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annotate +scheme/Elastic2dCurvilinearAnisotropic.m @ 1211:3d7faa2ca312 feature/poroelastic

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Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
author Martin Almquist <malmquist@stanford.edu>
date Fri, 27 Sep 2019 13:18:09 -0700
parents 67eee83fd9c9
children 43f1cd11e8e8
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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
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28 % Boundary operators in cell format, used for BC
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29 T_w, T_e, T_s, T_n
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30
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31 % Traction operators
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32 tau_w, tau_e, tau_s, tau_n % Return vector field
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33 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
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34 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
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35
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36 % Inner products
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37 H
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38
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39 % Boundary inner products (for scalar field)
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40 H_w, H_e, H_s, H_n
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41
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42 % Surface Jacobian vectors
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43 s_w, s_e, s_s, s_n
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44
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45 % Boundary restriction operators
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46 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
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47 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
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48 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
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49 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
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50
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51 % E{i}^T picks out component i
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52 E
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53
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54 % Elastic2dVariableAnisotropic object for reference domain
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55 refObj
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56 end
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57
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58 methods
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59
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60 % The coefficients can either be function handles or grid functions
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61 % optFlag -- if true, extra computations are performed, which may be helpful for optimization.
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62 function obj = Elastic2dCurvilinearAnisotropic(g, order, rho, C, opSet, optFlag)
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63 default_arg('rho', @(x,y) 0*x+1);
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64 default_arg('opSet',{@sbp.D2VariableCompatible, @sbp.D2VariableCompatible});
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65 default_arg('optFlag', false);
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66 dim = 2;
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67
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68 C_default = cell(dim,dim,dim,dim);
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69 for i = 1:dim
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70 for j = 1:dim
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71 for k = 1:dim
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72 for l = 1:dim
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73 C_default{i,j,k,l} = @(x,y) 0*x + 1;
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74 end
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75 end
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76 end
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77 end
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78 default_arg('C', C_default);
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79
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80 assert(isa(g, 'grid.Curvilinear'));
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81
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82 if isa(rho, 'function_handle')
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83 rho = grid.evalOn(g, rho);
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84 end
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85
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86 C_mat = cell(dim,dim,dim,dim);
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87 for i = 1:dim
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88 for j = 1:dim
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89 for k = 1:dim
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90 for l = 1:dim
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91 if isa(C{i,j,k,l}, 'function_handle')
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92 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
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93 end
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94 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
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95 end
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96 end
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97 end
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98 end
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99 obj.C = C_mat;
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100
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101 m = g.size();
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102 m_tot = g.N();
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103
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104 % 1D operators
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105 m_u = m(1);
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106 m_v = m(2);
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107 ops_u = opSet{1}(m_u, {0, 1}, order);
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108 ops_v = opSet{2}(m_v, {0, 1}, order);
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109
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110 h_u = ops_u.h;
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111 h_v = ops_v.h;
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112
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113 I_u = speye(m_u);
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114 I_v = speye(m_v);
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115
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116 D1_u = ops_u.D1;
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117 H_u = ops_u.H;
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118 Hi_u = ops_u.HI;
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119 e_l_u = ops_u.e_l;
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120 e_r_u = ops_u.e_r;
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121 d1_l_u = ops_u.d1_l;
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122 d1_r_u = ops_u.d1_r;
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123
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124 D1_v = ops_v.D1;
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125 H_v = ops_v.H;
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126 Hi_v = ops_v.HI;
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127 e_l_v = ops_v.e_l;
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128 e_r_v = ops_v.e_r;
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129 d1_l_v = ops_v.d1_l;
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130 d1_r_v = ops_v.d1_r;
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131
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132
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133 % Logical operators
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134 Du = kr(D1_u,I_v);
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135 Dv = kr(I_u,D1_v);
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136
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137 e_w = kr(e_l_u,I_v);
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138 e_e = kr(e_r_u,I_v);
