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annotate +scheme/elasticDilationVariable.m @ 678:06676c40e77f feature/poroelastic

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Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 05 Feb 2018 11:06:15 -0800
parents 9926efb39330
children
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1 classdef elasticDilationVariable < 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, RHOi % Density (as diagonal matrix here)
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13
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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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 Div % Divergence operator used for BC
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18 H, Hi % Inner products
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19 phi % Borrowing constant for (d1 - e^T*D1) from R
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20 H11 % First element of H
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21 e_l, e_r
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22 d1_l, d1_r % Normal derivatives at the boundary
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23 E % E{i}^T picks out component i
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24
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25 H_boundary % Boundary inner products
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26
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27 A_boundary_l % Variable coefficient at boundaries
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28 A_boundary_r %
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29
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30 % Kroneckered norms and coefficients
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31 RHOi_kron
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32 Hi_kron
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33 end
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34
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35 methods
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36 % Implements the shear part of the elastic wave equation, i.e.
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37 % rho u_{i,tt} = d_i a d_j u_j + d_j a d_j u_i
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38 % where a = mu.
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39
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40 function obj = elasticDilationVariable(g ,order, a_fun, rho_fun, opSet)
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41 default_arg('opSet',@sbp.D2Variable);
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42 default_arg('a_fun', @(x,y) 0*x+1);
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43 default_arg('rho_fun', @(x,y) 0*x+1);
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44 dim = 2;
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45
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46 assert(isa(g, 'grid.Cartesian'))
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47
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48 a = grid.evalOn(g, a_fun);
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49 rho = grid.evalOn(g, rho_fun);
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50 m = g.size();
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51 m_tot = g.N();
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52
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53 h = g.scaling();
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54 L = (m-1).*h;
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55
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56 % 1D operators
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57 ops = cell(dim,1);
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58 for i = 1:dim
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59 ops{i} = opSet(m(i), {0, L(i)}, order);
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60 end
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61
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62 % Borrowing constants
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63 beta = ops{1}.borrowing.R.delta_D;
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64 obj.H11 = ops{1}.borrowing.H11;
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65 obj.phi = beta/obj.H11;
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66
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67 I = cell(dim,1);
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68 D1 = cell(dim,1);
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69 D2 = cell(dim,1);
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70 H = cell(dim,1);
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71 Hi = cell(dim,1);
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72 e_l = cell(dim,1);
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73 e_r = cell(dim,1);
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74 d1_l = cell(dim,1);
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75 d1_r = cell(dim,1);
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76
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77 for i = 1:dim
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78 I{i} = speye(m(i));
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79 D1{i} = ops{i}.D1;
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80 D2{i} = ops{i}.D2;
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81 H{i} = ops{i}.H;
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82 Hi{i} = ops{i}.HI;
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83 e_l{i} = ops{i}.e_l;
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84 e_r{i} = ops{i}.e_r;
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85 d1_l{i} = ops{i}.d1_l;
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86 d1_r{i} = ops{i}.d1_r;
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87 end
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88
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89 %====== Assemble full operators ========
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90 A = spdiag(a);
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91 obj.A = A;
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92 RHO = spdiag(rho);
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93 obj.RHO = RHO;
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94 obj.RHOi = inv(RHO);
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95
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96 obj.D1 = cell(dim,1);
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97 obj.D2 = cell(dim,1);
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98 obj.e_l = cell(dim,1);
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99 obj.e_r = cell(dim,1);
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100 obj.d1_l = cell(dim,1);
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101 obj.d1_r = cell(dim,1);
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102
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103 % D1
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104 obj.D1{1} = kron(D1{1},I{2});
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105 obj.D1{2} = kron(I{1},D1{2});
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106
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107 % Boundary operators
