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First implementation of elastic shear operator with free boundary BC.
author Martin Almquist <malmquist@stanford.edu>
date Thu, 14 Dec 2017 13:54:20 -0800
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children 8e6dfd22fc59
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663
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
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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
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8 order % Order accuracy for the approximation
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9
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10 a % Variable coefficient lambda of the operator
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11 rho % Density
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12
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13 D % Total operator
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14 D1 % First derivatives
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15 D2 % Second derivatives
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16 H, Hi % Inner products
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17 e_l, e_r
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18 d_l, d_r % Normal derivatives at the boundary
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19 H_boundary % Boundary inner products
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20 end
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21
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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22 methods
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
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23 % Implements the shear part of the elastic wave equation, i.e.
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24 % rho u_{i,tt} = d_i a d_j u_j + d_j a d_j u_i
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25 % where a = lambda.
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26
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27 function obj = elasticShearVariable(g ,order, a_fun, rho_fun, opSet)
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28 default_arg('opSet',@sbp.D2Variable);
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29 default_arg('a_fun', @(x,y) 0*x+1);
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30 default_arg('rho_fun', @(x,y) 0*x+1);
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31 dim = 2;
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32
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33 assert(isa(g, 'grid.Cartesian'))
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34
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35 a = grid.evalOn(g, a_fun);
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36 rho = grid.evalOn(g, rho_fun);
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37 m = g.size();
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38 m_tot = g.N();
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39
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40 h = g.scaling();
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41
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42 % 1D operators
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43 ops = cell(dim,1);
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44 for i = 1:dim
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45 ops{i} = opSet(m(i), {0, 1}, order);
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46 end
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47
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48 I = cell(dim,1);
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49 D1 = cell(dim,1);
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50 D2 = cell(dim,1);
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51 H = cell(dim,1);
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52 Hi = cell(dim,1);
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53 e_l = cell(dim,1);
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54 e_r = cell(dim,1);
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55 d1_l = cell(dim,1);
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56 d1_r = cell(dim,1);
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57
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58 for i = 1:dim
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59 I{i} = speye{m(i));
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60 D1{i} = ops{i}.D1;
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61 D2{i} = ops{i}.D2;
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62 H{i} = ops{i}.H;
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63 Hi{i} = ops{i}.HI;
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64 e_l{i} = ops{i}.e_l;
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65 e_r{i} = ops{i}.e_r;
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66 d1_l{i} = ops{i}.d1_l;
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67 d1_r{i} = ops{i}.d1_r;
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68 end
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69
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70 %====== Assemble full operators ========
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71 A = spdiag(a);
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72 RHO = spdiag(rho);
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73
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74 obj.D1 = cell(dim,1);
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75 obj.D2 = cell(dim,1);
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76 obj.e_l = cell(dim,1);
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77 obj.e_r = cell(dim,1);
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78 obj.d1_l = cell(dim,1);
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79 obj.d1_r = cell(dim,1);
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80
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81 % D1
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82 obj.D1{1} = kron{D1{1},I(2)};
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83 obj.D1{2} = kron{I{1},D1(2)};
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84
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85 % Boundary operators
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86 obj.e_l{1} = kron{e_l{1},I(2)};
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87 obj.e_l{2} = kron{I{1},e_l(2)};
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88 obj.e_r{1} = kron{e_r{1},I(2)};
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89 obj.e_r{2} = kron{I{1},e_r(2)};
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90
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91 obj.d1_l{1} = kron{d1_l{1},I(2)};
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92 obj.d1_l{2} = kron{I{1},d1_l(2)};
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93 obj.d1_r{1} = kron{d1_r{1},I(2)};
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94 obj.d1_r{2} = kron{I{1},d1_r(2)};
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95
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96 % D2
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97 for i = 1:dim
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98 obj.D2{i} = sparse(m_tot);
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99 end
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100 ind = grid.funcToMatrix(g, 1:m_tot);
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101
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102 for i = 1:m(2)
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103 D = D2{1}(a(ind(:,i)));
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104 p = ind(:,i);
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105 obj.D2{1}(p,p) = D;
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106 end
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107
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108 for i = 1:m(1)
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109 D = D2{2}(a(ind(i,:)));
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110 p = ind(i,:);
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111 obj.D2{2}(p,p) = D;
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112 end
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113
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114 % Quadratures
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115 obj.H = kron(H{1},H{2});
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116 obj.H_boundary = cell(dim,1);
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117 obj.H_boundary{1} = H{2};
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118 obj.H_boundary{2} = H{1};
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119
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120 % Boundary coefficient matrices and quadratures
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121 obj.A_boundary_l = cell(dim,1);
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122 obj.A_boundary_r = cell(dim,1);
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123 for i = 1:dim
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124 obj.A_boundary_l{i} = e_l{i}'*A*e_l{i};
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125 obj.A_boundary_r{i} = e_r{i}'*A*e_r{i};
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126 end
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127
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128 % E{i}^T picks out component i.
