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Massive boundary operator cleanup in Elastic2dVariable
author Martin Almquist <malmquist@stanford.edu>
date Sat, 26 Jan 2019 15:38:58 -0800
parents 84933722ec0e
children e40899094f20
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 classdef Elastic2dVariable < 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} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i
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5 % opSet should be cell array of opSets, one per dimension. This
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6 % is useful if we have periodic BC in one direction.
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7
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8 properties
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9 m % Number of points in each direction, possibly a vector
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10 h % Grid spacing
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11
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12 grid
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13 dim
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14
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15 order % Order of accuracy for the approximation
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16
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17 % Diagonal matrices for varible coefficients
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18 LAMBDA % Lame's first parameter, related to dilation
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19 MU % Shear modulus
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20 RHO, RHOi, RHOi_kron % Density
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21
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22 D % Total operator
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23 D1 % First derivatives
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24
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25 % Second derivatives
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26 D2_lambda
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27 D2_mu
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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, Hi, Hi_kron, H_1D
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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 % Boundary restriction operators
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44 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
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45 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
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46 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
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47 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
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48
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49 % E{i}^T picks out component i
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50 E
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51
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52 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
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53 theta_R % Borrowing (d1- D1)^2 from R
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54 theta_H % First entry in norm matrix
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55 theta_M % Borrowing d1^2 from M.
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56
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57 % Structures used for adjoint optimization
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58 B
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59 end
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60
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61 methods
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62
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63 % The coefficients can either be function handles or grid functions
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64 function obj = Elastic2dVariable(g ,order, lambda, mu, rho, opSet)
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65 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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66 default_arg('lambda', @(x,y) 0*x+1);
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67 default_arg('mu', @(x,y) 0*x+1);
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68 default_arg('rho', @(x,y) 0*x+1);
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69 dim = 2;
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70
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71 assert(isa(g, 'grid.Cartesian'))
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72
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73 if isa(lambda, 'function_handle')
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74 lambda = grid.evalOn(g, lambda);
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75 end
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76 if isa(mu, 'function_handle')
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77 mu = grid.evalOn(g, mu);
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78 end
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79 if isa(rho, 'function_handle')
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80 rho = grid.evalOn(g, rho);
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81 end
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82
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83 m = g.size();
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84 m_tot = g.N();
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85
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86 h = g.scaling();
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87 lim = g.lim;
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88 if isempty(lim)
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89 x = g.x;
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90 lim = cell(length(x),1);
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91 for i = 1:length(x)
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92 lim{i} = {min(x{i}), max(x{i})};
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93 end
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94 end
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95
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96 % 1D operators
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97 ops = cell(dim,1);
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98 for i = 1:dim
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99 ops{i} = opSet{i}(m(i), lim{i}, order);
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100 end
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101
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102 % Borrowing constants
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103 for i = 1:dim
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104 obj.theta_R{i} = h(i)*ops{i}.borrowing.R.delta_D;
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105 obj.theta_H{i} = h(i)*ops{i}.borrowing.H11;
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106 obj.theta_M{i} = h(i)*ops{i}.borrowing.M.d1;
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107 end
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108
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109 I = cell(dim,1);
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110 D1 = cell(dim,1);
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111 D2 = cell(dim,1);
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112 H = cell(dim,1);
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113 Hi = cell(dim,1);
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114 e_0 = cell(dim,1);
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115 e_m = cell(dim,1);
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116 d1_0 = cell(dim,1);
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117 d1_m = cell(dim,1);
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118
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119 for i = 1:dim
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120 I{i} = speye(m(i));
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121 D1{i} = ops{i}.D1;
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122 D2{i} = ops{i}.D2;
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123 H{i} = ops{i}.H;
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124 Hi{i} = ops{i}.HI;
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125 e_0{i} = ops{i}.e_l;
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126 e_m{i} = ops{i}.e_r;
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127 d1_0{i} = ops{i}.d1_l;
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128 d1_m{i} = ops{i}.d1_r;
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129 end
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130
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131 %====== Assemble full operators ========
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132 LAMBDA = spdiag(lambda);
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133 obj.LAMBDA = LAMBDA;
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134 MU = spdiag(mu);
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135 obj.MU = MU;
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136 RHO = spdiag(rho);
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137 obj.RHO = RHO;
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138 obj.RHOi = inv(RHO);
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139
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 obj.D1 = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 obj.D2_lambda = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 obj.D2_mu = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 % D1
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145 obj.D1{1} = kron(D1{1},I{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 obj.D1{2} = kron(I{1},D1{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
148 % Boundary restriction operators
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
149 e_l = cell(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
150 e_r = cell(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
151 e_l{1} = kron(e_0{1}, I{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
152 e_l{2} = kron(I{1}, e_0{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
153 e_r{1} = kron(e_m{1}, I{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
154 e_r{2} = kron(I{1}, e_m{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
155
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
156 e_scalar_w = e_l{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
157 e_scalar_e = e_r{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
158 e_scalar_s = e_l{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
159 e_scalar_n = e_r{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
160
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
161 I_dim = speye(dim, dim);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
162 e_w = kron(e_scalar_w, I_dim);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
163 e_e = kron(e_scalar_e, I_dim);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
164 e_s = kron(e_scalar_s, I_dim);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
165 e_n = kron(e_scalar_n, I_dim);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
167 % Boundary derivatives
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
168 d1_l = cell(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
169 d1_r = cell(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
170 d1_l{1} = kron(d1_0{1}, I{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
171 d1_l{2} = kron(I{1}, d1_0{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
172 d1_r{1} = kron(d1_m{1}, I{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
173 d1_r{2} = kron(I{1}, d1_m{2});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
174
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
175
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
176 % E{i}^T picks out component i.
