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annotate +scheme/Elastic2dVariable.m @ 987:1d70f29c7ab2

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Add assertLength
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 08 Jan 2019 14:59:43 +0100
parents 21394c78c72e
children a4ad90b37998 a2fcc4cf2298
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
687
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Martin Almquist <malmquist@stanford.edu>
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1 classdef Elastic2dVariable < scheme.Scheme
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2
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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9 m % Number of points in each direction, possibly a vector
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Martin Almquist <malmquist@stanford.edu>
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10 h % Grid spacing
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11
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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18 LAMBDA % Variable coefficient, related to dilation
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Martin Almquist <malmquist@stanford.edu>
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19 MU % Shear modulus, variable coefficient
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Martin Almquist <malmquist@stanford.edu>
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20 RHO, RHOi % Density, variable
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Martin Almquist <malmquist@stanford.edu>
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21
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Martin Almquist <malmquist@stanford.edu>
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22 D % Total operator
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Martin Almquist <malmquist@stanford.edu>
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23 D1 % First derivatives
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Martin Almquist <malmquist@stanford.edu>
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24
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Martin Almquist <malmquist@stanford.edu>
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25 % Second derivatives
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Martin Almquist <malmquist@stanford.edu>
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26 D2_lambda
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Martin Almquist <malmquist@stanford.edu>
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27 D2_mu
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28
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Martin Almquist <malmquist@stanford.edu>
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29 % Traction operators used for BC
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Martin Almquist <malmquist@stanford.edu>
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30 T_l, T_r
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Martin Almquist <malmquist@stanford.edu>
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31 tau_l, tau_r
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32
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33 H, Hi % Inner products
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34
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35 phi % Borrowing constant for (d1 - e^T*D1) from R
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36 gamma % Borrowing constant for d1 from M
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37 H11 % First element of H
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38
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39 % Borrowing from H, M, and R
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40 thH
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41 thM
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42 thR
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43
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44 e_l, e_r
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45 d1_l, d1_r % Normal derivatives at the boundary
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46 E % E{i}^T picks out component i
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47
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48 H_boundary % Boundary inner products
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49
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Martin Almquist <malmquist@stanford.edu>
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50 % Kroneckered norms and coefficients
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Martin Almquist <malmquist@stanford.edu>
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51 RHOi_kron
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52 Hi_kron
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53 end
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54
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55 methods
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56
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Martin Almquist <malmquist@stanford.edu>
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57 function obj = Elastic2dVariable(g ,order, lambda_fun, mu_fun, rho_fun, opSet)
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58 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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59 default_arg('lambda_fun', @(x,y) 0*x+1);
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60 default_arg('mu_fun', @(x,y) 0*x+1);
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61 default_arg('rho_fun', @(x,y) 0*x+1);
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62 dim = 2;
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63
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64 assert(isa(g, 'grid.Cartesian'))
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65
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66 lambda = grid.evalOn(g, lambda_fun);
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67 mu = grid.evalOn(g, mu_fun);
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68 rho = grid.evalOn(g, rho_fun);
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Martin Almquist <malmquist@stanford.edu>
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69 m = g.size();
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Martin Almquist <malmquist@stanford.edu>
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70 m_tot = g.N();
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71
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Martin Almquist <malmquist@stanford.edu>
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72 h = g.scaling();
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Martin Almquist <malmquist@stanford.edu>
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73 lim = g.lim;
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74 if isempty(lim)
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75 x = g.x;
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76 lim = cell(length(x),1);
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77 for i = 1:length(x)
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78 lim{i} = {min(x{i}), max(x{i})};
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79 end
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80 end
687
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81
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82 % 1D operators
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83 ops = cell(dim,1);
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84 for i = 1:dim
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85 ops{i} = opSet{i}(m(i), lim{i}, order);
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86 end
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87
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88 % Borrowing constants
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89 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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90 beta = ops{i}.borrowing.R.delta_D;
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91 obj.H11{i} = ops{i}.borrowing.H11;
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Martin Almquist <malmquist@stanford.edu>
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92 obj.phi{i} = beta/obj.H11{i};
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Martin Almquist <malmquist@stanford.edu>
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93 obj.gamma{i} = ops{i}.borrowing.M.d1;
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94
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95 % Better names
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96 obj.thR{i} = ops{i}.borrowing.R.delta_D;
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97 obj.thM{i} = ops{i}.borrowing.M.d1;
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98 obj.thH{i} = ops{i}.borrowing.H11;
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99 end
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100
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101 I = cell(dim,1);
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102 D1 = cell(dim,1);
