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annotate +scheme/elasticShearVariable.m @ 664:8e6dfd22fc59 feature/poroelastic

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Free BC now yields symmetric negative semidefinite discretization.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 15 Dec 2017 16:23:10 -0800
parents b45ec2b28cc2
children ed853945ee99
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b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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1 classdef elasticShearVariable < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5
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6 grid
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7 dim
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8
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9 order % Order accuracy for the approximation
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10
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11 A % Variable coefficient lambda of the operator (as diagonal matrix here)
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12 RHO % Density (as diagonal matrix here)
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13
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14 D % Total operator
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15 D1 % First derivatives
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16 D2 % Second derivatives
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17 H, Hi % Inner products
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18 e_l, e_r
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19 d1_l, d1_r % Normal derivatives at the boundary
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20 E % E{i}^T picks out component i
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21
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22 H_boundary % Boundary inner products
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23
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24 A_boundary_l % Variable coefficient at boundaries
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25 A_boundary_r %
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26 end
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27
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28 methods
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29 % Implements the shear part of the elastic wave equation, i.e.
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30 % rho u_{i,tt} = d_i a d_j u_j + d_j a d_j u_i
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31 % where a = lambda.
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32
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33 function obj = elasticShearVariable(g ,order, a_fun, rho_fun, opSet)
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34 default_arg('opSet',@sbp.D2Variable);
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35 default_arg('a_fun', @(x,y) 0*x+1);
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36 default_arg('rho_fun', @(x,y) 0*x+1);
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37 dim = 2;
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38
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39 assert(isa(g, 'grid.Cartesian'))
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40
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41 a = grid.evalOn(g, a_fun);
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42 rho = grid.evalOn(g, rho_fun);
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43 m = g.size();
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44 m_tot = g.N();
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45
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46 h = g.scaling();
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47
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48 % 1D operators
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49 ops = cell(dim,1);
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50 for i = 1:dim
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51 ops{i} = opSet(m(i), {0, 1}, order);
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52 end
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53
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54 I = cell(dim,1);
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55 D1 = cell(dim,1);
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56 D2 = cell(dim,1);
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57 H = cell(dim,1);
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58 Hi = cell(dim,1);
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59 e_l = cell(dim,1);
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60 e_r = cell(dim,1);
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61 d1_l = cell(dim,1);
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62 d1_r = cell(dim,1);
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64 for i = 1:dim
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65 I{i} = speye(m(i));
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66 D1{i} = ops{i}.D1;
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67 D2{i} = ops{i}.D2;
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68 H{i} = ops{i}.H;
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69 Hi{i} = ops{i}.HI;
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70 e_l{i} = ops{i}.e_l;
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71 e_r{i} = ops{i}.e_r;
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72 d1_l{i} = ops{i}.d1_l;
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73 d1_r{i} = ops{i}.d1_r;
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74 end
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75
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76 %====== Assemble full operators ========
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77 A = spdiag(a);
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78 obj.A = A;
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79 RHO = spdiag(rho);
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80 obj.RHO = RHO;
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81
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82
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83 obj.D1 = cell(dim,1);
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84 obj.D2 = cell(dim,1);
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85 obj.e_l = cell(dim,1);
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86 obj.e_r = cell(dim,1);
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87 obj.d1_l = cell(dim,1);
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88 obj.d1_r = cell(dim,1);
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89
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90 % D1
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91 obj.D1{1} = kron(D1{1},I{2});
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92 obj.D1{2} = kron(I{1},D1{2});
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93
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94 % Boundary operators
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95 obj.e_l{1} = kron(e_l{1},I{2});
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96 obj.e_l{2} = kron(I{1},e_l{2});
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97 obj.e_r{1} = kron(e_r{1},I{2});
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98 obj.e_r{2} = kron(I{1},e_r{2});
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99
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100 obj.d1_l{1} = kron(d1_l{1},I{2});
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101 obj.d1_l{2} = kron(I{1},d1_l{2});
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102 obj.d1_r{1} = kron(d1_r{1},I{2});
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103 obj.d1_r{2} = kron(I{1},d1_r{2});
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104
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105 % D2
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106 for i = 1:dim
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107 obj.D2{i} = sparse(m_tot);
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108 end
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109 ind = grid.funcToMatrix(g, 1:m_tot);
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110
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111 for i = 1:m(2)
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112 D = D2{1}(a(ind(:,i)));
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113 p = ind(:,i);
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114 obj.D2{1}(p,p) = D;
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115 end
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116
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117 for i = 1:m(1)
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118 D = D2{2}(a(ind(i,:)));
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119 p = ind(i,:);
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120 obj.D2{2}(p,p) = D;
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121 end
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122
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123 % Quadratures
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124 obj.H = kron(H{1},H{2});
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125 obj.Hi = inv(obj.H);
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126 obj.H_boundary = cell(dim,1);
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127 obj.H_boundary{1} = H{2};
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128 obj.H_boundary{2} = H{1};
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129
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130 % Boundary coefficient matrices and quadratures
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131 obj.A_boundary_l = cell(dim,1);
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132 obj.A_boundary_r = cell(dim,1);
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133 for i = 1:dim
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134 obj.A_boundary_l{i} = obj.e_l{i}'*A*obj.e_l{i};
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135 obj.A_boundary_r{i} = obj.e_r{i}'*A*obj.e_r{i};
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
136 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 % E{i}^T picks out component i.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 E = cell(dim,1);
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
140 I = speye(m_tot,m_tot);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 for i = 1:dim
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 e = sparse(dim,1);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 e(i) = 1;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
144 E{i} = kron(I,e);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 obj.E = E;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148 % Differentiation matrix D (without SAT)
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
149 D2 = obj.D2;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
150 D1 = obj.D1;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
151 D = sparse(dim*m_tot,dim*m_tot);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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parents:
