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author Martin Almquist <malmquist@stanford.edu>
date Sat, 24 Nov 2018 15:43:34 -0800
parents b9c98661ff5d
children 21394c78c72e
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687
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Martin Almquist <malmquist@stanford.edu>
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1 classdef Elastic2dVariable < scheme.Scheme
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2
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3 % Discretizes the elastic wave equation:
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4 % rho u_{i,tt} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i
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5 % opSet should be cell array of opSets, one per dimension. This
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6 % is useful if we have periodic BC in one direction.
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7
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8 properties
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Martin Almquist <malmquist@stanford.edu>
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9 m % Number of points in each direction, possibly a vector
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Martin Almquist <malmquist@stanford.edu>
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10 h % Grid spacing
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11
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12 grid
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13 dim
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14
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15 order % Order of accuracy for the approximation
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16
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Martin Almquist <malmquist@stanford.edu>
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17 % Diagonal matrices for varible coefficients
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Martin Almquist <malmquist@stanford.edu>
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18 LAMBDA % Variable coefficient, related to dilation
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Martin Almquist <malmquist@stanford.edu>
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19 MU % Shear modulus, variable coefficient
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Martin Almquist <malmquist@stanford.edu>
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20 RHO, RHOi % Density, variable
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Martin Almquist <malmquist@stanford.edu>
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21
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Martin Almquist <malmquist@stanford.edu>
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22 D % Total operator
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Martin Almquist <malmquist@stanford.edu>
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23 D1 % First derivatives
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Martin Almquist <malmquist@stanford.edu>
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24
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Martin Almquist <malmquist@stanford.edu>
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25 % Second derivatives
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Martin Almquist <malmquist@stanford.edu>
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26 D2_lambda
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Martin Almquist <malmquist@stanford.edu>
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27 D2_mu
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Martin Almquist <malmquist@stanford.edu>
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28
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Martin Almquist <malmquist@stanford.edu>
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29 % Traction operators used for BC
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Martin Almquist <malmquist@stanford.edu>
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30 T_l, T_r
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Martin Almquist <malmquist@stanford.edu>
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31 tau_l, tau_r
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32
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Martin Almquist <malmquist@stanford.edu>
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33 H, Hi % Inner products
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34 phi % Borrowing constant for (d1 - e^T*D1) from R
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Martin Almquist <malmquist@stanford.edu>
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35 gamma % Borrowing constant for d1 from M
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Martin Almquist <malmquist@stanford.edu>
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36 H11 % First element of H
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Martin Almquist <malmquist@stanford.edu>
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37 e_l, e_r
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Martin Almquist <malmquist@stanford.edu>
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38 d1_l, d1_r % Normal derivatives at the boundary
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Martin Almquist <malmquist@stanford.edu>
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39 E % E{i}^T picks out component i
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40
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41 H_boundary % Boundary inner products
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42
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Martin Almquist <malmquist@stanford.edu>
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43 % Kroneckered norms and coefficients
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Martin Almquist <malmquist@stanford.edu>
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44 RHOi_kron
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Martin Almquist <malmquist@stanford.edu>
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45 Hi_kron
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46 end
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Martin Almquist <malmquist@stanford.edu>
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47
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48 methods
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49
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Martin Almquist <malmquist@stanford.edu>
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50 function obj = Elastic2dVariable(g ,order, lambda_fun, mu_fun, rho_fun, opSet)
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51 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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52 default_arg('lambda_fun', @(x,y) 0*x+1);
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Martin Almquist <malmquist@stanford.edu>
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53 default_arg('mu_fun', @(x,y) 0*x+1);
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Martin Almquist <malmquist@stanford.edu>
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54 default_arg('rho_fun', @(x,y) 0*x+1);
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Martin Almquist <malmquist@stanford.edu>
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55 dim = 2;
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56
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Martin Almquist <malmquist@stanford.edu>
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57 assert(isa(g, 'grid.Cartesian'))
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58
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Martin Almquist <malmquist@stanford.edu>
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59 lambda = grid.evalOn(g, lambda_fun);
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Martin Almquist <malmquist@stanford.edu>
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60 mu = grid.evalOn(g, mu_fun);
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Martin Almquist <malmquist@stanford.edu>
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61 rho = grid.evalOn(g, rho_fun);
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Martin Almquist <malmquist@stanford.edu>
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62 m = g.size();
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Martin Almquist <malmquist@stanford.edu>
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63 m_tot = g.N();
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64
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Martin Almquist <malmquist@stanford.edu>
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65 h = g.scaling();
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Martin Almquist <malmquist@stanford.edu>