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103 D2 = cell(dim,1);
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104 H = cell(dim,1);
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105 Hi = cell(dim,1);
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106 e_l = cell(dim,1);
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107 e_r = cell(dim,1);
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108 d1_l = cell(dim,1);
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109 d1_r = cell(dim,1);
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110
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111 for i = 1:dim
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112 I{i} = speye(m(i));
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113 D1{i} = ops{i}.D1;
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114 D2{i} = ops{i}.D2;
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115 H{i} = ops{i}.H;
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116 Hi{i} = ops{i}.HI;
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117 e_l{i} = ops{i}.e_l;
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118 e_r{i} = ops{i}.e_r;
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119 d1_l{i} = ops{i}.d1_l;
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120 d1_r{i} = ops{i}.d1_r;
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121 end
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122
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123 %====== Assemble full operators ========
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124 LAMBDA = spdiag(lambda);
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125 obj.LAMBDA = LAMBDA;
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126 MU = spdiag(mu);
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127 obj.MU = MU;
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128 RHO = spdiag(rho);
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Martin Almquist <malmquist@stanford.edu>
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129 obj.RHO = RHO;
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Martin Almquist <malmquist@stanford.edu>
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130 obj.RHOi = inv(RHO);
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131
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132 obj.D1 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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133 obj.D2_lambda = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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134 obj.D2_mu = cell(dim,1);
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135 obj.e_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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136 obj.e_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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137 obj.d1_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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138 obj.d1_r = cell(dim,1);
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139
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Martin Almquist <malmquist@stanford.edu>
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140 % D1
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Martin Almquist <malmquist@stanford.edu>
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141 obj.D1{1} = kron(D1{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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142 obj.D1{2} = kron(I{1},D1{2});
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Martin Almquist <malmquist@stanford.edu>
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143
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Martin Almquist <malmquist@stanford.edu>
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144 % Boundary operators
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Martin Almquist <malmquist@stanford.edu>
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145 obj.e_l{1} = kron(e_l{1},I{2});
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146 obj.e_l{2} = kron(I{1},e_l{2});
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Martin Almquist <malmquist@stanford.edu>
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147 obj.e_r{1} = kron(e_r{1},I{2});
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148 obj.e_r{2} = kron(I{1},e_r{2});
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149
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diff changeset
150 obj.d1_l{1} = kron(d1_l{1},I{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151 obj.d1_l{2} = kron(I{1},d1_l{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 obj.d1_r{1} = kron(d1_r{1},I{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 obj.d1_r{2} = kron(I{1},d1_r{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 % D2
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 obj.D2_lambda{i} = sparse(m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 obj.D2_mu{i} = sparse(m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 ind = grid.funcToMatrix(g, 1:m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 for i = 1:m(2)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 D_lambda = D2{1}(lambda(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 D_mu = D2{1}(mu(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 p = ind(:,i);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 obj.D2_lambda{1}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 obj.D2_mu{1}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 for i = 1:m(1)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 D_lambda = D2{2}(lambda(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 D_mu = D2{2}(mu(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 p = ind(i,:);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 obj.D2_lambda{2}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 obj.D2_mu{2}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 % Quadratures
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 obj.H = kron(H{1},H{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 obj.Hi = inv(obj.H);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 obj.H_boundary = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 obj.H_boundary{1} = H{2};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 obj.H_boundary{2} = H{1};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 % E{i}^T picks out component i.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 E = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 I = speye(m_tot,m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 e = sparse(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 e(i) = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 E{i} = kron(I,e);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 obj.E = E;
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 % Differentiation matrix D (without SAT)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 D2_lambda = obj.D2_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 D2_mu = obj.D2_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 D = sparse(dim*m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 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
207 db(i,j)*D1{i}*LAMBDA*D1{j}*E{j}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 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
210 db(i,j)*D1{j}*MU*D1{i}*E{j}' + ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 D2_mu{j}*E{i}' ...
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 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 obj.D = D;
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
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 % Numerical traction operators for BC.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 % Because d1 =/= e0^T*D1, the numerical tractions are different
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 % at every boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 T_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 T_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 tau_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 tau_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 % tau^{j}_i = sum_k T^{j}_{ik} u_k
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 d1_l = obj.d1_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 d1_r = obj.d1_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 e_l = obj.e_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 e_r = obj.e_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 % Loop over boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 T_l{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 T_r{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 tau_l{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 tau_r{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 % Loop over components
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 tau_l{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 tau_r{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 for k = 1:dim
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
245 T_l{j}{i,k} = ...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 -d(i,j)*LAMBDA*(d(i,k)*e_l{k}*d1_l{k}' + db(i,k)*D1{k})...
