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annotate +scheme/Staggered1DAcousticsVariable.m @ 652:be941bb0a11a feature/d1_staggered

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Add staggered 1D variable coefficient. Convergence study working.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 04 Dec 2017 11:11:03 -0800
parents
children 2351a7690e8a
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652
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
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1 classdef Staggered1DAcousticsVariable < scheme.Scheme
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Martin Almquist <malmquist@stanford.edu>
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2 properties
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Martin Almquist <malmquist@stanford.edu>
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3 m % Number of points of primal grid in each direction, possibly a vector
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Martin Almquist <malmquist@stanford.edu>
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4 h % Grid spacing
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Martin Almquist <malmquist@stanford.edu>
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5
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Martin Almquist <malmquist@stanford.edu>
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6 % Grids
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Martin Almquist <malmquist@stanford.edu>
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7 grid % Total grid object
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Martin Almquist <malmquist@stanford.edu>
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8 grid_primal
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Martin Almquist <malmquist@stanford.edu>
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9 grid_dual
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Martin Almquist <malmquist@stanford.edu>
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10
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Martin Almquist <malmquist@stanford.edu>
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11 order % Order accuracy for the approximation
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Martin Almquist <malmquist@stanford.edu>
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12
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Martin Almquist <malmquist@stanford.edu>
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13 H % Combined norm
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Martin Almquist <malmquist@stanford.edu>
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14 Hi % Inverse
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Martin Almquist <malmquist@stanford.edu>
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15 D % Semi-discrete approximation matrix
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Martin Almquist <malmquist@stanford.edu>
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16
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Martin Almquist <malmquist@stanford.edu>
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17 D1_primal
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Martin Almquist <malmquist@stanford.edu>
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18 D1_dual
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Martin Almquist <malmquist@stanford.edu>
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19
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
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20 % Pick out left or right boundary
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Martin Almquist <malmquist@stanford.edu>
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21 e_l
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Martin Almquist <malmquist@stanford.edu>
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22 e_r
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Martin Almquist <malmquist@stanford.edu>
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23
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Martin Almquist <malmquist@stanford.edu>
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24 % Initial data
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Martin Almquist <malmquist@stanford.edu>
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25 v0
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Martin Almquist <malmquist@stanford.edu>
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26
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Martin Almquist <malmquist@stanford.edu>
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27 % Pick out primal or dual component
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Martin Almquist <malmquist@stanford.edu>
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28 e_primal
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Martin Almquist <malmquist@stanford.edu>
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29 e_dual
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Martin Almquist <malmquist@stanford.edu>
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30
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Martin Almquist <malmquist@stanford.edu>
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31 % System matrices
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Martin Almquist <malmquist@stanford.edu>
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32 A
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Martin Almquist <malmquist@stanford.edu>
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33 B
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Martin Almquist <malmquist@stanford.edu>
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34
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Martin Almquist <malmquist@stanford.edu>
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35 %
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Martin Almquist <malmquist@stanford.edu>
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36 A_l, A_r
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Martin Almquist <malmquist@stanford.edu>
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37 B_l, B_r
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Martin Almquist <malmquist@stanford.edu>
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38 end
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Martin Almquist <malmquist@stanford.edu>
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39
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Martin Almquist <malmquist@stanford.edu>
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40
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Martin Almquist <malmquist@stanford.edu>
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41 methods
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Martin Almquist <malmquist@stanford.edu>
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42 % Scheme for A*u_t + B u_x = 0,
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Martin Almquist <malmquist@stanford.edu>
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43 % u = [p, v];
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Martin Almquist <malmquist@stanford.edu>
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44 % A: Diagonal and A > 0,
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Martin Almquist <malmquist@stanford.edu>
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45 % A = [a1, 0;
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Martin Almquist <malmquist@stanford.edu>
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46 % 0, a2]
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Martin Almquist <malmquist@stanford.edu>
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47 %
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Martin Almquist <malmquist@stanford.edu>
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48 % B = B^T and with diagonal entries = 0.