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
177 E = cell(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
178 I = speye(m_tot,m_tot);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
179 for i = 1:dim
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
180 e = sparse(dim,1);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
181 e(i) = 1;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
182 E{i} = kron(I,e);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
183 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
184 obj.E = E;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
185
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
186 e1_w = (e_scalar_w'*E{1}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
187 e1_e = (e_scalar_e'*E{1}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
188 e1_s = (e_scalar_s'*E{1}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
189 e1_n = (e_scalar_n'*E{1}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
190
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
191 e2_w = (e_scalar_w'*E{2}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
192 e2_e = (e_scalar_e'*E{2}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
193 e2_s = (e_scalar_s'*E{2}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
194 e2_n = (e_scalar_n'*E{2}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
195
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 % D2
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 obj.D2_lambda{i} = sparse(m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 obj.D2_mu{i} = sparse(m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 ind = grid.funcToMatrix(g, 1:m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 for i = 1:m(2)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 D_lambda = D2{1}(lambda(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 D_mu = D2{1}(mu(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 p = ind(:,i);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 obj.D2_lambda{1}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 obj.D2_mu{1}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 for i = 1:m(1)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 D_lambda = D2{2}(lambda(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 D_mu = D2{2}(mu(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 p = ind(i,:);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 obj.D2_lambda{2}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 obj.D2_mu{2}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 % Quadratures
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 obj.H = kron(H{1},H{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 obj.Hi = inv(obj.H);
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
225 obj.H_w = H{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
226 obj.H_e = H{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
227 obj.H_s = H{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
228 obj.H_n = H{1};
855
5751262b323b Add 1D quadrature matrices as property in Elastic2dVariable.
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
229 obj.H_1D = {H{1}, H{2}};
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 % Differentiation matrix D (without SAT)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 D2_lambda = obj.D2_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 D2_mu = obj.D2_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 D = sparse(dim*m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 D = D + E{i}*inv(RHO)*( d(i,j)*D2_lambda{i}*E{j}' +...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 db(i,j)*D1{i}*LAMBDA*D1{j}*E{j}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 D = D + E{i}*inv(RHO)*( d(i,j)*D2_mu{i}*E{j}' +...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 db(i,j)*D1{j}*MU*D1{i}*E{j}' + ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 D2_mu{j}*E{i}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 obj.D = D;
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
250 %=========================================%'
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 % Numerical traction operators for BC.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 % Because d1 =/= e0^T*D1, the numerical tractions are different
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 % at every boundary.
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
255 %
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
256 % Formula at boundary j: % tau^{j}_i = sum_k T^{j}_{ik} u_k
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
257 %
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 T_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 T_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 tau_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 tau_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 % Loop over boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 T_l{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 T_r{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 tau_l{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 tau_r{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
272 LAMBDA_l = e_l{j}'*LAMBDA*e_l{j};
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
273 LAMBDA_r = e_r{j}'*LAMBDA*e_r{j};
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
274 MU_l = e_l{j}'*MU*e_l{j};
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
275 MU_r = e_r{j}'*MU*e_r{j};
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
276
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
277 [~, n_l] = size(e_l{j});
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
278 [~, n_r] = size(e_r{j});
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
279
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
280 % Loop over components
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 for i = 1:dim
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
282 tau_l{j}{i} = sparse(dim*m_tot, n_l);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
283 tau_r{j}{i} = sparse(dim*m_tot, n_r);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 for k = 1:dim
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
285 T_l{j}{i,k} = ...
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
286 (-d(i,j)*LAMBDA_l*(d(i,k)*d1_l{j}' + db(i,k)*e_l{j}'*D1{k})...