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108 obj.e_l{1} = kron(e_l{1},I{2});
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109 obj.e_l{2} = kron(I{1},e_l{2});
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110 obj.e_r{1} = kron(e_r{1},I{2});
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111 obj.e_r{2} = kron(I{1},e_r{2});
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112
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113 obj.d1_l{1} = kron(d1_l{1},I{2});
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114 obj.d1_l{2} = kron(I{1},d1_l{2});
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115 obj.d1_r{1} = kron(d1_r{1},I{2});
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116 obj.d1_r{2} = kron(I{1},d1_r{2});
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117
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118 % D2
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119 for i = 1:dim
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120 obj.D2{i} = sparse(m_tot);
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121 end
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122 ind = grid.funcToMatrix(g, 1:m_tot);
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123
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124 for i = 1:m(2)
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125 D = D2{1}(a(ind(:,i)));
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126 p = ind(:,i);
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127 obj.D2{1}(p,p) = D;
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128 end
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129
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130 for i = 1:m(1)
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131 D = D2{2}(a(ind(i,:)));
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132 p = ind(i,:);
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133 obj.D2{2}(p,p) = D;
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134 end
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135
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136 % Quadratures
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137 obj.H = kron(H{1},H{2});
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 obj.Hi = inv(obj.H);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 obj.H_boundary = cell(dim,1);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 obj.H_boundary{1} = H{2};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 obj.H_boundary{2} = H{1};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 % Boundary coefficient matrices and quadratures
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 obj.A_boundary_l = cell(dim,1);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145 obj.A_boundary_r = cell(dim,1);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 for i = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 obj.A_boundary_l{i} = obj.e_l{i}'*A*obj.e_l{i};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148 obj.A_boundary_r{i} = obj.e_r{i}'*A*obj.e_r{i};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151 % E{i}^T picks out component i.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 E = cell(dim,1);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 I = speye(m_tot,m_tot);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 for i = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 e = sparse(dim,1);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 e(i) = 1;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 E{i} = kron(I,e);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 obj.E = E;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 % Differentiation matrix D (without SAT)
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 D2 = obj.D2;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 D1 = obj.D1;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 D = sparse(dim*m_tot,dim*m_tot);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 d = @kroneckerDelta; % Kronecker delta
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 for i = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 for j = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 D = D + E{i}*inv(RHO)*( d(i,j)*D2{i}*E{j}' +...
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 db(i,j)*D1{i}*A*D1{j}*E{j}' ...
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 );
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 obj.D = D;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 %=========================================%
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 % Divergence operator for BC
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 Div = cell(dim,1);
675
90bf651abc7c Add Dirichlet BC to dilation. Stable with variable coeff and conv study yields p+1/2 which probably is ok.
Martin Almquist <malmquist@stanford.edu>
parents: 674
diff changeset
179 % Loop over boundaries
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 for i = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 Div{i} = sparse(m_tot,dim*m_tot);
675
90bf651abc7c Add Dirichlet BC to dilation. Stable with variable coeff and conv study yields p+1/2 which probably is ok.
Martin Almquist <malmquist@stanford.edu>
parents: 674
diff changeset
182 % Loop over components
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 for j = 1:dim
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 Div{i} = Div{i} + d(i,j)*(obj.e_l{i}*obj.d1_l{i}' + obj.e_r{i}*obj.d1_r{i}')*E{j}' ...
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 + db(i,j)*obj.D1{j}*E{j}';
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 obj.Div = Div;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
190 % Kroneckered norms and coefficients
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
191 I_dim = speye(dim);
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
192 obj.RHOi_kron = kron(obj.RHOi, I_dim);
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
193 obj.Hi_kron = kron(obj.Hi, I_dim);
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
194
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 % Misc.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 obj.m = m;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 obj.h = h;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 obj.order = order;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 obj.grid = g;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 obj.dim = dim;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 % Closure functions return the operators applied to the own domain to close the boundary
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 % type is a string specifying the type of boundary condition if there are several.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 % data is a function returning the data that should be applied at the boundary.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 % neighbour_scheme is an instance of Scheme that should be interfaced to.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 % neighbour_boundary is a string specifying which boundary to interface to.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 default_arg('type','free');
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 default_arg('parameter', []);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 % j is the coordinate direction of the boundary
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 % nj: outward unit normal component.
