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annotate +scheme/Staggered1DAcousticsVariable.m @ 761:8ed102db8e9c feature/d1_staggered

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Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 18 Jun 2018 16:36:24 -0700
parents ec0ac76006e2
children 18e10217dca9
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef Staggered1DAcousticsVariable < scheme.Scheme
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2 properties
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3 m % Number of points of primal grid in each direction, possibly a vector
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4 h % Grid spacing
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5
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6 % Grids
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7 grid % Total grid object
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8 grid_primal
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9 grid_dual
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10
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11 order % Order accuracy for the approximation
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12
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13 H % Combined norm
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14 Hi % Inverse
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15 D % Semi-discrete approximation matrix
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16
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17 D1_primal
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18 D1_dual
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19
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20 % Pick out left or right boundary
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21 e_l
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22 e_r
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23
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24 % Initial data
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25 v0
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26
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27 % Pick out primal or dual component
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28 e_primal
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29 e_dual
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30
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31 % System matrices, cell matrices of function handles
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32 A
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33 B
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34
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35 % Variable coefficient matrices evaluated at boundaries.
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36 A_l, A_r
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37 B_l, B_r
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38 end
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39
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40
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41 methods
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42 % Scheme for A*u_t + B u_x = 0,
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43 % u = [p, v];
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44 % A: Diagonal and A > 0,
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45 % A = [a1, 0;
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46 % 0, a2]
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47 %
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48 % B = B^T and with diagonal entries = 0.
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49 % B = [0 b
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50 % b 0]
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51 % Here we store p on the primal grid and v on the dual
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52 % A and B are cell matrices of function handles
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53 function obj = Staggered1DAcousticsVariable(g, order, A, B)
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54 default_arg('B',{@(x)0*x, @(x)0*x+1; @(x)0*x+1, @(x)0*x});
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55 default_arg('A',{@(x)0*x+1, @(x)0*x; @(x)0*x, @(x)0*x+1});
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56
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57 obj.order = order;
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58 obj.A = A;
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59 obj.B = B;
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60
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61 % Grids
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62 obj.m = g.size();
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Martin Almquist <malmquist@stanford.edu>
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63 xl = g.getBoundary('l');
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64 xr = g.getBoundary('r');
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65 xlim = {xl, xr};
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66 obj.grid = g;
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67 obj.grid_primal = g.grids{1};
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68 obj.grid_dual = g.grids{2};
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69 x_primal = obj.grid_primal.points();
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70 x_dual = obj.grid_dual.points();
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71
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72 % Boundary matrices
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73 obj.A_l = [A{1,1}(xl), A{1,2}(xl);....
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74 A{2,1}(xl), A{2,2}(xl)];
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75 obj.A_r = [A{1,1}(xr), A{1,2}(xr);....
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76 A{2,1}(xr), A{2,2}(xr)];
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77 obj.B_l = [B{1,1}(xl), B{1,2}(xl);....
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78 B{2,1}(xl), B{2,2}(xl)];
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79 obj.B_r = [B{1,1}(xr), B{1,2}(xr);....
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80 B{2,1}(xr), B{2,2}(xr)];
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81
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82 % Get operators
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83 ops = sbp.D1StaggeredUpwind(obj.m, xlim, order);
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84 obj.h = ops.h;
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85
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86 % Build combined operators
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87 H_primal = ops.H_primal;
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88 H_dual = ops.H_dual;
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89 obj.H = blockmatrix.toMatrix( {H_primal, []; [], H_dual } );
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90 obj.Hi = inv(obj.H);
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91
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92 D1_primal = ops.D1_primal;
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93 D1_dual = ops.D1_dual;
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94 A11_B12 = spdiag(-1./A{1,1}(x_primal).*B{1,2}(x_primal), 0);
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95 A22_B21 = spdiag(-1./A{2,2}(x_dual).*B{2,1}(x_dual), 0);
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96 D = {[], A11_B12*D1_primal;...
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97 A22_B21*D1_dual, []};
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98 obj.D = blockmatrix.toMatrix(D);
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99 obj.D1_primal = D1_primal;
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100 obj.D1_dual = D1_dual;
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101
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102 % Combined boundary operators
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103 e_primal_l = ops.e_primal_l;
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104 e_primal_r = ops.e_primal_r;
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105 e_dual_l = ops.e_dual_l;
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106 e_dual_r = ops.e_dual_r;
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107 e_l = {e_primal_l, [];...