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139 e_s = kr(I_u,e_l_v);
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140 e_n = kr(I_u,e_r_v);
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141
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142 % Metric coefficients
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143 coords = g.points();
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144 x = coords(:,1);
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145 y = coords(:,2);
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146
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147 x_u = Du*x;
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148 x_v = Dv*x;
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149 y_u = Du*y;
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150 y_v = Dv*y;
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151
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152 J = x_u.*y_v - x_v.*y_u;
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153
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154 K = cell(dim, dim);
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155 K{1,1} = y_v./J;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 K{1,2} = -y_u./J;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 K{2,1} = -x_v./J;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 K{2,2} = x_u./J;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159
1211
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
160 % Physical derivatives
3d7faa2ca312 Add physical derivatives Dx and Dy to ElasticCurvilinearAnisotropic
Martin Almquist <malmquist@stanford.edu>
parents: 1209
diff changeset
161 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
162 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
163
1205
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 % Wrap around Aniosotropic Cartesian
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 rho_tilde = J.*rho;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 PHI = cell(dim,dim,dim,dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 for i = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 for j = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 for k = 1:dim
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 for l = 1:dim
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 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
173 for m = 1:dim
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 for n = 1:dim
1209
67eee83fd9c9 Swap indices in anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 1205
diff changeset
175 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
176 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 end
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
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 gRef = grid.equidistant([m_u, m_v], {0,1}, {0,1});
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 refObj = scheme.Elastic2dVariableAnisotropic(gRef, order, rho_tilde, PHI, opSet);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 %---- Set object properties ------
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 obj.RHO = spdiag(rho);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 % Volume quadrature
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 obj.J = spdiag(J);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 obj.Ji = spdiag(1./J);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 obj.H = obj.J*kr(H_u,H_v);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 % Boundary quadratures
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 s_w = sqrt((e_w'*x_v).^2 + (e_w'*y_v).^2);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 s_e = sqrt((e_e'*x_v).^2 + (e_e'*y_v).^2);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 s_s = sqrt((e_s'*x_u).^2 + (e_s'*y_u).^2);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 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
199 obj.s_w = s_w;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 obj.s_e = s_e;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 obj.s_s = s_s;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 obj.s_n = s_n;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 obj.H_w = H_v*spdiag(s_w);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 obj.H_e = H_v*spdiag(s_e);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 obj.H_s = H_u*spdiag(s_s);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 obj.H_n = H_u*spdiag(s_n);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 % Restriction operators
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 obj.e_w = refObj.e_w;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 obj.e_e = refObj.e_e;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 obj.e_s = refObj.e_s;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 obj.e_n = refObj.e_n;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 % Adapt things from reference object
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 obj.D = refObj.D;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 obj.E = refObj.E;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 obj.e1_w = refObj.e1_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 obj.e1_e = refObj.e1_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 obj.e1_s = refObj.e1_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 obj.e1_n = refObj.e1_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 obj.e2_w = refObj.e2_w;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 obj.e2_e = refObj.e2_e;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 obj.e2_s = refObj.e2_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 obj.e2_n = refObj.e2_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 obj.e_scalar_w = refObj.e_scalar_w;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 obj.e_scalar_e = refObj.e_scalar_e;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 obj.e_scalar_s = refObj.e_scalar_s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 obj.e_scalar_n = refObj.e_scalar_n;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 e1_w = (obj.e_scalar_w'*obj.E{1}')';
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 e1_e = (obj.e_scalar_e'*obj.E{1}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 e1_s = (obj.e_scalar_s'*obj.E{1}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 e1_n = (obj.e_scalar_n'*obj.E{1}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 e2_w = (obj.e_scalar_w'*obj.E{2}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 e2_e = (obj.e_scalar_e'*obj.E{2}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 e2_s = (obj.e_scalar_s'*obj.E{2}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 e2_n = (obj.e_scalar_n'*obj.E{2}')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 obj.tau1_w = (spdiag(1./s_w)*refObj.tau1_w')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 obj.tau1_e = (spdiag(1./s_e)*refObj.tau1_e')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 obj.tau1_s = (spdiag(1./s_s)*refObj.tau1_s')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 obj.tau1_n = (spdiag(1./s_n)*refObj.tau1_n')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 obj.tau2_w = (spdiag(1./s_w)*refObj.tau2_w')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 obj.tau2_e = (spdiag(1./s_e)*refObj.tau2_e')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 obj.tau2_s = (spdiag(1./s_s)*refObj.tau2_s')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 obj.tau2_n = (spdiag(1./s_n)*refObj.tau2_n')';
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 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
255 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
256 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
257 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
258
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 % Misc.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 obj.refObj = refObj;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 obj.m = refObj.m;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 obj.h = refObj.h;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 obj.order = order;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 obj.grid = g;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 obj.dim = dim;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 % 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
271 % 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
272 % 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
273 % 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
274 % on the first component. Can also be e.g.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 % {'normal', 'd'} or {'tangential', 't'} for conditions on
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 % tangential/normal component.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277 % 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
278 % 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
