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annotate +scheme/Elastic2dVariable.m @ 729:aa8cf3851de8 feature/poroelastic

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Update multiblock.DiffOp to work for systems.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 20 Apr 2018 16:56:49 -0700
parents 6d5953fc090e
children 9f28cf266f86
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
687
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Martin Almquist <malmquist@stanford.edu>
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1 classdef Elastic2dVariable < scheme.Scheme
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Martin Almquist <malmquist@stanford.edu>
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2
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Martin Almquist <malmquist@stanford.edu>
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3 % Discretizes the elastic wave equation:
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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5 % opSet should be cell array of opSets, one per dimension. This
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Martin Almquist <malmquist@stanford.edu>
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6 % is useful if we have periodic BC in one direction.
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7
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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11
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Martin Almquist <malmquist@stanford.edu>
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12 grid
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Martin Almquist <malmquist@stanford.edu>
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13 dim
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Martin Almquist <malmquist@stanford.edu>
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14
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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40
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Martin Almquist <malmquist@stanford.edu>
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41 H_boundary % Boundary inner products
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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46 end
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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 methods
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Martin Almquist <malmquist@stanford.edu>
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49
e8fc3aa1faf6 Rename elastic scheme.
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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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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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;
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
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67 if isempty(lim)
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Martin Almquist <malmquist@stanford.edu>
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68 x = g.x;
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Martin Almquist <malmquist@stanford.edu>
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69 lim = cell(length(x),1);
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Martin Almquist <malmquist@stanford.edu>
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70 for i = 1:length(x)
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71 lim{i} = {min(x{i}), max(x{i})};
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Martin Almquist <malmquist@stanford.edu>
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72 end
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
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73 end
687
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Martin Almquist <malmquist@stanford.edu>
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74
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Martin Almquist <malmquist@stanford.edu>
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75 % 1D operators
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Martin Almquist <malmquist@stanford.edu>
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76 ops = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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77 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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78 ops{i} = opSet{i}(m(i), lim{i}, order);
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Martin Almquist <malmquist@stanford.edu>
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79 end
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Martin Almquist <malmquist@stanford.edu>
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80
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Martin Almquist <malmquist@stanford.edu>
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81 % Borrowing constants
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Martin Almquist <malmquist@stanford.edu>
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82 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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83 beta = ops{i}.borrowing.R.delta_D;
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Martin Almquist <malmquist@stanford.edu>
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84 obj.H11{i} = ops{i}.borrowing.H11;
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Martin Almquist <malmquist@stanford.edu>
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85 obj.phi{i} = beta/obj.H11{i};
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Martin Almquist <malmquist@stanford.edu>
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86 obj.gamma{i} = ops{i}.borrowing.M.d1;
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Martin Almquist <malmquist@stanford.edu>
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87 end
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Martin Almquist <malmquist@stanford.edu>
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88
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Martin Almquist <malmquist@stanford.edu>
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89 I = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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90 D1 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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91 D2 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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92 H = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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93 Hi = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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94 e_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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95 e_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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96 d1_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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97 d1_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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98
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Martin Almquist <malmquist@stanford.edu>
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99 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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100 I{i} = speye(m(i));
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Martin Almquist <malmquist@stanford.edu>
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101 D1{i} = ops{i}.D1;
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Martin Almquist <malmquist@stanford.edu>
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102 D2{i} = ops{i}.D2;
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Martin Almquist <malmquist@stanford.edu>
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103 H{i} = ops{i}.H;
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Martin Almquist <malmquist@stanford.edu>
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104 Hi{i} = ops{i}.HI;
