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annotate +scheme/Elastic2dCurvilinearAnisotropic.m @ 1213:43f1cd11e8e8 feature/poroelastic

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Add physical normals to AnisotropicCurvilinear
author Martin Almquist <malmquist@stanford.edu>
date Mon, 14 Oct 2019 13:54:50 -0700
parents 3d7faa2ca312
children e1d4cb8b5309
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1 classdef Elastic2dCurvilinearAnisotropic < scheme.Scheme
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2
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3 % Discretizes the elastic wave equation:
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4 % rho u_{i,tt} = dj C_{ijkl} dk u_j
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5 % in curvilinear coordinates.
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6 % opSet should be cell array of opSets, one per dimension. This
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7 % is useful if we have periodic BC in one direction.
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8 % Assumes fully compatible operators.
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9
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10 properties
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11 m % Number of points in each direction, possibly a vector
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12 h % Grid spacing
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13
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14 grid
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15 dim
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16
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17 order % Order of accuracy for the approximation
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18
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19 % Diagonal matrices for variable coefficients
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20 J, Ji
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21 RHO % Density
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22 C % Elastic stiffness tensor
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23
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24 D % Total operator
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25
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26 Dx, Dy % Physical derivatives
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27 n_w, n_e, n_s, n_n % Physical normals
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28
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29 % Boundary operators in cell format, used for BC
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30 T_w, T_e, T_s, T_n
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31
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32 % Traction operators
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33 tau_w, tau_e, tau_s, tau_n % Return vector field
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34 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
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35 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
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36
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37 % Inner products
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38 H
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39
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40 % Boundary inner products (for scalar field)
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41 H_w, H_e, H_s, H_n
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42
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43 % Surface Jacobian vectors
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44 s_w, s_e, s_s, s_n
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45
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46 % Boundary restriction operators
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47 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
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48 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
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49 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
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50 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
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51 en_w, en_e, en_s, en_n % Act on vector field, return normal component
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52
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53 % E{i}^T picks out component i
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54 E
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55
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56 % Elastic2dVariableAnisotropic object for reference domain
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57 refObj
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58 end
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59
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60 methods
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61
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62 % The coefficients can either be function handles or grid functions
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63 % optFlag -- if true, extra computations are performed, which may be helpful for optimization.
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64 function obj = Elastic2dCurvilinearAnisotropic(g, order, rho, C, opSet, optFlag)
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65 default_arg('rho', @(x,y) 0*x+1);
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66 default_arg('opSet',{@sbp.D2VariableCompatible, @sbp.D2VariableCompatible});
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67 default_arg('optFlag', false);
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68 dim = 2;
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69
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70 C_default = cell(dim,dim,dim,dim);
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71 for i = 1:dim
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72 for j = 1:dim
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73 for k = 1:dim
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74 for l = 1:dim
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75 C_default{i,j,k,l} = @(x,y) 0*x + 1;
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76 end
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77 end
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78 end
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79 end
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80 default_arg('C', C_default);
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81
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82 assert(isa(g, 'grid.Curvilinear'));
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83
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84 if isa(rho, 'function_handle')
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85 rho = grid.evalOn(g, rho);
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86 end
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87
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88 C_mat = cell(dim,dim,dim,dim);
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89 for i = 1:dim
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90 for j = 1:dim
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91 for k = 1:dim
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92 for l = 1:dim
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93 if isa(C{i,j,k,l}, 'function_handle')
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94 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
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95 end