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Martin Almquist <malmquist@stanford.edu>
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49 % B = [0 b
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Martin Almquist <malmquist@stanford.edu>
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50 % b 0]
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Martin Almquist <malmquist@stanford.edu>
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51 % Here we store p on the primal grid and v on the dual
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Martin Almquist <malmquist@stanford.edu>
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52 function obj = Staggered1DAcousticsVariable(g, order, A, B)
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Martin Almquist <malmquist@stanford.edu>
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53 default_arg('B',{@(x)0*x, @(x)0*x+1; @(x)0*x+1, @(x)0*x});
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Martin Almquist <malmquist@stanford.edu>
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54 default_arg('A',{@(x)0*x+1, @(x)0*x; @(x)0*x, @(x)0*x+1});
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Martin Almquist <malmquist@stanford.edu>
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55
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Martin Almquist <malmquist@stanford.edu>
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56 obj.order = order;
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Martin Almquist <malmquist@stanford.edu>
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57 obj.A = A;
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Martin Almquist <malmquist@stanford.edu>
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58 obj.B = B;
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Martin Almquist <malmquist@stanford.edu>
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59
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Martin Almquist <malmquist@stanford.edu>
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60 % Grids
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Martin Almquist <malmquist@stanford.edu>
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61 obj.m = g.size();
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Martin Almquist <malmquist@stanford.edu>
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62 xl = g.getBoundary('l');
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Martin Almquist <malmquist@stanford.edu>
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63 xr = g.getBoundary('r');
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Martin Almquist <malmquist@stanford.edu>
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64 xlim = {xl, xr};
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Martin Almquist <malmquist@stanford.edu>
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65
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Martin Almquist <malmquist@stanford.edu>
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66 % Boundary matrices
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Martin Almquist <malmquist@stanford.edu>
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67 obj.A_l = [A{1,1}(xl), A{1,2}(xl);....
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Martin Almquist <malmquist@stanford.edu>
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68 A{2,1}(xl), A{2,2}(xl)];
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Martin Almquist <malmquist@stanford.edu>
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69 obj.A_r = [A{1,1}(xr), A{1,2}(xr);....
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Martin Almquist <malmquist@stanford.edu>
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70 A{2,1}(xr), A{2,2}(xr)];
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Martin Almquist <malmquist@stanford.edu>
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71 obj.B_l = [B{1,1}(xl), B{1,2}(xl);....
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Martin Almquist <malmquist@stanford.edu>
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72 B{2,1}(xl), B{2,2}(xl)];
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Martin Almquist <malmquist@stanford.edu>
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73 obj.B_r = [B{1,1}(xr), B{1,2}(xr);....
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Martin Almquist <malmquist@stanford.edu>
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74 B{2,1}(xr), B{2,2}(xr)];
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Martin Almquist <malmquist@stanford.edu>
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75
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Martin Almquist <malmquist@stanford.edu>
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76 obj.grid = g;
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Martin Almquist <malmquist@stanford.edu>
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77 obj.grid_primal = g.grids{1};
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Martin Almquist <malmquist@stanford.edu>
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78 obj.grid_dual = g.grids{2};
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Martin Almquist <malmquist@stanford.edu>
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79 x_primal = obj.grid_primal.points();
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Martin Almquist <malmquist@stanford.edu>
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80 x_dual = obj.grid_dual.points();
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Martin Almquist <malmquist@stanford.edu>
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81
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Martin Almquist <malmquist@stanford.edu>
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82 % Get operators
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Martin Almquist <malmquist@stanford.edu>
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83 ops = sbp.D1StaggeredUpwind(obj.m, xlim, order);
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Martin Almquist <malmquist@stanford.edu>
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84 obj.h = ops.h;
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Martin Almquist <malmquist@stanford.edu>
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85
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Martin Almquist <malmquist@stanford.edu>
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86 % Build combined operators
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Martin Almquist <malmquist@stanford.edu>
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87 H_primal = ops.H_primal;
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Martin Almquist <malmquist@stanford.edu>
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88 H_dual = ops.H_dual;
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Martin Almquist <malmquist@stanford.edu>
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89 obj.H = blockmatrix.toMatrix( {H_primal, []; [], H_dual } );
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Martin Almquist <malmquist@stanford.edu>
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90 obj.Hi = inv(obj.H);
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Martin Almquist <malmquist@stanford.edu>
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91
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Martin Almquist <malmquist@stanford.edu>
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92 D1_primal = ops.D1_primal;
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Martin Almquist <malmquist@stanford.edu>
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93 D1_dual = ops.D1_dual;
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Martin Almquist <malmquist@stanford.edu>
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94 A11_B12 = spdiag(-1./A{1,1}(x_primal).*B{1,2}(x_primal), 0);
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Martin Almquist <malmquist@stanford.edu>
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95 A22_B21 = spdiag(-1./A{2,2}(x_dual).*B{2,1}(x_dual), 0);
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Martin Almquist <malmquist@stanford.edu>
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96 D = {[], A11_B12*D1_primal;...