diff changeset
152 d = @kroneckerDelta; % Kronecker delta
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
153 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 for i = 1:dim
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 for j = 1:dim
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
156 D = D + E{i}*inv(RHO)*( d(i,j)*D2{i}*E{j}' +...
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 db(i,j)*D1{j}*A*D1{i}*E{j}' + ...
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 D2{j}*E{i}' ...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 );
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 obj.D = D;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 %=========================================%
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
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164
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 % Misc.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 obj.m = m;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 obj.h = h;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 obj.order = order;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 obj.grid = g;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
170 obj.dim = dim;
663
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 % obj.gamm_u = h_u*ops_u.borrowing.M.d1;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 % obj.gamm_v = h_v*ops_v.borrowing.M.d1;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 % Closure functions return the operators applied to the own domain to close the boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 % type is a string specifying the type of boundary condition if there are several.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 % data is a function returning the data that should be applied at the boundary.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 % neighbour_scheme is an instance of Scheme that should be interfaced to.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 % neighbour_boundary is a string specifying which boundary to interface to.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 default_arg('type','free');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 default_arg('parameter', []);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 delta = @kroneckerDelta; % Kronecker delta
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
189 delta_b = @(i,j) 1-delta(i,j); % Logical not of Kronecker delta
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 % j is the coordinate direction of the boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 % nj: outward unit normal component.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 % nj = -1 for west, south, bottom boundaries
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 % nj = 1 for east, north, top boundaries
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 [j, nj] = obj.get_boundary_number(boundary);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 switch nj
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 case 1
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 e = obj.e_r;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
199 d = obj.d1_r;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 case -1
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 e = obj.e_l;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
202 d = obj.d1_l;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 E = obj.E;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 Hi = obj.Hi;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 H_gamma = obj.H_boundary{j};
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 A = obj.A;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
209 RHO = obj.RHO;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
210 D1 = obj.D1;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 switch type
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 % Dirichlet boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 case {'D','d','dirichlet'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 error('Dirichlet not implemented')
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 b1 = gamm*obj.lambda./obj.a11.^2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 b2 = gamm*obj.lambda./obj.a22.^2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 tau1 = tuning * spdiag(-1./b1 - 1./b2);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 tau2 = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 tau = (tau1*e + tau2*d)*H_b;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 closure = obj.a*obj.Hi*tau*e';
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 penalty = -obj.a*obj.Hi*tau;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 % Free boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 case {'F','f','Free','free'}
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
233 closure = sparse(obj.dim*obj.grid.N,obj.dim*obj.grid.N);
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
234 penalty = sparse(obj.dim*obj.grid.N,obj.dim*obj.grid.N);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 % Loop over components
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
236 for i = 1:obj.dim
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
237 closure = closure + E{i}*inv(RHO)*(-nj)*Hi*e{j}*H_gamma*(...
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 e{j}'*A*e{j}*d{j}'*E{i}' + ...
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
239 delta(i,j)*e{j}'*A*e{i}*d{i}'*E{j}' + ...
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
240 delta_b(i,j)*e{j}'*A*D1{i}*E{j}' ...
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 );
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
242 penalty = penalty - E{i}*inv(RHO)*(-nj)*Hi*e{j}*H_gamma*e{j}'*E{j}';
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
245
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 % Unknown boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 otherwise
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 error('No such boundary condition: type = %s',type);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 % u denotes the solution in the own domain
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 % v denotes the solution in the neighbour domain
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 error('Interface not implemented');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
260 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 function [j, nj] = get_boundary_number(obj, boundary)
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 switch boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 j = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 j = 2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 otherwise
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 error('No such boundary: boundary = %s',boundary);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 switch boundary
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273 case {'w','W','west','West','s','S','south','South'}
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274 nj = -1;
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275 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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276 nj = 1;
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277 end
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278 end
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279
664
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280 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
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281 function [return_op] = get_boundary_operator(obj, op, boundary)
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282
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283 switch boundary
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284 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
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285 j = 1;
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286 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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287 j = 2;
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288 otherwise
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289 error('No such boundary: boundary = %s',boundary);
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290 end
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291
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292 switch op
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293 case 'e'
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294 switch boundary
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295 case {'w','W','west','West','s','S','south','South'}
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296 return_op = obj.e_l{j};
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297 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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298 return_op = obj.e_r{j};
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299 end
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300 case 'd'
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301 switch boundary
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302 case {'w','W','west','West','s','S','south','South'}
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303 return_op = obj.d_l{j};
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304 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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305 return_op = obj.d_r{j};
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306 end
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307 otherwise
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308 error(['No such operator: operatr = ' op]);
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309 end
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310
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311 end
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312
663
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313 function N = size(obj)
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314 N = prod(obj.m);
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315 end
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316 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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317 end