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annotate +scheme/Staggered1DAcousticsVariable.m @ 1081:9c74d96fc9e2 feature/d1_staggered

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Bugfix in interface SATs, Staggered1DAcousticsVariable
author Martin Almquist <malmquist@stanford.edu>
date Tue, 05 Mar 2019 11:18:44 -0800
parents 18e10217dca9
children
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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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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 % If coefficients are function handles, evaluate them
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73 if isa(A{1,1}, 'function_handle')
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74 A{1,1} = A{1,1}(x_primal);
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75 A{1,2} = A{1,2}(x_dual);
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76 A{2,1} = A{2,1}(x_primal);
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77 A{2,2} = A{2,2}(x_dual);
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78 end
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79
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80 if isa(B{1,1}, 'function_handle')
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81 B{1,1} = B{1,1}(x_primal);
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82 B{1,2} = B{1,2}(x_primal);
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83 B{2,1} = B{2,1}(x_dual);
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84 B{2,2} = B{2,2}(x_dual);
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85 end
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86
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87 % If coefficents are vectors, turn them into diagonal matrices
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88 [m, n] = size(A{1,1});
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89 if m==1 || n == 1
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90 A{1,1} = spdiag(A{1,1}, 0);
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91 A{2,1} = spdiag(A{2,1}, 0);
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92 A{1,2} = spdiag(A{1,2}, 0);
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93 A{2,2} = spdiag(A{2,2}, 0);
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94 end
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95
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96 [m, n] = size(B{1,1});
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97 if m==1 || n == 1
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98 B{1,1} = spdiag(B{1,1}, 0);
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99 B{2,1} = spdiag(B{2,1}, 0);
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100 B{1,2} = spdiag(B{1,2}, 0);
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101 B{2,2} = spdiag(B{2,2}, 0);
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102 end
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103
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104 % Boundary matrices
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105 obj.A_l = full([A{1,1}(1,1), A{1,2}(1,1);....
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106 A{2,1}(1,1), A{2,2}(1,1)]);
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107 obj.A_r = full([A{1,1}(end,end), A{1,2}(end,end);....
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108 A{2,1}(end,end), A{2,2}(end,end)]);
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109 obj.B_l = full([B{1,1}(1,1), B{1,2}(1,1);....
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110 B{2,1}(1,1), B{2,2}(1,1)]);
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111 obj.B_r = full([B{1,1}(end,end), B{1,2}(end,end);....
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112 B{2,1}(end,end), B{2,2}(end,end)]);
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113
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114 % Get operators
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115 ops = sbp.D1StaggeredUpwind(obj.m, xlim, order);
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116 obj.h = ops.h;
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117
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118 % Build combined operators
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119 H_primal = ops.H_primal;
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120 H_dual = ops.H_dual;
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121 obj.H = blockmatrix.toMatrix( {H_primal, []; [], H_dual } );
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122 obj.Hi = inv(obj.H);
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123
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124 D1_primal = ops.D1_primal;
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125 D1_dual = ops.D1_dual;
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
126 A11_B12 = -A{1,1}\B{1,2};
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
127 A22_B21 = -A{2,2}\B{2,1};
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
128 D = {[], A11_B12*D1_primal;...
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
129 A22_B21*D1_dual, []};
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
130 obj.D = blockmatrix.toMatrix(D);
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
131 obj.D1_primal = D1_primal;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
132 obj.D1_dual = D1_dual;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
133
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
134 % Combined boundary operators
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
135 e_primal_l = ops.e_primal_l;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
136 e_primal_r = ops.e_primal_r;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137 e_dual_l = ops.e_dual_l;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 e_dual_r = ops.e_dual_r;
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
139 e_l = {e_primal_l, [];...
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 [] , e_dual_l};
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
141 e_r = {e_primal_r, [];...
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 [] , e_dual_r};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 obj.e_l = blockmatrix.toMatrix(e_l);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 obj.e_r = blockmatrix.toMatrix(e_r);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 % Pick out first or second component of solution
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 N_primal = obj.grid_primal.N();
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148 N_dual = obj.grid_dual.N();
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 obj.e_primal = [speye(N_primal, N_primal); sparse(N_dual, N_primal)];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 obj.e_dual = [sparse(N_primal, N_dual); speye(N_dual, N_dual)];
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 end
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 % Closure functions return the operators applied to the own domain to close the boundary
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 % 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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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 % type is a string specifying the type of boundary condition if there are several.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 % neighbour_boundary is a string specifying which boundary to interface to.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 function [closure, penalty] = boundary_condition(obj, boundary, type)
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
161
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 default_arg('type','p');
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 % type = 'p' => boundary condition for p
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 % type = 'v' => boundary condition for v
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 % No other types implemented yet
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 % BC on the form Lu - g = 0;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169
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
170 % 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
171 % 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
172 % 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
173
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 % Get boundary matrices
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 case 'l'
653
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
177 A = obj.A_l;
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
178 B = obj.B_l;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 case 'r'
653
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
180 A = obj.A_r;
2351a7690e8a Clean up and improve comments in StaggeredVariable
Martin Almquist <malmquist@stanford.edu>
parents: 652
diff changeset
181 B = obj.B_r;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 end
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
183 C = inv(A)*B;
652
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184
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
185 % 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
186 [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
187 Lambda = T'*B*T;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 lambda = diag(Lambda);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 % Identify in- and outgoing characteristic variables
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 Iplus = lambda > 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 Iminus = lambda < 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 case 'l'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 Iin = Iplus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 case 'r'
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 Iin = Iminus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 Tin = T(:,Iin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 switch type
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 case 'p'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 L = [1, 0];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 case 'v'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 L = [0, 1];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 case 'characteristic'
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
208 % Diagonalize C
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
209 [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
210 lambda_C = diag(Lambda_C);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
211 % 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
212 Iplus = lambda_C > 0;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
213 Iminus = lambda_C < 0;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
214
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
215 switch boundary
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
216 case 'l'
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
217 Iin_C = Iplus;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
218 case 'r'
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
219 Iin_C = Iminus;
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
220 end
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
221 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
222 L = T_C_inv(Iin_C,:);
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 otherwise
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 error('Boundary condition not implemented.');
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 % Penalty parameters
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 sigma = [0; 0];
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 sigma(Iin) = lambda(Iin);
672
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
230
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
231 % Sparsify
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
232 A = sparse(A);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
233 T = sparse(T);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
234 sigma = sparse(sigma);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
235 L = sparse(L);
82024d32e333 Correct char BC in staggered acoustics 1D variable coeff.