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108 [] , e_dual_l};
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109 e_r = {e_primal_r, [];...
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110 [] , e_dual_r};
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111 obj.e_l = blockmatrix.toMatrix(e_l);
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112 obj.e_r = blockmatrix.toMatrix(e_r);
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113
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114 % Pick out first or second component of solution
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115 N_primal = obj.grid_primal.N();
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116 N_dual = obj.grid_dual.N();
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117 obj.e_primal = [speye(N_primal, N_primal); sparse(N_dual, N_primal)];
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118 obj.e_dual = [sparse(N_primal, N_dual); speye(N_dual, N_dual)];
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119
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120
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121 end
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122 % Closure functions return the operators applied to the own domain to close the boundary
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123 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
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124 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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125 % type is a string specifying the type of boundary condition if there are several.
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126 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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127 % neighbour_boundary is a string specifying which boundary to interface to.
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128 function [closure, penalty] = boundary_condition(obj, boundary, type)
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129
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130 default_arg('type','p');
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131
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132 % type = 'p' => boundary condition for p
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133 % type = 'v' => boundary condition for v
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
134 % No other types implemented yet
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
135
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
136 % BC on the form Lu - g = 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137
682
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
138 % Need a transformation T such that w = T^{−1}*u is a
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
139 % meaningful change of variables and T^T*B*T is block-diagonal,
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
140 % For linear acoustics, T = T_C meets these criteria.
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
141
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 % Get boundary matrices
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 case 'l'
653
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
145 A = obj.A_l;
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
146 B = obj.B_l;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 case 'r'
653
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
148 A = obj.A_r;
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
149 B = obj.B_r;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 end
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
151 C = inv(A)*B;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152
682
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
153 % Diagonalize C and use T_C to diagonalize B
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
154 [T, ~] = eig(C);
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
155 Lambda = T'*B*T;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 lambda = diag(Lambda);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 % Identify in- and outgoing characteristic variables
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 Iplus = lambda > 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 Iminus = lambda < 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 case 'l'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 Iin = Iplus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 case 'r'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 Iin = Iminus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 Tin = T(:,Iin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 switch type
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 case 'p'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 L = [1, 0];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 case 'v'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 L = [0, 1];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 case 'characteristic'
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
176 % Diagonalize C
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
177 [T_C, Lambda_C] = eig(C);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
178 lambda_C = diag(Lambda_C);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
179 % Identify in- and outgoing characteristic variables
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
180 Iplus = lambda_C > 0;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
181 Iminus = lambda_C < 0;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
182
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
183 switch boundary
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
184 case 'l'
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
185 Iin_C = Iplus;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
186 case 'r'
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
187 Iin_C = Iminus;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
188 end
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
189 T_C_inv = inv(T_C);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
190 L = T_C_inv(Iin_C,:);
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 otherwise
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 error('Boundary condition not implemented.');
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 % Penalty parameters
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 sigma = [0; 0];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 sigma(Iin) = lambda(Iin);
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
198
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
199 % Sparsify
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
200 A = sparse(A);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
201 T = sparse(T);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
202 sigma = sparse(sigma);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
203 L = sparse(L);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
204 Tin = sparse(Tin);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
205
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 case 'l'
682
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
208 tau = -1*obj.e_l * inv(A) * inv(T)' * sigma * inv(L*Tin);
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 closure = obj.Hi*tau*L*obj.e_l';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 case 'r'
682
ec0ac76006e2 Modify BC in Staggered 1D acoustics to ensure that only physically meaningful changes of variables are used. See hypsyst varcoeff sec 3.
Martin Almquist <malmquist@stanford.edu>
parents: 672
diff changeset
212 tau = 1*obj.e_r * inv(A) * inv(T)' * sigma * inv(L*Tin);
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 closure = obj.Hi*tau*L*obj.e_r';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 penalty = -obj.Hi*tau;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
221 % Uses the hat variable method for the interface coupling,
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
222 % see hypsyst_varcoeff.pdf in the hypsyst repository.
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
223 % Notation: u for left side of interface, v for right side.