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
247 -d(j,k)*MU*(d(i,j)*e_l{i}*d1_l{i}' + db(i,j)*D1{i})...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 -d(i,k)*MU*e_l{j}*d1_l{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
250 T_r{j}{i,k} = ...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 d(i,j)*LAMBDA*(d(i,k)*e_r{k}*d1_r{k}' + db(i,k)*D1{k})...
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
252 +d(j,k)*MU*(d(i,j)*e_r{i}*d1_r{i}' + db(i,j)*D1{i})...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 +d(i,k)*MU*e_r{j}*d1_r{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 tau_l{j}{i} = tau_l{j}{i} + T_l{j}{i,k}*E{k}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 tau_r{j}{i} = tau_r{j}{i} + T_r{j}{i,k}*E{k}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 obj.T_l = T_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 obj.T_r = T_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 obj.tau_l = tau_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 obj.tau_r = tau_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 % Kroneckered norms and coefficients
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 I_dim = speye(dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 obj.RHOi_kron = kron(obj.RHOi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 obj.Hi_kron = kron(obj.Hi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 % Misc.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 obj.m = m;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 obj.h = h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 obj.order = order;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 obj.grid = g;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 obj.dim = dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
278 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
279
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
280
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 % 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
282 % 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
283 % 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
284 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
285 % on the first component.
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
286 % 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
287 % neighbour_scheme is an instance of Scheme that should be interfaced to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 % 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
289 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
290 default_arg('tuning', 1.2);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
292 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
293 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
294 type = bc{2};
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
295
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296 % j is the coordinate direction of the boundary
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
297 j = obj.get_boundary_number(boundary);
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
298 [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300 E = obj.E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301 Hi = obj.Hi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 LAMBDA = obj.LAMBDA;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303 MU = obj.MU;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 RHOi = obj.RHOi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 dim = obj.dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307 m_tot = obj.grid.N();
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 % Preallocate
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310 closure = sparse(dim*m_tot, dim*m_tot);
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
311 penalty = sparse(dim*m_tot, m_tot/obj.m(j));
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
313 k = comp;
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
314 switch type
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
315
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
316 % 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
317 case {'D','d','dirichlet','Dirichlet'}
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
319 phi = obj.phi{j};
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
320 h = obj.h(j);
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
321 h11 = obj.H11{j}*h;
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
322 gamma = obj.gamma{j};
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
324 a_lambda = dim/h11 + 1/(h11*phi);
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
325 a_mu_i = 2/(gamma*h);
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
326 a_mu_ij = 2/h11 + 1/(h11*phi);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
328 d = @kroneckerDelta; % Kronecker delta
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
329 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
330 alpha = @(i,j) tuning*( d(i,j)* a_lambda*LAMBDA ...
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
331 + d(i,j)* a_mu_i*MU ...
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
332 + db(i,j)*a_mu_ij*MU );
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
334 % 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
335 for i = 1:dim
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
336 C = T{k,i};
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
337 A = -d(i,k)*alpha(i,j);
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
338 B = A + C;
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
339 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
340 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
341 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
343 % 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
344 case {'F','f','Free','free','traction','Traction','t','T'}
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
345 closure = closure - E{k}*RHOi*Hi*e*H_gamma* (e'*tau{k} );
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
346 penalty = penalty + E{k}*RHOi*Hi*e*H_gamma;
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347
795
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
348 % 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
349 otherwise
1f6b2fb69225 Revert bcSetup and update bc functions in elastic schemes to be compatible.
Martin Almquist <malmquist@stanford.edu>
parents: 738
diff changeset
350 error('No such boundary condition: type = %s',type);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 % u denotes the solution in the own domain
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 % v denotes the solution in the neighbour domain
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
357 % Operators without subscripts are from the own domain.