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96 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
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97 end
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98 end
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99 end
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100 end
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101 obj.C = C_mat;
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102
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103 m = g.size();
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104 m_tot = g.N();
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105
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106 % 1D operators
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107 m_u = m(1);
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108 m_v = m(2);
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109 ops_u = opSet{1}(m_u, {0, 1}, order);
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110 ops_v = opSet{2}(m_v, {0, 1}, order);
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111
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112 h_u = ops_u.h;
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113 h_v = ops_v.h;
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114
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115 I_u = speye(m_u);
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116 I_v = speye(m_v);
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117
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118 D1_u = ops_u.D1;
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119 H_u = ops_u.H;
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120 Hi_u = ops_u.HI;
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121 e_l_u = ops_u.e_l;
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122 e_r_u = ops_u.e_r;
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123 d1_l_u = ops_u.d1_l;
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124 d1_r_u = ops_u.d1_r;
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125
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126 D1_v = ops_v.D1;
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127 H_v = ops_v.H;
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128 Hi_v = ops_v.HI;
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129 e_l_v = ops_v.e_l;
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130 e_r_v = ops_v.e_r;
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131 d1_l_v = ops_v.d1_l;
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132 d1_r_v = ops_v.d1_r;
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133
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134
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135 % Logical operators
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136 Du = kr(D1_u,I_v);
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137 Dv = kr(I_u,D1_v);
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138
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139 e_w = kr(e_l_u,I_v);
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140 e_e = kr(e_r_u,I_v);
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141 e_s = kr(I_u,e_l_v);
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142 e_n = kr(I_u,e_r_v);
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143
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144 % Metric coefficients
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145 coords = g.points();
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146 x = coords(:,1);
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147 y = coords(:,2);
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148
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149 x_u = Du*x;
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150 x_v = Dv*x;
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151 y_u = Du*y;
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152 y_v = Dv*y;
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153
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154 J = x_u.*y_v - x_v.*y_u;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 K = cell(dim, dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 K{1,1} = y_v./J;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 K{1,2} = -y_u./J;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 K{2,1} = -x_v./J;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 K{2,2} = x_u./J;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161
1211
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
162 % Physical derivatives
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
163 obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv;
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
164 obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv;
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
165
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 % Wrap around Aniosotropic Cartesian
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 rho_tilde = J.*rho;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 PHI = cell(dim,dim,dim,dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 for i = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 for j = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 for k = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 for l = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 PHI{i,j,k,l} = 0*C{i,j,k,l};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 for m = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 for n = 1:dim
1209
67eee83fd9c9 Swap indices in anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1205
diff changeset
177 PHI{i,j,k,l} = PHI{i,j,k,l} + J.*K{m,i}.*C{m,j,n,l}.*K{n,k};
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 gRef = grid.equidistant([m_u, m_v], {0,1}, {0,1});
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 refObj = scheme.Elastic2dVariableAnisotropic(gRef, order, rho_tilde, PHI, opSet);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 %---- Set object properties ------
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 obj.RHO = spdiag(rho);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 % Volume quadrature
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 obj.J = spdiag(J);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 obj.Ji = spdiag(1./J);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 obj.H = obj.J*kr(H_u,H_v);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 % Boundary quadratures
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 s_w = sqrt((e_w'*x_v).^2 + (e_w'*y_v).^2);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 s_e = sqrt((e_e'*x_v).^2 + (e_e'*y_v).^2);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 s_s = sqrt((e_s'*x_u).^2 + (e_s'*y_u).^2);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 s_n = sqrt((e_n'*x_u).^2 + (e_n'*y_u).^2);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 obj.s_w = s_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 obj.s_e = s_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 obj.s_s = s_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 obj.s_n = s_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 obj.H_w = H_v*spdiag(s_w);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 obj.H_e = H_v*spdiag(s_e);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 obj.H_s = H_u*spdiag(s_s);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 obj.H_n = H_u*spdiag(s_n);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 % Restriction operators
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 obj.e_w = refObj.e_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 obj.e_e = refObj.e_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 obj.e_s = refObj.e_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 obj.e_n = refObj.e_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 % Adapt things from reference object