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66 lim = g.lim;
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Martin Almquist <malmquist@stanford.edu>
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67
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Martin Almquist <malmquist@stanford.edu>
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68 % 1D operators
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Martin Almquist <malmquist@stanford.edu>
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69 ops = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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70 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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71 ops{i} = opSet{i}(m(i), lim{i}, order);
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Martin Almquist <malmquist@stanford.edu>
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72 end
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Martin Almquist <malmquist@stanford.edu>
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73
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74 % Borrowing constants
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Martin Almquist <malmquist@stanford.edu>
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75 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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76 beta = ops{i}.borrowing.R.delta_D;
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Martin Almquist <malmquist@stanford.edu>
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77 obj.H11{i} = ops{i}.borrowing.H11;
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Martin Almquist <malmquist@stanford.edu>
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78 obj.phi{i} = beta/obj.H11{i};
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Martin Almquist <malmquist@stanford.edu>
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79 obj.gamma{i} = ops{i}.borrowing.M.d1;
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80 end
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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 I = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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83 D1 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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84 D2 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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85 H = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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86 Hi = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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87 e_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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88 e_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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89 d1_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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90 d1_r = cell(dim,1);
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91
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92 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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93 I{i} = speye(m(i));
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Martin Almquist <malmquist@stanford.edu>
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94 D1{i} = ops{i}.D1;
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Martin Almquist <malmquist@stanford.edu>
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95 D2{i} = ops{i}.D2;
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Martin Almquist <malmquist@stanford.edu>
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96 H{i} = ops{i}.H;
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Martin Almquist <malmquist@stanford.edu>
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97 Hi{i} = ops{i}.HI;
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Martin Almquist <malmquist@stanford.edu>
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98 e_l{i} = ops{i}.e_l;
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Martin Almquist <malmquist@stanford.edu>
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99 e_r{i} = ops{i}.e_r;
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Martin Almquist <malmquist@stanford.edu>
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100 d1_l{i} = ops{i}.d1_l;
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Martin Almquist <malmquist@stanford.edu>
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101 d1_r{i} = ops{i}.d1_r;
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Martin Almquist <malmquist@stanford.edu>
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102 end
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103
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Martin Almquist <malmquist@stanford.edu>
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104 %====== Assemble full operators ========
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Martin Almquist <malmquist@stanford.edu>
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105 LAMBDA = spdiag(lambda);
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Martin Almquist <malmquist@stanford.edu>
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106 obj.LAMBDA = LAMBDA;
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Martin Almquist <malmquist@stanford.edu>
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107 MU = spdiag(mu);
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Martin Almquist <malmquist@stanford.edu>
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108 obj.MU = MU;
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Martin Almquist <malmquist@stanford.edu>
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109 RHO = spdiag(rho);
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Martin Almquist <malmquist@stanford.edu>
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110 obj.RHO = RHO;
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Martin Almquist <malmquist@stanford.edu>
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111 obj.RHOi = inv(RHO);
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Martin Almquist <malmquist@stanford.edu>
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112
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Martin Almquist <malmquist@stanford.edu>
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113 obj.D1 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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114 obj.D2_lambda = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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115 obj.D2_mu = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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116 obj.e_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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117 obj.e_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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118 obj.d1_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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119 obj.d1_r = cell(dim,1);
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120
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Martin Almquist <malmquist@stanford.edu>
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121 % D1
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Martin Almquist <malmquist@stanford.edu>
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122 obj.D1{1} = kron(D1{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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123 obj.D1{2} = kron(I{1},D1{2});
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Martin Almquist <malmquist@stanford.edu>
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124
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125 % Boundary operators
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Martin Almquist <malmquist@stanford.edu>
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126 obj.e_l{1} = kron(e_l{1},I{2});
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127 obj.e_l{2} = kron(I{1},e_l{2});
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128 obj.e_r{1} = kron(e_r{1},I{2});
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129 obj.e_r{2} = kron(I{1},e_r{2});
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130
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Martin Almquist <malmquist@stanford.edu>
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131 obj.d1_l{1} = kron(d1_l{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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132 obj.d1_l{2} = kron(I{1},d1_l{2});
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133 obj.d1_r{1} = kron(d1_r{1},I{2});
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134 obj.d1_r{2} = kron(I{1},d1_r{2});
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135