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
287 -d(j,k)*MU_l*(d(i,j)*d1_l{j}' + db(i,j)*e_l{j}'*D1{i})...
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
288 -d(i,k)*MU_l*d1_l{j}')';
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
289
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
290 T_r{j}{i,k} = ...
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
291 (d(i,j)*LAMBDA_r*(d(i,k)*d1_r{j}' + db(i,k)*e_r{j}'*D1{k})...
966
4a85cff53107 Fix bug in Elastic2dVariable that caused crash for m_x neq m_y
Martin Almquist <malmquist@stanford.edu>
parents: 965
diff changeset
292 +d(j,k)*MU_r*(d(i,j)*d1_r{j}' + db(i,j)*e_r{j}'*D1{i})...
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
293 +d(i,k)*MU_r*d1_r{j}')';
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
295 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,k}'*E{k}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
296 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,k}'*E{k}')';
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300 end
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
301
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
302 % Traction tensors, T_ij
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
303 obj.T_w = T_l{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
304 obj.T_e = T_r{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
305 obj.T_s = T_l{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
306 obj.T_n = T_r{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
307
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
308 % Restriction operators
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
309 obj.e_w = e_w;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
310 obj.e_e = e_e;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
311 obj.e_s = e_s;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
312 obj.e_n = e_n;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
313
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
314 obj.e1_w = e1_w;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
315 obj.e1_e = e1_e;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
316 obj.e1_s = e1_s;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
317 obj.e1_n = e1_n;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
318
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
319 obj.e2_w = e2_w;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
320 obj.e2_e = e2_e;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
321 obj.e2_s = e2_s;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
322 obj.e2_n = e2_n;
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
323
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
324 obj.e_scalar_w = e_scalar_w;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
325 obj.e_scalar_e = e_scalar_e;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
326 obj.e_scalar_s = e_scalar_s;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
327 obj.e_scalar_n = e_scalar_n;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
328
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
329 % First component of traction
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
330 obj.tau1_w = tau_l{1}{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
331 obj.tau1_e = tau_r{1}{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
332 obj.tau1_s = tau_l{2}{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
333 obj.tau1_n = tau_r{2}{1};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
334
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
335 % Second component of traction
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
336 obj.tau2_w = tau_l{1}{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
337 obj.tau2_e = tau_r{1}{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
338 obj.tau2_s = tau_l{2}{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
339 obj.tau2_n = tau_r{2}{2};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
340
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
341 % Traction vectors
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
342 obj.tau_w = (e_w'*e1_w*obj.tau1_w')' + (e_w'*e2_w*obj.tau2_w')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
343 obj.tau_e = (e_e'*e1_e*obj.tau1_e')' + (e_e'*e2_e*obj.tau2_e')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
344 obj.tau_s = (e_s'*e1_s*obj.tau1_s')' + (e_s'*e2_s*obj.tau2_s')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
345 obj.tau_n = (e_n'*e1_n*obj.tau1_n')' + (e_n'*e2_n*obj.tau2_n')';
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347 % Kroneckered norms and coefficients
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 obj.RHOi_kron = kron(obj.RHOi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 obj.Hi_kron = kron(obj.Hi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 % Misc.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 obj.m = m;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 obj.h = h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 obj.order = order;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 obj.grid = g;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 obj.dim = dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357
965
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
358 % B, used for adjoint optimization
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
359 B = cell(dim, 1);
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
360 for i = 1:dim
965
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
361 B{i} = cell(m_tot, 1);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
362 end
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
363
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
364 for i = 1:dim
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
365 for j = 1:m_tot
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
366 B{i}{j} = sparse(m_tot, m_tot);
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
367 end
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
368 end
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
369
965
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
370 ind = grid.funcToMatrix(g, 1:m_tot);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
371
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
372 % Direction 1
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
373 for k = 1:m(1)
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
374 c = sparse(m(1),1);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
375 c(k) = 1;
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
376 [~, B_1D] = ops{1}.D2(c);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
377 for l = 1:m(2)
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
378 p = ind(:,l);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
379 B{1}{(k-1)*m(2) + l}(p, p) = B_1D;
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
380 end
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
381 end
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
382
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
383 % Direction 2
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
384 for k = 1:m(2)
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
385 c = sparse(m(2),1);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
386 c(k) = 1;
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
387 [~, B_1D] = ops{2}.D2(c);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
388 for l = 1:m(1)
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
389 p = ind(l,:);
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
390 B{2}{(l-1)*m(2) + k}(p, p) = B_1D;
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
391 end
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
392 end
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
393
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
394 obj.B = B;
db3411264b96 Remove use of tensor library in B assembly
Martin Almquist <malmquist@stanford.edu>
parents: 963
diff changeset
395
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
396 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 % Closure functions return the operators applied to the own domain to close the boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
400 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
401 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
402 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
1056
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
403 % on the first component. Can also be e.g.