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 obj.D = refObj.D;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 obj.E = refObj.E;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 obj.e1_w = refObj.e1_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 obj.e1_e = refObj.e1_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 obj.e1_s = refObj.e1_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 obj.e1_n = refObj.e1_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 obj.e2_w = refObj.e2_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 obj.e2_e = refObj.e2_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 obj.e2_s = refObj.e2_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 obj.e2_n = refObj.e2_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 obj.e_scalar_w = refObj.e_scalar_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 obj.e_scalar_e = refObj.e_scalar_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 obj.e_scalar_s = refObj.e_scalar_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 obj.e_scalar_n = refObj.e_scalar_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
236 e1_w = obj.e1_w;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
237 e1_e = obj.e1_e;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
238 e1_s = obj.e1_s;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
239 e1_n = obj.e1_n;
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
241 e2_w = obj.e2_w;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
242 e2_e = obj.e2_e;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
243 e2_s = obj.e2_s;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
244 e2_n = obj.e2_n;
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 obj.tau1_w = (spdiag(1./s_w)*refObj.tau1_w')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 obj.tau1_e = (spdiag(1./s_e)*refObj.tau1_e')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 obj.tau1_s = (spdiag(1./s_s)*refObj.tau1_s')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 obj.tau1_n = (spdiag(1./s_n)*refObj.tau1_n')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 obj.tau2_w = (spdiag(1./s_w)*refObj.tau2_w')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 obj.tau2_e = (spdiag(1./s_e)*refObj.tau2_e')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 obj.tau2_s = (spdiag(1./s_s)*refObj.tau2_s')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 obj.tau2_n = (spdiag(1./s_n)*refObj.tau2_n')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 obj.tau_w = (refObj.e_w'*obj.e1_w*obj.tau1_w')' + (refObj.e_w'*obj.e2_w*obj.tau2_w')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 obj.tau_e = (refObj.e_e'*obj.e1_e*obj.tau1_e')' + (refObj.e_e'*obj.e2_e*obj.tau2_e')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 obj.tau_s = (refObj.e_s'*obj.e1_s*obj.tau1_s')' + (refObj.e_s'*obj.e2_s*obj.tau2_s')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 obj.tau_n = (refObj.e_n'*obj.e1_n*obj.tau1_n')' + (refObj.e_n'*obj.e2_n*obj.tau2_n')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
261 % Physical normals
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
262 e_w = obj.e_scalar_w;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
263 e_e = obj.e_scalar_e;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
264 e_s = obj.e_scalar_s;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
265 e_n = obj.e_scalar_n;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
266
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
267 e_w_vec = obj.e_w;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
268 e_e_vec = obj.e_e;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
269 e_s_vec = obj.e_s;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
270 e_n_vec = obj.e_n;
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
271
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
272 nu_w = [-1,0];
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
273 nu_e = [1,0];
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
274 nu_s = [0,-1];
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
275 nu_n = [0,1];
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
276
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
277 obj.n_w = cell(2,1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
278 obj.n_e = cell(2,1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
279 obj.n_s = cell(2,1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
280 obj.n_n = cell(2,1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
281
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
282 n_w_1 = (1./s_w).*e_w'*(J.*(K{1,1}*nu_w(1) + K{1,2}*nu_w(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
283 n_w_2 = (1./s_w).*e_w'*(J.*(K{2,1}*nu_w(1) + K{2,2}*nu_w(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
284 obj.n_w{1} = spdiag(n_w_1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
285 obj.n_w{2} = spdiag(n_w_2);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
286
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
287 n_e_1 = (1./s_e).*e_e'*(J.*(K{1,1}*nu_e(1) + K{1,2}*nu_e(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
288 n_e_2 = (1./s_e).*e_e'*(J.*(K{2,1}*nu_e(1) + K{2,2}*nu_e(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
289 obj.n_e{1} = spdiag(n_e_1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
290 obj.n_e{2} = spdiag(n_e_2);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
291
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
292 n_s_1 = (1./s_s).*e_s'*(J.*(K{1,1}*nu_s(1) + K{1,2}*nu_s(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
293 n_s_2 = (1./s_s).*e_s'*(J.*(K{2,1}*nu_s(1) + K{2,2}*nu_s(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
294 obj.n_s{1} = spdiag(n_s_1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
295 obj.n_s{2} = spdiag(n_s_2);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
296
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
297 n_n_1 = (1./s_n).*e_n'*(J.*(K{1,1}*nu_n(1) + K{1,2}*nu_n(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
298 n_n_2 = (1./s_n).*e_n'*(J.*(K{2,1}*nu_n(1) + K{2,2}*nu_n(2)));
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
299 obj.n_n{1} = spdiag(n_n_1);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
300 obj.n_n{2} = spdiag(n_n_2);
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
301
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
302 % Operators that extract the normal component
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
303 obj.en_w = (obj.n_w{1}*obj.e1_w' + obj.n_w{2}*obj.e2_w')';
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
304 obj.en_e = (obj.n_e{1}*obj.e1_e' + obj.n_e{2}*obj.e2_e')';
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
305 obj.en_s = (obj.n_s{1}*obj.e1_s' + obj.n_s{2}*obj.e2_s')';
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
306 obj.en_n = (obj.n_n{1}*obj.e1_n' + obj.n_n{2}*obj.e2_n')';
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
307
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 % Misc.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 obj.refObj = refObj;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310 obj.m = refObj.m;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311 obj.h = refObj.h;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 obj.order = order;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 obj.grid = g;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314 obj.dim = dim;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 % Closure functions return the operators applied to the own domain to close the boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323 % on the first component. Can also be e.g.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 % {'normal', 'd'} or {'tangential', 't'} for conditions on
