Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinear.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 706d1c2b4199
children a0b3161e44f3
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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
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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
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159 D = D2_v(a22(ind(i,:)));
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160 p = ind(i,:);
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161 Dvv(p,p) = D;
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162 end
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163
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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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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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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);
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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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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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249 b2 = gamm*obj.lambda./obj.a22.^2;
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250
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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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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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279 % -- interpolation: type of interpolation, default 'none'
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280 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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parents: 925
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281
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282 defaultType.tuning = 1.2;
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283 defaultType.interpolation = 'none';
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284 default_struct('type', defaultType);
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285
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286 switch type.interpolation
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parents: 925
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287 case {'none', ''}
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parents: 938
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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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parents: 927
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
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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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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
417 gamm = obj.gamm_v;
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
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>
parents:
diff changeset
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