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
404 % {'normal', 'd'} or {'tangential', 't'} for conditions on
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
405 % tangential/normal component.
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
406 % data is a function returning the data that should be applied at the boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
407 % neighbour_scheme is an instance of Scheme that should be interfaced to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
408 % neighbour_boundary is a string specifying which boundary to interface to.
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
409 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
738
aa4ef495f1fd Set Dirichlet tuning as parameter in BC function in Elastic2dVariable.
Martin Almquist <malmquist@stanford.edu>
parents: 734
diff changeset
410 default_arg('tuning', 1.2);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
412 assert( iscell(bc), 'The BC type must be a 2x1 cell array' );
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
413 comp = bc{1};
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
414 type = bc{2};
1056
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
415 if ischar(comp)
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
416 comp = obj.getComponent(comp, boundary);
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
417 end
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
418
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
419 e = obj.getBoundaryOperatorForScalarField('e', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
420 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
421 T = obj.getBoundaryTractionOperator(boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
422 alpha = obj.getBoundaryOperatorForScalarField('alpha', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
423 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
424
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
425 E = obj.E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
426 Hi = obj.Hi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
427 LAMBDA = obj.LAMBDA;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
428 MU = obj.MU;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
429 RHOi = obj.RHOi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
430
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
431 dim = obj.dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
432 m_tot = obj.grid.N();
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
433
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
434 % Preallocate
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
435 [~, col] = size(tau);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
436 closure = sparse(dim*m_tot, dim*m_tot);
1058
84933722ec0e Remove superfluous method get_boundary_number in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1057
diff changeset
437 penalty = sparse(dim*m_tot, col);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
438
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
439 k = comp;
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
440 switch type
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
441
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
442 % Dirichlet boundary condition
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
443 case {'D','d','dirichlet','Dirichlet'}
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
444
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
445 % Loop over components that Dirichlet penalties end up on
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
446 for i = 1:dim
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
447 C = transpose(T{k,i});
974
1c334842bf23 Extract tuning from alpha.
Martin Almquist <malmquist@stanford.edu>
parents: 973
diff changeset
448 A = -tuning*e*transpose(alpha{i,k});
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
449 B = A + e*C;
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
450 closure = closure + E{i}*RHOi*Hi*B'*e*H_gamma*(e'*E{k}' );
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
451 penalty = penalty - E{i}*RHOi*Hi*B'*e*H_gamma;
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
452 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
453
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
454 % Free boundary condition
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
455 case {'F','f','Free','free','traction','Traction','t','T'}
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
456 closure = closure - E{k}*RHOi*Hi*e*H_gamma*tau';
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
457 penalty = penalty + E{k}*RHOi*Hi*e*H_gamma;
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
458
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
459 % Unknown boundary condition
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
460 otherwise
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
461 error('No such boundary condition: type = %s',type);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
462 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
463 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
464
960
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
465 % type Struct that specifies the interface coupling.
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
466 % Fields:
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
467 % -- tuning: penalty strength, defaults to 1.2
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
468 % -- interpolation: type of interpolation, default 'none'
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
469 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
470
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
471 defaultType.tuning = 1.2;
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
472 defaultType.interpolation = 'none';
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
473 default_struct('type', defaultType);
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
474
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
475 switch type.interpolation
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
476 case {'none', ''}
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
477 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
478 case {'op','OP'}
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
479 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
480 otherwise
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
481 error('Unknown type of interpolation: %s ', type.interpolation);
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
482 end
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
483 end
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
484
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
485 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
963
c75ddd568fcc Turn alpha into a boundary operator. Add properties H_w etc for getBoundaryQuadrature to work.
