
388 I = ind(1,:);
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
389 case 'e'
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
390 e = obj.e_e;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
391 d = obj.d_e;
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
392 H_b = obj.H_e;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
393 I = ind(end,:);
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
394 case 's'
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
395 e = obj.e_s;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
396 d = obj.d_s;
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_s;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
398 I = ind(:,1)';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
399 case 'n'
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
400 e = obj.e_n;
561
3a13916f8ff0 Switch to using boundary ops for normal derivative
Jonatan Werpers <jonatan@werpers.com>
parents: 560
diff changeset
401 d = obj.d_n;
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_n;
337
e070ebd94d9d Updated Wave2dCurve to use the new grid classes.
Jonatan Werpers <jonatan@werpers.com>
parents: 303
diff changeset
403 I = ind(:,end)';
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
404 otherwise
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
405 error('No such boundary: boundary = %s',boundary);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
406 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
407
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
408 switch boundary
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
409 case {'w','e'}
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
410 gamm = obj.gamm_u;
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
411 case {'s','n'}
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
412 gamm = obj.gamm_v;
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
413 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
414 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
415
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
416 function N = size(obj)
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
417 N = prod(obj.m);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
418 end
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
419 end
566
9c98a0526afc Switch implementation of boundary and interface to SBP notation
Jonatan Werpers <jonatan@werpers.com>
parents: 565
diff changeset
420 end