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 tuning = 1.2;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
359
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
360 % j is the coordinate direction of the boundary
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
361 j = obj.get_boundary_number(boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
362 j_v = neighbour_scheme.get_boundary_number(neighbour_boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
363
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
364 % Get boundary operators
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
365 [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
366 [e_v, tau_v] = neighbour_scheme.get_boundary_operator({'e','tau'}, neighbour_boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
367
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
368 % Operators and quantities that correspond to the own domain only
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
369 Hi = obj.Hi;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
370 RHOi = obj.RHOi;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
371 dim = obj.dim;
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
372
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
373 %--- Other operators ----
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
374 m_tot_u = obj.grid.N();
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
375 E = obj.E;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
376 LAMBDA_u = obj.LAMBDA;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
377 MU_u = obj.MU;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
378 lambda_u = e'*LAMBDA_u*e;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
379 mu_u = e'*MU_u*e;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
380
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
381 m_tot_v = neighbour_scheme.grid.N();
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
382 E_v = neighbour_scheme.E;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
383 LAMBDA_v = neighbour_scheme.LAMBDA;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
384 MU_v = neighbour_scheme.MU;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
385 lambda_v = e_v'*LAMBDA_v*e_v;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
386 mu_v = e_v'*MU_v*e_v;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
387 %-------------------------
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
388
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
389 % Borrowing constants
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
390 h_u = obj.h(j);
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
391 thR_u = obj.thR{j}*h_u;
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
392 thM_u = obj.thM{j}*h_u;
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
393 thH_u = obj.thH{j}*h_u;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
394
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
395 h_v = neighbour_scheme.h(j_v);
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
396 thR_v = neighbour_scheme.thR{j_v}*h_v;
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
397 thH_v = neighbour_scheme.thH{j_v}*h_v;
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
398 thM_v = neighbour_scheme.thM{j_v}*h_v;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
399
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
400 % alpha = penalty strength for normal component, beta for tangential
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
401 alpha_u = dim*lambda_u/(4*thH_u) + lambda_u/(4*thR_u) + mu_u/(2*thM_u);
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
402 alpha_v = dim*lambda_v/(4*thH_v) + lambda_v/(4*thR_v) + mu_v/(2*thM_v);
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
403 beta_u = mu_u/(2*thH_u) + mu_u/(4*thR_u);
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
404 beta_v = mu_v/(2*thH_v) + mu_v/(4*thR_v);
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
405 alpha = alpha_u + alpha_v;
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
406 beta = beta_u + beta_v;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
407
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
408 d = @kroneckerDelta; % Kronecker delta
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
409 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
410 strength = @(i,j) tuning*(d(i,j)*alpha + db(i,j)*beta);
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
411
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
412 % Preallocate
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
413 closure = sparse(dim*m_tot_u, dim*m_tot_u);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
414 penalty = sparse(dim*m_tot_u, dim*m_tot_v);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
415
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
416 % Loop over components that penalties end up on
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
417 for i = 1:dim
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
418 closure = closure - E{i}*RHOi*Hi*e*strength(i,j)*H_gamma*e'*E{i}';
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
419 penalty = penalty + E{i}*RHOi*Hi*e*strength(i,j)*H_gamma*e_v'*E_v{i}';
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
420
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
421 closure = closure - 1/2*E{i}*RHOi*Hi*e*H_gamma*e'*tau{i};
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
422 penalty = penalty - 1/2*E{i}*RHOi*Hi*e*H_gamma*e_v'*tau_v{i};
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
423
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
424 % Loop over components that we have interface conditions on
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
425 for k = 1:dim
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
426 closure = closure + 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e'*E{k}';
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
427 penalty = penalty - 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e_v'*E_v{k}';
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
428 end
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
429 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
430 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
431
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
432 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
433 function [j, nj] = get_boundary_number(obj, boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
434
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
435 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
436 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
437 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
438 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
439 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
440 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
441 error('No such boundary: boundary = %s',boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
442 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
443
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
444 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
445 case {'w','W','west','West','s','S','south','South'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
446 nj = -1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
447 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
448 nj = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
449 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
450 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
451
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
452 % Returns the boundary operator op for the boundary specified by the string boundary.
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
453 % op: may be a cell array of strings
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
454 function [varargout] = get_boundary_operator(obj, op, boundary)
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
455
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
456 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
457 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
458 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
459 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
460 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
461 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
462 error('No such boundary: boundary = %s',boundary);
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
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
465 if ~iscell(op)
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
466 op = {op};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
467 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
468
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
469 for i = 1:length(op)
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
470 switch op{i}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
471 case 'e'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
472 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
473 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
474 varargout{i} = obj.e_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
475 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
476 varargout{i} = obj.e_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
477 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
478 case 'd'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
479 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
480 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
481 varargout{i} = obj.d1_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
482 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
483 varargout{i} = obj.d1_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
484 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
485 case 'H'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
486 varargout{i} = obj.H_boundary{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
487 case 'T'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
488 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
489 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
490 varargout{i} = obj.T_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
491 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
492 varargout{i} = obj.T_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
493 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
494 case 'tau'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
495 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
496 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
497 varargout{i} = obj.tau_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
498 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
499 varargout{i} = obj.tau_r{j};
813
b374a8aa9246 Correct interface penalty strength in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 795
diff changeset
500 end
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
501 otherwise
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
502 error(['No such operator: operator = ' op{i}]);
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
503 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
504 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
505
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
506 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
507
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
508 function N = size(obj)
734
eebe24a636c7 Make Elastic2dVariable.size account for components.
Martin Almquist <malmquist@stanford.edu>
parents: 730
diff changeset
509 N = obj.dim*prod(obj.m);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
510 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
511 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
512 end