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 % nj = -1 for west, south, bottom boundaries
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 % nj = 1 for east, north, top boundaries
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 [j, nj] = obj.get_boundary_number(boundary);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 switch nj
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 case 1
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 e = obj.e_r;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 d = obj.d1_r;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 case -1
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 e = obj.e_l;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 d = obj.d1_l;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 E = obj.E;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 Hi = obj.Hi;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 H_gamma = obj.H_boundary{j};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 A = obj.A;
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
234 RHOi = obj.RHOi;
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 phi = obj.phi;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 H11 = obj.H11;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 h = obj.h;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
240 RHOi_kron = obj.RHOi_kron;
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
241 Hi_kron = obj.Hi_kron;
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
242
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
243 % Divergence operator
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
244 Div = obj.Div{j};
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
245
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 switch type
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 % Dirichlet boundary condition
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 case {'D','d','dirichlet'}
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 tuning = 1.2;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 phi = obj.phi;
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
252 sigma = tuning * obj.dim/(H11*h(j)) +...
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
253 tuning * 1/(H11*h(j)*phi);
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
255 closure = - sigma*E{j}*RHOi*Hi*A*e{j}*H_gamma*e{j}'*E{j}' ...
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
256 + nj*RHOi_kron*Hi_kron*Div'*A*e{j}*H_gamma*e{j}'*E{j}';
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
258 penalty = + sigma*E{j}*RHOi*Hi*A*e{j}*H_gamma ...
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
259 - nj*RHOi_kron*Hi_kron*Div'*A*e{j}*H_gamma;
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 % Free boundary condition
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 case {'F','f','Free','free'}
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
264 closure = -nj*E{j}*RHOi*Hi*e{j} ...
675
90bf651abc7c Add Dirichlet BC to dilation. Stable with variable coeff and conv study yields p+1/2 which probably is ok.
Martin Almquist <malmquist@stanford.edu>
parents: 674
diff changeset
265 *H_gamma*e{j}'*A*e{j}*e{j}'*Div;
676
9926efb39330 Clean up dilation BC code.
Martin Almquist <malmquist@stanford.edu>
parents: 675
diff changeset
266 penalty = nj*E{j}*RHOi*Hi*e{j} ...
675
90bf651abc7c Add Dirichlet BC to dilation. Stable with variable coeff and conv study yields p+1/2 which probably is ok.
Martin Almquist <malmquist@stanford.edu>
parents: 674
diff changeset
267 *H_gamma*e{j}'*A*e{j};
674
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 % Unknown boundary condition
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 otherwise
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 error('No such boundary condition: type = %s',type);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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275
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276 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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277 % u denotes the solution in the own domain
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278 % v denotes the solution in the neighbour domain
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279 tuning = 1.2;
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280 % tuning = 20.2;
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281 error('Interface not implemented');
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282 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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283
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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284 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
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285 function [j, nj] = get_boundary_number(obj, boundary)
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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286
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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287 switch boundary
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288 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
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289 j = 1;
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290 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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291 j = 2;
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292 otherwise
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293 error('No such boundary: boundary = %s',boundary);
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294 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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295
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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296 switch boundary
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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297 case {'w','W','west','West','s','S','south','South'}
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298 nj = -1;
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299 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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300 nj = 1;
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301 end
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302 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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303
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304 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
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305 function [return_op] = get_boundary_operator(obj, op, boundary)
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306
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307 switch boundary
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308 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
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309 j = 1;
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310 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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311 j = 2;
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312 otherwise
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313 error('No such boundary: boundary = %s',boundary);
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314 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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315
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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316 switch op
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317 case 'e'
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318 switch boundary
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319 case {'w','W','west','West','s','S','south','South'}
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320 return_op = obj.e_l{j};
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321 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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322 return_op = obj.e_r{j};
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323 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
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324 case 'd'
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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325 switch boundary
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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326 case {'w','W','west','West','s','S','south','South'}
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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327 return_op = obj.d_l{j};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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parents:
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328 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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329 return_op = obj.d_r{j};
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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parents:
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330 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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331 otherwise
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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332 error(['No such operator: operatr = ' op]);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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parents:
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333 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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334
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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335 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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336
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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337 function N = size(obj)
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
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338 N = prod(obj.m);
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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339 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
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340 end
dd84b8862aa8 First implementation of elastic dilation variable. Constant coeff is stable.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 end