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Martin Almquist <malmquist@stanford.edu>
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105 e_l{i} = ops{i}.e_l;
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Martin Almquist <malmquist@stanford.edu>
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106 e_r{i} = ops{i}.e_r;
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Martin Almquist <malmquist@stanford.edu>
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107 d1_l{i} = ops{i}.d1_l;
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Martin Almquist <malmquist@stanford.edu>
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108 d1_r{i} = ops{i}.d1_r;
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Martin Almquist <malmquist@stanford.edu>
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109 end
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Martin Almquist <malmquist@stanford.edu>
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110
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Martin Almquist <malmquist@stanford.edu>
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111 %====== Assemble full operators ========
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Martin Almquist <malmquist@stanford.edu>
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112 LAMBDA = spdiag(lambda);
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Martin Almquist <malmquist@stanford.edu>
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113 obj.LAMBDA = LAMBDA;
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Martin Almquist <malmquist@stanford.edu>
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114 MU = spdiag(mu);
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Martin Almquist <malmquist@stanford.edu>
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115 obj.MU = MU;
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Martin Almquist <malmquist@stanford.edu>
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116 RHO = spdiag(rho);
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Martin Almquist <malmquist@stanford.edu>
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117 obj.RHO = RHO;
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Martin Almquist <malmquist@stanford.edu>
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118 obj.RHOi = inv(RHO);
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Martin Almquist <malmquist@stanford.edu>
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119
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Martin Almquist <malmquist@stanford.edu>
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120 obj.D1 = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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121 obj.D2_lambda = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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122 obj.D2_mu = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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123 obj.e_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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124 obj.e_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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125 obj.d1_l = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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126 obj.d1_r = cell(dim,1);
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Martin Almquist <malmquist@stanford.edu>
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127
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Martin Almquist <malmquist@stanford.edu>
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128 % D1
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Martin Almquist <malmquist@stanford.edu>
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129 obj.D1{1} = kron(D1{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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130 obj.D1{2} = kron(I{1},D1{2});
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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 % Boundary operators
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Martin Almquist <malmquist@stanford.edu>
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133 obj.e_l{1} = kron(e_l{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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134 obj.e_l{2} = kron(I{1},e_l{2});
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Martin Almquist <malmquist@stanford.edu>
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135 obj.e_r{1} = kron(e_r{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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136 obj.e_r{2} = kron(I{1},e_r{2});
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Martin Almquist <malmquist@stanford.edu>
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137
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Martin Almquist <malmquist@stanford.edu>
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138 obj.d1_l{1} = kron(d1_l{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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139 obj.d1_l{2} = kron(I{1},d1_l{2});
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Martin Almquist <malmquist@stanford.edu>
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140 obj.d1_r{1} = kron(d1_r{1},I{2});
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Martin Almquist <malmquist@stanford.edu>
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141 obj.d1_r{2} = kron(I{1},d1_r{2});
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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 % D2
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Martin Almquist <malmquist@stanford.edu>
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144 for i = 1:dim
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Martin Almquist <malmquist@stanford.edu>
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145 obj.D2_lambda{i} = sparse(m_tot);
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Martin Almquist <malmquist@stanford.edu>
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146 obj.D2_mu{i} = sparse(m_tot);
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Martin Almquist <malmquist@stanford.edu>
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147 end
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Martin Almquist <malmquist@stanford.edu>
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148 ind = grid.funcToMatrix(g, 1:m_tot);
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Martin Almquist <malmquist@stanford.edu>
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149
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Martin Almquist <malmquist@stanford.edu>
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150 for i = 1:m(2)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151 D_lambda = D2{1}(lambda(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 D_mu = D2{1}(mu(ind(:,i)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 p = ind(:,i);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 obj.D2_lambda{1}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 obj.D2_mu{1}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 for i = 1:m(1)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 D_lambda = D2{2}(lambda(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 D_mu = D2{2}(mu(ind(i,:)));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 p = ind(i,:);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 obj.D2_lambda{2}(p,p) = D_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 obj.D2_mu{2}(p,p) = D_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 end
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 % Quadratures