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Martin Almquist <malmquist@stanford.edu>
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136 % D2
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Martin Almquist <malmquist@stanford.edu>
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137 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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138 obj.D2_lambda{i} = sparse(m_tot);
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Martin Almquist <malmquist@stanford.edu>
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139 obj.D2_mu{i} = sparse(m_tot);
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Martin Almquist <malmquist@stanford.edu>
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140 end
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Martin Almquist <malmquist@stanford.edu>
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141 ind = grid.funcToMatrix(g, 1:m_tot);
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Martin Almquist <malmquist@stanford.edu>
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142
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Martin Almquist <malmquist@stanford.edu>
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143 for i = 1:m(2)
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Martin Almquist <malmquist@stanford.edu>
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144 D_lambda = D2{1}(lambda(ind(:,i)));
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Martin Almquist <malmquist@stanford.edu>
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145 D_mu = D2{1}(mu(ind(:,i)));
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Martin Almquist <malmquist@stanford.edu>
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146
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Martin Almquist <malmquist@stanford.edu>
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147 p = ind(:,i);
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Martin Almquist <malmquist@stanford.edu>
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148 obj.D2_lambda{1}(p,p) = D_lambda;
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Martin Almquist <malmquist@stanford.edu>
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149 obj.D2_mu{1}(p,p) = D_mu;
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Martin Almquist <malmquist@stanford.edu>
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150 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 for i = 1:m(1)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 D_lambda = D2{2}(lambda(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 D_mu = D2{2}(mu(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 p = ind(i,:);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 obj.D2_lambda{2}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 obj.D2_mu{2}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 % Quadratures
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 obj.H = kron(H{1},H{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 obj.Hi = inv(obj.H);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 obj.H_boundary = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 obj.H_boundary{1} = H{2};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 obj.H_boundary{2} = H{1};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 % E{i}^T picks out component i.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 E = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 I = speye(m_tot,m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 e = sparse(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 e(i) = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 E{i} = kron(I,e);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 obj.E = E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 % Differentiation matrix D (without SAT)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 D2_lambda = obj.D2_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 D2_mu = obj.D2_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 D = sparse(dim*m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 D = D + E{i}*inv(RHO)*( d(i,j)*D2_lambda{i}*E{j}' +...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 db(i,j)*D1{i}*LAMBDA*D1{j}*E{j}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 D = D + E{i}*inv(RHO)*( d(i,j)*D2_mu{i}*E{j}' +...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 db(i,j)*D1{j}*MU*D1{i}*E{j}' + ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 D2_mu{j}*E{i}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 obj.D = D;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 %=========================================%
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 % Numerical traction operators for BC.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 % Because d1 =/= e0^T*D1, the numerical tractions are different
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 % at every boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 T_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 T_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 tau_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 tau_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 % tau^{j}_i = sum_k T^{j}_{ik} u_k
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 d1_l = obj.d1_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 d1_r = obj.d1_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 e_l = obj.e_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 e_r = obj.e_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 % Loop over boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 T_l{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 T_r{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 tau_l{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 tau_r{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 % Loop over components
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 tau_l{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 tau_r{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 for k = 1:dim
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
226 T_l{j}{i,k} = ...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 -d(i,j)*LAMBDA*(d(i,k)*e_l{k}*d1_l{k}' + db(i,k)*D1{k})...
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
228 -d(j,k)*MU*(d(i,j)*e_l{i}*d1_l{i}' + db(i,j)*D1{i})...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 -d(i,k)*MU*e_l{j}*d1_l{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
231 T_r{j}{i,k} = ...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 d(i,j)*LAMBDA*(d(i,k)*e_r{k}*d1_r{k}' + db(i,k)*D1{k})...
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
233 +d(j,k)*MU*(d(i,j)*e_r{i}*d1_r{i}' + db(i,j)*D1{i})...
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 +d(i,k)*MU*e_r{j}*d1_r{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 tau_l{j}{i} = tau_l{j}{i} + T_l{j}{i,k}*E{k}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 tau_r{j}{i} = tau_r{j}{i} + T_r{j}{i,k}*E{k}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 obj.T_l = T_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 obj.T_r = T_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 obj.tau_l = tau_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 obj.tau_r = tau_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 % Kroneckered norms and coefficients
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 I_dim = speye(dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 obj.RHOi_kron = kron(obj.RHOi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 obj.Hi_kron = kron(obj.Hi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 % Misc.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 obj.m = m;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 obj.h = h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 obj.order = order;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 obj.grid = g;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 obj.dim = dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 % Closure functions return the operators applied to the own domain to close the boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 % type is a cell array of strings specifying the type of boundary condition for each component.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 % data is a function returning the data that should be applied at the boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 % neighbour_scheme is an instance of Scheme that should be interfaced to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 % neighbour_boundary is a string specifying which boundary to interface to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 default_arg('type',{'free','free'});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 default_arg('parameter', []);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 % j is the coordinate direction of the boundary
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
274 % nj: outward unit normal component.