Martin Almquist <malmquist@stanford.edu>
parents: 961
diff changeset
486 tuning = type.tuning;
c75ddd568fcc Turn alpha into a boundary operator. Add properties H_w etc for getBoundaryQuadrature to work.
Martin Almquist <malmquist@stanford.edu>
parents: 961
diff changeset
487
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
488 % u denotes the solution in the own domain
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
489 % v denotes the solution in the neighbour domain
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
490 % Operators without subscripts are from the own domain.
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
491
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
492 % Get boundary operators
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
493 e = obj.getBoundaryOperator('e', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
494 tau = obj.getBoundaryOperator('tau', boundary);
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
495
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
496 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
497 tau_v = neighbour_scheme.getBoundaryOperator('tau', neighbour_boundary);
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
498
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
499 H_gamma = obj.getBoundaryQuadrature(boundary);
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
500
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
501 % Operators and quantities that correspond to the own domain only
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
502 Hi = obj.Hi_kron;
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
503 RHOi = obj.RHOi_kron;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
504
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
505 % Penalty strength operators
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
506 alpha_u = 1/4*tuning*obj.getBoundaryOperator('alpha', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
507 alpha_v = 1/4*tuning*neighbour_scheme.getBoundaryOperator('alpha', neighbour_boundary);
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
508
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
509 closure = -RHOi*Hi*e*H_gamma*(alpha_u' + alpha_v'*e_v*e');
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
510 penalty = RHOi*Hi*e*H_gamma*(alpha_u'*e*e_v' + alpha_v');
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
511
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
512 closure = closure - 1/2*RHOi*Hi*e*H_gamma*tau';
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
513 penalty = penalty - 1/2*RHOi*Hi*e*H_gamma*tau_v';
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
514
972
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
515 closure = closure + 1/2*RHOi*Hi*tau*H_gamma*e';
104f0af001e0 Clean up Elastic2dVariable.interfaceStandard
Martin Almquist <malmquist@stanford.edu>
parents: 970
diff changeset
516 penalty = penalty - 1/2*RHOi*Hi*tau*H_gamma*e_v';
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
517
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
518 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
519
960
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
520 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
521 error('Non-conforming interfaces not implemented yet.');
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
522 end
ac566f3dc9b3 Add type to Elastic2dVariable.interface
Martin Almquist <malmquist@stanford.edu>
parents: 959
diff changeset
523
1056
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
524 % Returns the component number that is the tangential/normal component
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
525 % at the specified boundary
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
526 function comp = getComponent(obj, comp_str, boundary)
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
527 assertIsMember(comp_str, {'normal', 'tangential'});
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
528 assertIsMember(boundary, {'w', 'e', 's', 'n'});
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
529
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
530 switch boundary
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
531 case {'w', 'e'}
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
532 switch comp_str
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
533 case 'normal'
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
534 comp = 1;
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
535 case 'tangential'
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
536 comp = 2;
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
537 end
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
538 case {'s', 'n'}
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
539 switch comp_str
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
540 case 'normal'
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
541 comp = 2;
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
542 case 'tangential'
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
543 comp = 1;
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
544 end
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
545 end
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
546 end
b4fa176b4287 Elastic2dVariable: boundary condition type can now be a string, normal or tangential, as well as component number.
Martin Almquist <malmquist@stanford.edu>
parents: 974
diff changeset
547
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
548 % Returns the boundary operator op for the boundary specified by the string boundary.
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
549 % op -- string
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
550 function o = getBoundaryOperator(obj, op, boundary)
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
551 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
552 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2', 'alpha'})
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
553
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
554 switch op
970
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
555
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
556 case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
557 o = obj.([op, '_', boundary]);
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
558
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
559 case 'alpha'
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
560 % alpha = alpha(i,j) is the penalty strength for displacement BC.
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
561 e = obj.getBoundaryOperatorForScalarField('e', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
562 e_tot = obj.getBoundaryOperator('e', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
563 alpha = obj.getBoundaryOperatorForScalarField('alpha', boundary);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
564 E = obj.E;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
565 [m, n] = size(alpha{1,1});
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
566 alpha_tot = sparse(m*obj.dim, n*obj.dim);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
567 for i = 1:obj.dim
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
568 for l = 1:obj.dim
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
569 alpha_tot = alpha_tot + (e_tot'*E{i}*e*alpha{i,l}'*E{l}')';
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
570 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
571 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
572 o = alpha_tot;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
573 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
574
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
575 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
576
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
577 % Returns the boundary operator op for the boundary specified by the string boundary.