Martin Almquist <malmquist@stanford.edu>
parents: 653
diff changeset
236 Tin = sparse(Tin);
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
237
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 case 'l'
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
240 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
241 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
242
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 case 'r'
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
244 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
245 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
246
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 end
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
248
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 penalty = -obj.Hi*tau;
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
250
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 end
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
252
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
253 % 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
254 % see hypsyst_varcoeff.pdf in the hypsyst repository.
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
255 % 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
256 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
257
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
258 % 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
259 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
260 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
261 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
262 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
263 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
264 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
265
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
266 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
267 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
268 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
269 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
270 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
271 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
272 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
273 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
274 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
275
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
276 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
277 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
278 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
279 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
280 end
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
281 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
282 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
283
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
284 % Diagonalize C
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
285 [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
286 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
287 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
288 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
289
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
290 [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
291 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
292 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
293 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
294
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
295 % 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>
parents: 682
diff changeset
296 Im_u = lambda_u < 0;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
297 Ip_u = lambda_u > 0;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
298 Im_v = lambda_v < 0;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
299 Ip_v = lambda_v > 0;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
300
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
301 Tp_u = T_u(:,Ip_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
302 Tm_u = T_u(:,Im_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
303 Sp_u = S_u(Ip_u,:);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
304 Sm_u = S_u(Im_u,:);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
305
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
306 Tp_v = T_v(:,Ip_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
307 Tm_v = T_v(:,Im_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
308 Sp_v = S_v(Ip_v,:);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
309 Sm_v = S_v(Im_v,:);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
310
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
311 % Create S_tilde and T_tilde
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
312 Stilde = [Sp_u; Sm_v];
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
313 Ttilde = inv(Stilde);
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
314 Ttilde_p = Ttilde(:,1);
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
315 Ttilde_m = Ttilde(:,2);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
316
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
317 % Solve for penalty parameters theta_1,2
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
318 LHS = Ttilde_m*Sm_v*Tm_u;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
319 RHS = B_u*Tm_u;
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
320 th_u = RHS./LHS;
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
321 TH_u = diag(th_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
322
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
323 LHS = Ttilde_p*Sp_u*Tp_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
324 RHS = -B_v*Tp_v;
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
325 th_v = RHS./LHS;
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
326 TH_v = diag(th_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
327
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
328 % Construct penalty matrices
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
329 Z_u = TH_u*Ttilde_m*Sm_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
330 Z_u = sparse(Z_u);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
331
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
332 Z_v = TH_v*Ttilde_p*Sp_u;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
333 Z_v = sparse(Z_v);
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
334
1081
9c74d96fc9e2 Bugfix in interface SATs, Staggered1DAcousticsVariable
Martin Almquist <malmquist@stanford.edu>
parents: 885
diff changeset
335 closure_u = Hi_u*e_u*(A_u\Z_u)*e_u';
9c74d96fc9e2 Bugfix in interface SATs, Staggered1DAcousticsVariable
Martin Almquist <malmquist@stanford.edu>
parents: 885
diff changeset
336 penalty_u = -Hi_u*e_u*(A_u\Z_u)*e_v';
9c74d96fc9e2 Bugfix in interface SATs, Staggered1DAcousticsVariable
Martin Almquist <malmquist@stanford.edu>
parents: 885
diff changeset
337 closure_v = Hi_v*e_v*(A_v\Z_v)*e_v';
9c74d96fc9e2 Bugfix in interface SATs, Staggered1DAcousticsVariable
Martin Almquist <malmquist@stanford.edu>
parents: 885
diff changeset
338 penalty_v = -Hi_v*e_v*(A_v\Z_v)*e_u';
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
339
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 switch boundary
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
341 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
342 closure = closure_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
343 penalty = penalty_v;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
344 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
345 closure = closure_u;
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
346 penalty = penalty_u;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347 end
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
348
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 end
885
18e10217dca9 Generalize Staggered1DAcoustics to handle variable coefficients defined by both function handles and vectors.
Martin Almquist <malmquist@stanford.edu>
parents: 761
diff changeset
350
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 function N = size(obj)
761
8ed102db8e9c Add discont interface in 1D acoustics staggered, using the hat variable interface coupling.
Martin Almquist <malmquist@stanford.edu>
parents: 682
diff changeset
352 N = 2*obj.m+1;
652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 methods(Static)
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359 % and bound_v of scheme schm_v.
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 end