279 % 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
280
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 % For displacement bc:
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
282 % bc = {comp, 'd', dComps},
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
283 % where
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 % dComps = vector of components with displacement BC. Default: 1:dim.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
285 % 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
286 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287 default_arg('tuning', 1.0);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 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
289
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
290 [closure, penalty] = obj.refObj.boundary_condition(boundary, bc, tuning);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
292 type = bc{2};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
293
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294 switch type
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
295 case {'F','f','Free','free','traction','Traction','t','T'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296 s = obj.(['s_' boundary]);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297 s = spdiag(s);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298 penalty = penalty*s;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 % type Struct that specifies the interface coupling.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303 % Fields:
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 % -- tuning: penalty strength, defaults to 1.0
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305 % -- interpolation: type of interpolation, default 'none'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 defaultType.tuning = 1.0;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 defaultType.interpolation = 'none';
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310 default_struct('type', defaultType);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 [closure, penalty] = obj.refObj.interface(boundary,neighbour_scheme.refObj,neighbour_boundary,type);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315 % Returns the component number that is the tangential/normal component
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316 % at the specified boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317 function comp = getComponent(obj, comp_str, boundary)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318 assertIsMember(comp_str, {'normal', 'tangential'});
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 assertIsMember(boundary, {'w', 'e', 's', 'n'});
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 switch boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 case {'w', 'e'}
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323 switch comp_str
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 case 'normal'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 comp = 1;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 case 'tangential'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327 comp = 2;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 case {'s', 'n'}
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330 switch comp_str
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 case 'normal'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
332 comp = 2;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333 case 'tangential'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 comp = 1;
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 end
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 % Returns h11 for the boundary specified by the string boundary.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 % op -- string
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 function h11 = getBorrowing(obj, boundary)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 switch boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345 case {'w','e'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 h11 = obj.refObj.h11{1};
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347 case {'s', 'n'}
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 h11 = obj.refObj.h11{2};
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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 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 % Returns the outward unit normal vector for the boundary specified by the string boundary.
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 function nu = getNormal(obj, boundary)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 switch boundary
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 case 'w'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 nu = [-1,0];
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359 case 'e'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 nu = [1,0];
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 case 's'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 nu = [0,-1];
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 case 'n'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 nu = [0,1];
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368 % 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
369 % op -- string
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370 function o = getBoundaryOperator(obj, op, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374 switch op
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375 case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376 o = obj.([op, '_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
378
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
379 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
380
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381 % 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
382 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385 assertIsMember(op, {'e'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
386
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
387 switch op
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
388
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
389 case 'e'
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
390 o = obj.(['e_scalar', '_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
391 end
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 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
396 % Formula: tau_i = T_ij u_j
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397 % op -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398 function T = getBoundaryTractionOperator(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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 T = obj.(['T', '_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
402 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
403
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
404 % Returns square boundary quadrature matrix, of dimension
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
405 % corresponding to the number of boundary unknowns
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 % boundary -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
408 function H = getBoundaryQuadrature(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
409 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
410
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411 H = obj.getBoundaryQuadratureForScalarField(boundary);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
412 I_dim = speye(obj.dim, obj.dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
413 H = kron(H, I_dim);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
414 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
415
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
416 % Returns square boundary quadrature matrix, of dimension
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
417 % corresponding to the number of boundary grid points
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
418 %
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
419 % boundary -- string
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
420 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
421 assertIsMember(boundary, {'w', 'e', 's', 'n'})
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
422
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
423 H_b = obj.(['H_', boundary]);
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
424 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
425
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
426 function N = size(obj)
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
427 N = obj.dim*prod(obj.m);
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 end
3258dca12af8 Add scheme for anisotropic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
430 end