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 obj.H = kron(H{1},H{2});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 obj.Hi = inv(obj.H);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 obj.H_boundary = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 obj.H_boundary{1} = H{2};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 obj.H_boundary{2} = H{1};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 % E{i}^T picks out component i.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 E = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 I = speye(m_tot,m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 e = sparse(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 e(i) = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 E{i} = kron(I,e);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 obj.E = E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 % Differentiation matrix D (without SAT)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 D2_lambda = obj.D2_lambda;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 D2_mu = obj.D2_mu;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 D1 = obj.D1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 D = sparse(dim*m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 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
195 db(i,j)*D1{i}*LAMBDA*D1{j}*E{j}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 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
198 db(i,j)*D1{j}*MU*D1{i}*E{j}' + ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 D2_mu{j}*E{i}' ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 obj.D = D;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 %=========================================%
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 % Numerical traction operators for BC.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 % Because d1 =/= e0^T*D1, the numerical tractions are different
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 % at every boundary.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 T_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 T_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 tau_l = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 tau_r = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 % tau^{j}_i = sum_k T^{j}_{ik} u_k
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 d1_l = obj.d1_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 d1_r = obj.d1_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 e_l = obj.e_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 e_r = obj.e_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 D1 = obj.D1;
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 boundaries
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 for j = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 T_l{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 T_r{j} = cell(dim,dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 tau_l{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 tau_r{j} = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 % Loop over components
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 tau_l{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 tau_r{j}{i} = sparse(m_tot,dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 for k = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 T_l{j}{i,k} = ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 -d(i,j)*LAMBDA*(d(i,k)*e_l{k}*d1_l{k}' + db(i,k)*D1{k})...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 -d(j,k)*MU*(d(i,j)*e_l{i}*d1_l{i}' + db(i,j)*D1{i})...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 -d(i,k)*MU*e_l{j}*d1_l{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 T_r{j}{i,k} = ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 d(i,j)*LAMBDA*(d(i,k)*e_r{k}*d1_r{k}' + db(i,k)*D1{k})...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 +d(j,k)*MU*(d(i,j)*e_r{i}*d1_r{i}' + db(i,j)*D1{i})...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 +d(i,k)*MU*e_r{j}*d1_r{j}';
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 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
244 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
245 end
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 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 obj.T_l = T_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 obj.T_r = T_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 obj.tau_l = tau_l;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 obj.tau_r = tau_r;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 % Kroneckered norms and coefficients
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 I_dim = speye(dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 obj.RHOi_kron = kron(obj.RHOi, I_dim);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 obj.Hi_kron = kron(obj.Hi, I_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 % Misc.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 obj.m = m;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 obj.h = h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 obj.order = order;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 obj.grid = g;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 obj.dim = dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 % 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
270 % 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
271 % 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
272 % 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
273 % 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
274 % neighbour_scheme is an instance of Scheme that should be interfaced to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 % neighbour_boundary is a string specifying which boundary to interface to.
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277 default_arg('type',{'free','free'});
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
278 default_arg('parameter', []);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
279
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
280 if ~iscell(type)
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
281 type = {type, type};
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
282 end
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
283
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 % j is the coordinate direction of the boundary
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
285 j = obj.get_boundary_number(boundary);
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
286 [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary);
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 E = obj.E;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
289 Hi = obj.Hi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
290 LAMBDA = obj.LAMBDA;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291 MU = obj.MU;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
292 RHOi = obj.RHOi;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
293
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294 dim = obj.dim;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
295 m_tot = obj.grid.N();
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297 % Preallocate
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298 closure = sparse(dim*m_tot, dim*m_tot);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 penalty = cell(dim,1);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300 for k = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301 penalty{k} = sparse(dim*m_tot, m_tot/obj.m(j));
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 end
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 % Loop over components that we (potentially) have different BC on
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305 for k = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 switch type{k}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 % Dirichlet boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 case {'D','d','dirichlet','Dirichlet'}
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 tuning = 1.2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 phi = obj.phi{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 h = obj.h(j);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314 h11 = obj.H11{j}*h;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315 gamma = obj.gamma{j};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317 a_lambda = dim/h11 + 1/(h11*phi);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318 a_mu_i = 2/(gamma*h);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 a_mu_ij = 2/h11 + 1/(h11*phi);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 d = @kroneckerDelta; % Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323 alpha = @(i,j) tuning*( d(i,j)* a_lambda*LAMBDA ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 + d(i,j)* a_mu_i*MU ...