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129 E = cell(dim,1);
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130 I = speye{mtot,mtot};
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131 for i = 1:dim
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132 e = sparse(dim,1);
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133 e(i) = 1;
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134 E{i} = kron(e,I)
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135 end
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136 obj.E = E;
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137
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138 % Differentiation matrix D (without SAT)
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 D = 0;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 d = @kroneckerDelta; % Kronecker delta
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 db = @(i,j) 1-dij(i,j); % Logical not of Kronecker delta
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 for i = 1:dim
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 for j = 1:dim
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 D = D + E{i}*inv(rho)*( d(i,j)*D2{i}*E{j}' +...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145 db(i,j)*D1{j}*A*D1{i}*E{j}' + ...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 D2{j}*E{i}' ...
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 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 obj.D = D;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151 %=========================================%
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 % Misc.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 obj.m = m;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 obj.h = h;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 obj.order = order;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 obj.grid = g;
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 obj.a = a;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 obj.b = b;
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:
diff changeset
164 % obj.gamm_u = h_u*ops_u.borrowing.M.d1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 % obj.gamm_v = h_v*ops_v.borrowing.M.d1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 % 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
170 % 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
171 % 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
172 % 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
173 % 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
174 % 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
175 % 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
176 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
177 default_arg('type','free');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 default_arg('parameter', []);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 delta = @kroneckerDelta; % Kronecker delta
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 delta_b = @(i,j) 1-dij(i,j); % Logical not of Kronecker delta
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 % 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
184 % nj: outward unit normal component.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 % 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
186 % 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
187 [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
188 switch nj
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 case 1
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 e = obj.e_r;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 d = obj.d_r;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 case -1
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 e = obj.e_l;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 d = obj.d_l;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 E = obj.E;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 Hi = obj.Hi;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 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
200 A = obj.A;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 switch type
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 % Dirichlet boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 case {'D','d','dirichlet'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 error('Dirichlet not implemented')
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 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
210 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
211
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 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
213 tau2 = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 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
216
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 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
218 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
219
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 % Free boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 case {'F','f','Free','free'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 closure = 0;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 penalty = 0;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 % Loop over components
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 for i = 1:3
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 closure = closure + E{i}*(-sign)*Hi*e{j}*H_gamma*(...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 e{j}'*A*e{j}*d{j}'*E{i}' + ...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 delta(i,j)*e{j}'*A*e{i}*d{i}*E{j}' + ...
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 delta_b(i,j)*A*D1{i}*E{j}' ...
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 penalty = penalty - E{i}*(-sign)*Hi*e{j}*H_gamma;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 % Unknown boundary condition
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 otherwise
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 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
238 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 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
242 % 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
243 % 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
244 tuning = 1.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 % tuning = 20.2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 error('Interface not implemented');
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 % Ruturns the coordinate number and outward normal component for the boundary specified by the string boundary.
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 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
251
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 switch boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 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
254 j = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 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
256 j = 2;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 otherwise
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 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
259 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 switch boundary
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 case {'w','W','west','West','s','S','south','South'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 nj = -1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 nj = 1;
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 function N = size(obj)
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 N = prod(obj.m);
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 end
b45ec2b28cc2 First implementation of elastic shear operator with free boundary BC.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 end