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annotate +scheme/elasticShearVariable.m @ 667:ed853945ee99 feature/poroelastic

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Make free BC work with data. Bugfix domain size.
author Martin Almquist <malmquist@stanford.edu>
date Wed, 20 Dec 2017 06:52:17 +0100
parents 8e6dfd22fc59
children 17e62551cdc2
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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 L = (m-1).*h;
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48
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49 % 1D operators
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50 ops = cell(dim,1);
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51 for i = 1:dim
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52 ops{i} = opSet(m(i), {0, L(i)}, order);
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53 end
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54
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55 I = cell(dim,1);
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56 D1 = cell(dim,1);
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57 D2 = cell(dim,1);
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58 H = cell(dim,1);
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59 Hi = cell(dim,1);
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60 e_l = cell(dim,1);
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61 e_r = cell(dim,1);
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62 d1_l = cell(dim,1);
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63 d1_r = cell(dim,1);
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64
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65 for i = 1:dim
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66 I{i} = speye(m(i));
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67 D1{i} = ops{i}.D1;
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68 D2{i} = ops{i}.D2;
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69 H{i} = ops{i}.H;
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70 Hi{i} = ops{i}.HI;
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71 e_l{i} = ops{i}.e_l;
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72 e_r{i} = ops{i}.e_r;
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73 d1_l{i} = ops{i}.d1_l;
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74 d1_r{i} = ops{i}.d1_r;
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75 end
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76
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77 %====== Assemble full operators ========
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78 A = spdiag(a);
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79 obj.A = A;
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80 RHO = spdiag(rho);
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81 obj.RHO = RHO;
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82
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83
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84 obj.D1 = cell(dim,1);
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85 obj.D2 = cell(dim,1);
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86 obj.e_l = cell(dim,1);
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87 obj.e_r = cell(dim,1);
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88 obj.d1_l = cell(dim,1);
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89 obj.d1_r = cell(dim,1);
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90
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91 % D1
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92 obj.D1{1} = kron(D1{1},I{2});
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93 obj.D1{2} = kron(I{1},D1{2});
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94
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95 % Boundary operators
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96 obj.e_l{1} = kron(e_l{1},I{2});
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97 obj.e_l{2} = kron(I{1},e_l{2});
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98 obj.e_r{1} = kron(e_r{1},I{2});
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99 obj.e_r{2} = kron(I{1},e_r{2});
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100
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101 obj.d1_l{1} = kron(d1_l{1},I{2});
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102 obj.d1_l{2} = kron(I{1},d1_l{2});
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103 obj.d1_r{1} = kron(d1_r{1},I{2});
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104 obj.d1_r{2} = kron(I{1},d1_r{2});
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105
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106 % D2
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107 for i = 1:dim
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108 obj.D2{i} = sparse(m_tot);
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109 end
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110 ind = grid.funcToMatrix(g, 1:m_tot);
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111
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112 for i = 1:m(2)
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113 D = D2{1}(a(ind(:,i)));
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114 p = ind(:,i);
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115 obj.D2{1}(p,p) = D;
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116 end
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117
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118 for i = 1:m(1)
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119 D = D2{2}(a(ind(i,:)));
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120 p = ind(i,:);
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121 obj.D2{2}(p,p) = D;
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122 end
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123
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124 % Quadratures
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125 obj.H = kron(H{1},H{2});
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126 obj.Hi = inv(obj.H);
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127 obj.H_boundary = cell(dim,1);
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128 obj.H_boundary{1} = H{2};
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129 obj.H_boundary{2} = H{1};
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130
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131 % Boundary coefficient matrices and quadratures
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132 obj.A_boundary_l = cell(dim,1);
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133 obj.A_boundary_r = cell(dim,1);
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134 for i = 1:dim
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135 obj.A_boundary_l{i} = obj.e_l{i}'*A*obj.e_l{i};
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Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
136 obj.A_boundary_r{i} = obj.e_r{i}'*A*obj.e_r{i};
663
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 % 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
140 E = cell(dim,1);
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
141 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
142 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 e = sparse(dim,1);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 e(i) = 1;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
145 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
146 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 obj.E = E;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 % Differentiation matrix D (without SAT)
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
150 D2 = obj.D2;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
151 D1 = obj.D1;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
152 D = sparse(dim*m_tot,dim*m_tot);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 d = @kroneckerDelta; % Kronecker delta
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
154 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
155 for i = 1:dim
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 for j = 1:dim
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
157 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
158 db(i,j)*D1{j}*A*D1{i}*E{j}' + ...