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 + db(i,j)*a_mu_ij*MU );
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327 % Loop over components that Dirichlet penalties end up on
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 for i = 1:dim
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 C = T{k,i};
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330 A = -d(i,k)*alpha(i,j);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 B = A + C;
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
332 closure = closure + E{i}*RHOi*Hi*B'*e*H_gamma*(e'*E{k}' );
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
333 penalty{k} = penalty{k} - E{i}*RHOi*Hi*B'*e*H_gamma;
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 % Free boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 case {'F','f','Free','free','traction','Traction','t','T'}
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
338 closure = closure - E{k}*RHOi*Hi*e*H_gamma* (e'*tau{k} );
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
339 penalty{k} = penalty{k} + E{k}*RHOi*Hi*e*H_gamma;
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 % Unknown boundary condition
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343 error('No such boundary condition: type = %s',type);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 end
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 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 % u denotes the solution in the own domain
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350 % v denotes the solution in the neighbour domain
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
351 % Operators without subscripts are from the own domain.
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 tuning = 1.2;
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
353
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
354 % j is the coordinate direction of the boundary
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
355 j = obj.get_boundary_number(boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
356 j_v = neighbour_scheme.get_boundary_number(neighbour_boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
357
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
358 % Get boundary operators
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
359 [e, T, tau, H_gamma] = obj.get_boundary_operator({'e','T','tau','H'}, boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
360 [e_v, tau_v] = neighbour_scheme.get_boundary_operator({'e','tau'}, neighbour_boundary);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
361
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
362 % Operators and quantities that correspond to the own domain only
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
363 Hi = obj.Hi;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
364 RHOi = obj.RHOi;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
365 dim = obj.dim;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
366
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
367 %--- Other operators ----
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
368 m_tot_u = obj.grid.N();
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
369 E = obj.E;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
370 LAMBDA_u = obj.LAMBDA;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
371 MU_u = obj.MU;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
372 lambda_u = e'*LAMBDA_u*e;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
373 mu_u = e'*MU_u*e;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
374
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
375 m_tot_v = neighbour_scheme.grid.N();
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
376 E_v = neighbour_scheme.E;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
377 LAMBDA_v = neighbour_scheme.LAMBDA;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
378 MU_v = neighbour_scheme.MU;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
379 lambda_v = e_v'*LAMBDA_v*e_v;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
380 mu_v = e_v'*MU_v*e_v;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
381 %-------------------------
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
382
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
383 % Borrowing constants
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
384 phi_u = obj.phi{j};
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
385 h_u = obj.h(j);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
386 h11_u = obj.H11{j}*h_u;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
387 gamma_u = obj.gamma{j};
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
388
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
389 phi_v = neighbour_scheme.phi{j_v};
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
390 h_v = neighbour_scheme.h(j_v);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
391 h11_v = neighbour_scheme.H11{j_v}*h_v;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
392 gamma_v = neighbour_scheme.gamma{j_v};
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
393
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
394 % E > sum_i 1/(2*alpha_ij)*(tau_i)^2
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
395 function [alpha_ii, alpha_ij] = computeAlpha(phi,h,h11,gamma,lambda,mu)
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
396 th1 = h11/(2*dim);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
397 th2 = h11*phi/2;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
398 th3 = h*gamma;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
399 a1 = ( (th1 + th2)*th3*lambda + 4*th1*th2*mu ) / (2*th1*th2*th3);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
400 a2 = ( 16*(th1 + th2)*lambda*mu ) / (th1*th2*th3);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
401 alpha_ii = a1 + sqrt(a2 + a1^2);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
402
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
403 alpha_ij = 2/h11 + 1/(phi*h11);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
404 end
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
405
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
406 [alpha_ii_u, alpha_ij_u] = computeAlpha(phi_u,h_u,h11_u,gamma_u,lambda_u,mu_u);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
407 [alpha_ii_v, alpha_ij_v] = computeAlpha(phi_v,h_v,h11_v,gamma_v,lambda_v,mu_v);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
408 sigma_ii = tuning*(alpha_ii_u + alpha_ii_v)/4;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
409 sigma_ij = tuning*(alpha_ij_u + alpha_ij_v)/4;
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
410
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
411 d = @kroneckerDelta; % Kronecker delta
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
412 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
413 sigma = @(i,j) tuning*(d(i,j)*sigma_ii + db(i,j)*sigma_ij);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
414
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
415 % Preallocate
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
416 closure = sparse(dim*m_tot_u, dim*m_tot_u);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