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
578 % op -- string
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
579 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
580 assertIsMember(boundary, {'w', 'e', 's', 'n'})
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
581 assertIsMember(op, {'e', 'alpha'})
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
582
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
583 switch op
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
584
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
585 case 'e'
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
586 o = obj.(['e_scalar', '_', boundary]);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
587
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
588 case 'alpha'
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
589 % alpha = alpha(i,j) is the penalty strength for displacement BC.
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
590 e = obj.getBoundaryOperatorForScalarField('e', boundary);
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
591
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
592 LAMBDA = obj.LAMBDA;
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
593 MU = obj.MU;
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
594 dim = obj.dim;
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
595
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
596 switch boundary
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
597 case {'w', 'e'}
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
598 k = 1;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
599 case {'s', 'n'}
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
600 k = 2;
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
601 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
602
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
603 theta_R = obj.theta_R{k};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
604 theta_H = obj.theta_H{k};
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
605 theta_M = obj.theta_M{k};
861
607c631f175e Small changes to Elastic2dVariable to facilitate adjoing gradient computation.
Martin Almquist <malmquist@stanford.edu>
parents: 855
diff changeset
606
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
607 a_lambda = dim/theta_H + 1/theta_R;
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
608 a_mu_i = 2/theta_M;
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
609 a_mu_ij = 2/theta_H + 1/theta_R;
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
610
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
611 d = @kroneckerDelta; % Kronecker delta
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
612 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
613 alpha = cell(obj.dim, obj.dim);
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
614
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
615 alpha_func = @(i,j) d(i,j)* a_lambda*LAMBDA ...
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
616 + d(i,j)* a_mu_i*MU ...
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
617 + db(i,j)*a_mu_ij*MU;
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
618 for i = 1:obj.dim
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
619 for j = 1:obj.dim
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
620 alpha{i,j} = d(i,j)*alpha_func(i,k)*e;
958
72cd29107a9a Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
Martin Almquist <malmquist@stanford.edu>
parents: 919
diff changeset
621 end
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
622 end
919
e30aaa4a3e09 Bugfix in Elastic2dVariable.get_boundary_ops
Martin Almquist <malmquist@stanford.edu>
parents: 882
diff changeset
623
1057
ff274c7404cc In Elastic2dVariable: copy-paste from feature/getBoundaryOp and fix bugs introduced there.
Martin Almquist <malmquist@stanford.edu>
parents: 1056
diff changeset
624 o = alpha;
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
625 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
626
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
627 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
628
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
629 % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
630 % op -- string
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
631 function T = getBoundaryTractionOperator(obj, boundary)
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
632 assertIsMember(boundary, {'w', 'e', 's', 'n'})
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
633
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
634 T = obj.(['T', '_', boundary]);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
635 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
636
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
637 % Returns square boundary quadrature matrix, of dimension
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
638 % corresponding to the number of boundary unknowns
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
639 %
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
640 % boundary -- string
970
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
641 function H = getBoundaryQuadrature(obj, boundary)
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
642 assertIsMember(boundary, {'w', 'e', 's', 'n'})
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
643
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
644 H = obj.getBoundaryQuadratureForScalarField(boundary);
970
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
645 I_dim = speye(obj.dim, obj.dim);
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
646 H = kron(H, I_dim);
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
647 end
23d9ca6755be Add getBoundaryQuadrature in Elastic2dVariable. Rename get_boundary_operator -> getBoundaryOperator. Add operators in getBoundaryOperator, with full size so that they work with multiblock.DiffOp.getBoundaryOperator.
Martin Almquist <malmquist@stanford.edu>
parents: 968
diff changeset
648
1059
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
649 % Returns square boundary quadrature matrix, of dimension
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
650 % corresponding to the number of boundary grid points
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
651 %
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
652 % boundary -- string
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
653 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
654 assertIsMember(boundary, {'w', 'e', 's', 'n'})
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
655
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
656 H_b = obj.(['H_', boundary]);
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
657 end
d8ab528f10f6 Massive boundary operator cleanup in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 1058
diff changeset
658
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
659 function N = size(obj)
734
eebe24a636c7 Make Elastic2dVariable.size account for components.
Martin Almquist <malmquist@stanford.edu>
parents: 730
diff changeset
660 N = obj.dim*prod(obj.m);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
661 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
662 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
663 end