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 % tangential/normal component.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 % data is a function returning the data that should be applied at the boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327 % neighbour_scheme is an instance of Scheme that should be interfaced to.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 % neighbour_boundary is a string specifying which boundary to interface to.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330 % For displacement bc:
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 % bc = {comp, 'd', dComps},
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
332 % where
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333 % dComps = vector of components with displacement BC. Default: 1:dim.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 % In this way, we can specify one BC at a time even though the SATs depend on all BC.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 default_arg('tuning', 1.0);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
338
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
339 [closure, penalty] = obj.refObj.boundary_condition(boundary, bc, tuning);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 type = bc{2};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343 switch type
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 case {'F','f','Free','free','traction','Traction','t','T'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345 s = obj.(['s_' boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 s = spdiag(s);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347 penalty = penalty*s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 % type Struct that specifies the interface coupling.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 % Fields:
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 % -- tuning: penalty strength, defaults to 1.0
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 % -- interpolation: type of interpolation, default 'none'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 defaultType.tuning = 1.0;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 defaultType.interpolation = 'none';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359 default_struct('type', defaultType);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 [closure, penalty] = obj.refObj.interface(boundary,neighbour_scheme.refObj,neighbour_boundary,type);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 % Returns h11 for the boundary specified by the string boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 function h11 = getBorrowing(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
369 switch boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370 case {'w','e'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371 h11 = obj.refObj.h11{1};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 case {'s', 'n'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373 h11 = obj.refObj.h11{2};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377 % Returns the outward unit normal vector for the boundary specified by the string boundary.
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
378 % n is a cell of diagonal matrices for each normal component, n{1} = n_1, n{2} = n_2.
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
379 function n = getNormal(obj, boundary)
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
380 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
382 n = obj.(['n_' boundary]);
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385 % Returns the boundary operator op for the boundary specified by the string boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
386 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
387 function o = getBoundaryOperator(obj, op, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
388 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
389 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2', 'en'})
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
390
1213
43f1cd11e8e8 Add physical normals to AnisotropicCurvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1211
diff changeset
391 o = obj.([op, '_', boundary]);
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
392
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
393 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
394
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
395 % Returns the boundary operator op for the boundary specified by the string boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
396 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 assertIsMember(op, {'e'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
400
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
401 switch op
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
402
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
403 case 'e'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
404 o = obj.(['e_scalar', '_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
405 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
406
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
407 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
408
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
409 % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
410 % Formula: tau_i = T_ij u_j
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
412 function T = getBoundaryTractionOperator(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
413 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
414
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
415 T = obj.(['T', '_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
416 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
417
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
418 % Returns square boundary quadrature matrix, of dimension
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
419 % corresponding to the number of boundary unknowns
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
420 %
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
421 % boundary -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
422 function H = getBoundaryQuadrature(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
423 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
424
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
425 H = obj.getBoundaryQuadratureForScalarField(boundary);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
426 I_dim = speye(obj.dim, obj.dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
427 H = kron(H, I_dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
428 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
429
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
430 % Returns square boundary quadrature matrix, of dimension
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
431 % corresponding to the number of boundary grid points
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
432 %
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
433 % boundary -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
434 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
435 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
436
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
437 H_b = obj.(['H_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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438 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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439
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
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440 function N = size(obj)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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441 N = obj.dim*prod(obj.m);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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442 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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443 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
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444 end