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
226 % Get boundary matrices
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
227 switch boundary
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
228 case 'l'
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
229 A_v = obj.A_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
230 B_v = obj.B_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
231 Hi_v = obj.Hi;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
232 e_v = obj.e_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
233
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
234 A_u = neighbour_scheme.A_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
235 B_u = neighbour_scheme.B_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
236 Hi_u = neighbour_scheme.Hi;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
237 e_u = neighbour_scheme.e_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
238 case 'r'
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
239 A_u = obj.A_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
240 B_u = obj.B_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
241 Hi_u = obj.Hi;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
242 e_u = obj.e_r;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
243
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
244 A_v = neighbour_scheme.A_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
245 B_v = neighbour_scheme.B_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
246 Hi_v = neighbour_scheme.Hi;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
247 e_v = neighbour_scheme.e_l;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
248 end
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
249 C_u = inv(A_u)*B_u;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
250 C_v = inv(A_v)*B_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
251
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
252 % Diagonalize C
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
253 [T_u, ~] = eig(C_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
254 Lambda_u = inv(T_u)*C_u*T_u;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
255 lambda_u = diag(Lambda_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
256 S_u = inv(T_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
257
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
258 [T_v, ~] = eig(C_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
259 Lambda_v = inv(T_v)*C_v*T_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
260 lambda_v = diag(Lambda_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
261 S_v = inv(T_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
262
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
263 % Identify in- and outgoing characteristic variables
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
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264 Im_u = lambda_u < 0;
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265 Ip_u = lambda_u > 0;
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266 Im_v = lambda_v < 0;
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267 Ip_v = lambda_v > 0;
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268
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269 Tp_u = T_u(:,Ip_u);
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270 Tm_u = T_u(:,Im_u);
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271 Sp_u = S_u(Ip_u,:);
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272 Sm_u = S_u(Im_u,:);
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273
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274 Tp_v = T_v(:,Ip_v);
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275 Tm_v = T_v(:,Im_v);
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276 Sp_v = S_v(Ip_v,:);
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277 Sm_v = S_v(Im_v,:);
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278
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279 % Create S_tilde and T_tilde
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280 Stilde = [Sp_u; Sm_v];
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281 Ttilde = inv(Stilde);
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282 Ttilde_p = Ttilde(:,1);
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283 Ttilde_m = Ttilde(:,2);
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284
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285 % Solve for penalty parameters theta_1,2
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286 LHS = Ttilde_m*Sm_v*Tm_u;
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287 RHS = B_u*Tm_u;
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288 th_u = RHS./LHS;
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289 TH_u = diag(th_u);
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290
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291 LHS = Ttilde_p*Sp_u*Tp_v;
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292 RHS = -B_v*Tp_v;
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293 th_v = RHS./LHS;
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294 TH_v = diag(th_v);
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295
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296 % Construct penalty matrices
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297 Z_u = TH_u*Ttilde_m*Sm_v;
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298 Z_u = sparse(Z_u);
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299
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diff changeset
300 Z_v = TH_v*Ttilde_p*Sp_u;
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301 Z_v = sparse(Z_v);
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302
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diff changeset
303 closure_u = Hi_u*e_u*Z_u*e_u';
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diff changeset
304 penalty_u = -Hi_u*e_u*Z_u*e_v';
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305 closure_v = Hi_v*e_v*Z_v*e_v';
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306 penalty_v = -Hi_v*e_v*Z_v*e_u';
652
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307
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
308 switch boundary
761
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309 case 'l'
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310 closure = closure_v;
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311 penalty = penalty_v;
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312 case 'r'
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diff changeset
313 closure = closure_u;
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diff changeset
314 penalty = penalty_u;
652
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315 end
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316
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317 end
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318
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diff changeset
319 function N = size(obj)
761
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diff changeset
320 N = 2*obj.m+1;
652
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321 end
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322
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323 end
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diff changeset
324
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diff changeset
325 methods(Static)
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diff changeset
326 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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diff changeset
327 % and bound_v of scheme schm_v.
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diff changeset
328 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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parents:
diff changeset
329 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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parents:
diff changeset
330 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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diff changeset
331 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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parents:
diff changeset
332 end
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parents:
diff changeset
333 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 end