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 D2{j}*E{i}' ...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 );
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 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 obj.D = D;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 %=========================================%
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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parents:
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165
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 % Misc.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 obj.m = m;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 obj.h = h;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 obj.order = order;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 obj.grid = g;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
171 obj.dim = dim;
663
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parents:
diff changeset
172
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 % obj.gamm_u = h_u*ops_u.borrowing.M.d1;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 % obj.gamm_v = h_v*ops_v.borrowing.M.d1;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 end
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
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 % Closure functions return the operators applied to the own domain to close the boundary
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 % 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
180 % 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
181 % 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
182 % 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
183 % 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
184 % 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
185 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
186 default_arg('type','free');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 default_arg('parameter', []);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 delta = @kroneckerDelta; % Kronecker delta
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
190 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
191
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 % 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
193 % nj: outward unit normal component.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 % 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
195 % 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
196 [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
197 switch nj
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 case 1
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 e = obj.e_r;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
200 d = obj.d1_r;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 case -1
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 e = obj.e_l;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
203 d = obj.d1_l;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 E = obj.E;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 Hi = obj.Hi;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 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
209 A = obj.A;
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
210 RHO = obj.RHO;
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
211 D1 = obj.D1;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 switch type
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 % Dirichlet boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 case {'D','d','dirichlet'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 error('Dirichlet not implemented')
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 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
221 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
222
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 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
224 tau2 = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 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
227
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 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
229 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
230
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 % Free boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 case {'F','f','Free','free'}
667
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
234 closures = cell(obj.dim,1);
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
235 penalties = cell(obj.dim,1);
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 % Loop over components
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
237 for i = 1:obj.dim
667
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
238 closures{i} = 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
239 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
240 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
241 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
242 );
667
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
243 penalties{i} = - 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
244 end
667
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
245 [rows, cols] = size(closures{1});
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
246 closure = sparse(rows, cols);
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
247 for i = 1:obj.dim
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
248 closure = closure + closures{i};
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
249 end
ed853945ee99 Make free BC work with data. Bugfix domain size.
Martin Almquist <malmquist@stanford.edu>
parents: 664
diff changeset
250 penalty = penalties;
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
252
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 % Unknown boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 otherwise
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 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
256 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 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
260 % 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
261 % 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
262 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 error('Interface not implemented');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266
664
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
Martin Almquist <malmquist@stanford.edu>
parents: 663
diff changeset
267 % 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
268 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
269
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 switch boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 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
272 j = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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273 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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274 j = 2;
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275 otherwise
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276 error('No such boundary: boundary = %s',boundary);
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277 end
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278
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279 switch boundary
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280 case {'w','W','west','West','s','S','south','South'}
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281 nj = -1;
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282 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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283 nj = 1;
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284 end
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285 end
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286
664
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287 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
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288 function [return_op] = get_boundary_operator(obj, op, boundary)
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289
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290 switch boundary
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291 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
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292 j = 1;
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293 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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294 j = 2;
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295 otherwise
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296 error('No such boundary: boundary = %s',boundary);
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297 end
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298
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299 switch op
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300 case 'e'
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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.e_l{j};
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304 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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305 return_op = obj.e_r{j};
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306 end
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307 case 'd'
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308 switch boundary
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309 case {'w','W','west','West','s','S','south','South'}
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310 return_op = obj.d_l{j};
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311 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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312 return_op = obj.d_r{j};
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313 end
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314 otherwise
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315 error(['No such operator: operatr = ' op]);
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316 end
8e6dfd22fc59 Free BC now yields symmetric negative semidefinite discretization.
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317
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318 end
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319
663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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320 function N = size(obj)
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321 N = prod(obj.m);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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322 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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323 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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parents:
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324 end