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Martin Almquist <malmquist@stanford.edu>
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97 A22_B21*D1_dual, []};
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Martin Almquist <malmquist@stanford.edu>
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98 obj.D = blockmatrix.toMatrix(D);
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Martin Almquist <malmquist@stanford.edu>
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99 obj.D1_primal = D1_primal;
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Martin Almquist <malmquist@stanford.edu>
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100 obj.D1_dual = D1_dual;
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Martin Almquist <malmquist@stanford.edu>
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101
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Martin Almquist <malmquist@stanford.edu>
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102 % Combined boundary operators
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Martin Almquist <malmquist@stanford.edu>
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103 e_primal_l = ops.e_primal_l;
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Martin Almquist <malmquist@stanford.edu>
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104 e_primal_r = ops.e_primal_r;
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Martin Almquist <malmquist@stanford.edu>
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105 e_dual_l = ops.e_dual_l;
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Martin Almquist <malmquist@stanford.edu>
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106 e_dual_r = ops.e_dual_r;
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Martin Almquist <malmquist@stanford.edu>
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107 e_l = {e_primal_l, [];...
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Martin Almquist <malmquist@stanford.edu>
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108 [] , e_dual_l};
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Martin Almquist <malmquist@stanford.edu>
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109 e_r = {e_primal_r, [];...
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Martin Almquist <malmquist@stanford.edu>
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110 [] , e_dual_r};
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Martin Almquist <malmquist@stanford.edu>
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111 obj.e_l = blockmatrix.toMatrix(e_l);
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Martin Almquist <malmquist@stanford.edu>
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112 obj.e_r = blockmatrix.toMatrix(e_r);
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113
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Martin Almquist <malmquist@stanford.edu>
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114 % Pick out first or second component of solution
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Martin Almquist <malmquist@stanford.edu>
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115 N_primal = obj.grid_primal.N();
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Martin Almquist <malmquist@stanford.edu>
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116 N_dual = obj.grid_dual.N();
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Martin Almquist <malmquist@stanford.edu>
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117 obj.e_primal = [speye(N_primal, N_primal); sparse(N_dual, N_primal)];
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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120
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Martin Almquist <malmquist@stanford.edu>
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121 end
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Martin Almquist <malmquist@stanford.edu>
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122 % Closure functions return the operators applied to the own domain to close the boundary
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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125 % type is a string specifying the type of boundary condition if there are several.
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Martin Almquist <malmquist@stanford.edu>
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126 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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Martin Almquist <malmquist@stanford.edu>
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127 % neighbour_boundary is a string specifying which boundary to interface to.
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Martin Almquist <malmquist@stanford.edu>
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128 function [closure, penalty] = boundary_condition(obj, boundary, type)
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Martin Almquist <malmquist@stanford.edu>
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129
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Martin Almquist <malmquist@stanford.edu>
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130 default_arg('type','p');
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Martin Almquist <malmquist@stanford.edu>
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131
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Martin Almquist <malmquist@stanford.edu>
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132 % type = 'p' => boundary condition for p
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Martin Almquist <malmquist@stanford.edu>
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133 % type = 'v' => boundary condition for v
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Martin Almquist <malmquist@stanford.edu>
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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
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 % Get boundary matrices
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 case 'l'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 A = full(obj.A_l);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 B = full(obj.B_l);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
143 case 'r'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 A = full(obj.A_r);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145 B = full(obj.B_r);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148 % Diagonalize B
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 [T, Lambda] = eig(B);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 lambda = diag(Lambda);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
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 % Identify in- and outgoing characteristic variables
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 Iplus = lambda > 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 Iminus = lambda < 0;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 case 'l'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 Iout = Iminus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 Iin = Iplus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 case 'r'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 Iout = Iplus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 Iin = Iminus;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 Tin = T(:,Iin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 Tout = T(:,Iout);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 switch type
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 case 'p'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 L = [1, 0];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 case 'v'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 L = [0, 1];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 case 'characteristic'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 L = Tin';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 otherwise
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 error('Boundary condition not implemented.');
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 % Penalty parameters
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 sigma = [0; 0];
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 sigma(Iin) = lambda(Iin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 case 'l'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 tau = -1*obj.e_l * inv(A) * T * sigma * inv(L*Tin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 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
186
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 case 'r'
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 tau = 1*obj.e_r * inv(A) * T * sigma * inv(L*Tin);
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 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
190
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 penalty = -obj.Hi*tau;
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 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 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
198
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 error('Staggered1DAcoustics, interface not implemented');
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 switch boundary
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 % Upwind coupling
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 case {'l','left'}
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 tau = -1*obj.e_l;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 closure = obj.Hi*tau*obj.e_l';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 penalty = -obj.Hi*tau*neighbour_scheme.e_r';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 case {'r','right'}
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 tau = 0*obj.e_r;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 closure = obj.Hi*tau*obj.e_r';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 penalty = -obj.Hi*tau*neighbour_scheme.e_l';
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 end
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 function N = size(obj)
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 N = obj.m;
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 end
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
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 methods(Static)
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 % 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
223 % and bound_v of scheme schm_v.
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 % [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
225 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
226 [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
227 [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
228 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 end
be941bb0a11a Add staggered 1D variable coefficient. Convergence study working.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 end