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 % nj = -1 for west, south, bottom boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 % nj = 1 for east, north, top boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277 [j, nj] = obj.get_boundary_number(boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
278 switch nj
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
279 case 1
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
280 e = obj.e_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 d = obj.d1_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
282 tau = obj.tau_r{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
283 T = obj.T_r{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 case -1
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
285 e = obj.e_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
286 d = obj.d1_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287 tau = obj.tau_l{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 T = obj.T_l{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
289 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
290
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291 E = obj.E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
292 Hi = obj.Hi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
293 H_gamma = obj.H_boundary{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294 LAMBDA = obj.LAMBDA;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
295 MU = obj.MU;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296 RHOi = obj.RHOi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298 dim = obj.dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 m_tot = obj.grid.N();
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301 RHOi_kron = obj.RHOi_kron;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 Hi_kron = obj.Hi_kron;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 % Preallocate
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305 closure = sparse(dim*m_tot, dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 penalty = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307 for k = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 penalty{k} = sparse(dim*m_tot, m_tot/obj.m(j));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311 % Loop over components that we (potentially) have different BC on
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 for k = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 switch type{k}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315 % Dirichlet boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316 case {'D','d','dirichlet','Dirichlet'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318 tuning = 1.2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 phi = obj.phi{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320 h = obj.h(j);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 h11 = obj.H11{j}*h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 gamma = obj.gamma{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 a_lambda = dim/h11 + 1/(h11*phi);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 a_mu_i = 2/(gamma*h);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 a_mu_ij = 2/h11 + 1/(h11*phi);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330 alpha = @(i,j) tuning*( d(i,j)* a_lambda*LAMBDA ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 + d(i,j)* a_mu_i*MU ...
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
332 + db(i,j)*a_mu_ij*MU );
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 % Loop over components that Dirichlet penalties end up on
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 C = T{k,i};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 A = -d(i,k)*alpha(i,j);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
338 B = A + C;
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
339 closure = closure + E{i}*RHOi*Hi*B'*e{j}*H_gamma*(e{j}'*E{k}' );
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 penalty{k} = penalty{k} - E{i}*RHOi*Hi*B'*e{j}*H_gamma;
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
341 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343 % Free boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 case {'F','f','Free','free','traction','Traction','t','T'}
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
345 closure = closure - E{k}*RHOi*Hi*e{j}*H_gamma* (e{j}'*tau{k} );
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 penalty{k} = penalty{k} + E{k}*RHOi*Hi*e{j}*H_gamma;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 % Unknown boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350 error('No such boundary condition: type = %s',type);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354
910
b9c98661ff5d Change the name of the last interface method argument from type to opts in all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 905
diff changeset
355 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,opts)
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 % u denotes the solution in the own domain
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 % v denotes the solution in the neighbour domain
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 tuning = 1.2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359 % tuning = 20.2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 error('Interface not implemented');
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 function [j, nj] = get_boundary_number(obj, boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
369 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 error('No such boundary: boundary = %s',boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376 case {'w','W','west','West','s','S','south','South'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377 nj = -1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
378 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
379 nj = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
380 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
382
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384 function [return_op] = get_boundary_operator(obj, op, boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
386 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
387 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
388 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
389 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
390 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
391 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
392 error('No such boundary: boundary = %s',boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
393 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
394
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
395 switch op
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
396 case 'e'
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398 case {'w','W','west','West','s','S','south','South'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 return_op = obj.e_l{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
400 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
401 return_op = obj.e_r{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
402 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
403 case 'd'
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
404 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
405 case {'w','W','west','West','s','S','south','South'}
689
60eb7f46d8d9 Bugfix get_boundary_op in Elastic2d and Heat2d
Martin Almquist <malmquist@stanford.edu>
parents: 687
diff changeset
406 return_op = obj.d1_l{j};
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
407 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
689
60eb7f46d8d9 Bugfix get_boundary_op in Elastic2d and Heat2d
Martin Almquist <malmquist@stanford.edu>
parents: 687
diff changeset
408 return_op = obj.d1_r{j};
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
409 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
410 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411 error(['No such operator: operatr = ' op]);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
412 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
413
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
414 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
415
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
416 function N = size(obj)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
417 N = prod(obj.m);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
418 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
419 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
420 end