417 penalty = sparse(dim*m_tot_u, dim*m_tot_v);
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
418
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
419 % Loop over components that penalties end up on
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
420 for i = 1:dim
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
421 closure = closure - E{i}*RHOi*Hi*e*sigma(i,j)*H_gamma*e'*E{i}';
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
422 penalty = penalty + E{i}*RHOi*Hi*e*sigma(i,j)*H_gamma*e_v'*E_v{i}';
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
423
729
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
424 closure = closure - 1/2*E{i}*RHOi*Hi*e*H_gamma*e'*tau{i};
aa8cf3851de8 Update multiblock.DiffOp to work for systems.
Martin Almquist <malmquist@stanford.edu>
parents: 727
diff changeset
425 penalty = penalty - 1/2*E{i}*RHOi*Hi*e*H_gamma*e_v'*tau_v{i};
727
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
426
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
427 % Loop over components that we have interface conditions on
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
428 for k = 1:dim
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
429 closure = closure + 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e'*E{k}';
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
430 penalty = penalty - 1/2*E{i}*RHOi*Hi*T{k,i}'*e*H_gamma*e_v'*E_v{k}';
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
431 end
6d5953fc090e First implementation of elastic interface
Martin Almquist <malmquist@stanford.edu>
parents: 726
diff changeset
432 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
433 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
434
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
435 % 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
436 function [j, nj] = get_boundary_number(obj, boundary)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
437
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
438 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
439 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
440 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
441 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
442 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
443 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
444 error('No such boundary: boundary = %s',boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
445 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
446
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
447 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
448 case {'w','W','west','West','s','S','south','South'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
449 nj = -1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
450 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
451 nj = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
452 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
453 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
454
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
455 % Returns the boundary operator op for the boundary specified by the string boundary.
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
456 % op: may be a cell array of strings
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
457 function [varargout] = get_boundary_operator(obj, op, boundary)
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
458
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
459 switch boundary
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
460 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
461 j = 1;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
462 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
463 j = 2;
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
464 otherwise
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
465 error('No such boundary: boundary = %s',boundary);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
466 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
467
726
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
468 if ~iscell(op)
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
469 op = {op};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
470 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
471
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
472 for i = 1:length(op)
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
473 switch op{i}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
474 case 'e'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
475 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
476 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
477 varargout{i} = obj.e_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
478 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
479 varargout{i} = obj.e_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
480 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
481 case 'd'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
482 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
483 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
484 varargout{i} = obj.d1_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
485 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
486 varargout{i} = obj.d1_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
487 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
488 case 'H'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
489 varargout{i} = obj.H_boundary{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
490 case 'T'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
491 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
492 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
493 varargout{i} = obj.T_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
494 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
495 varargout{i} = obj.T_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
496 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
497 case 'tau'
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
498 switch boundary
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
499 case {'w','W','west','West','s','S','south','South'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
500 varargout{i} = obj.tau_l{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
501 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
502 varargout{i} = obj.tau_r{j};
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
503 end
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
504 otherwise
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
505 error(['No such operator: operator = ' op{i}]);
37d5d69b1a0d Refactor BC code in Elastic2dVariable
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
506 end
687
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
507 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
508
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
509 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
510
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
511 function N = size(obj)
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
512 N = prod(obj.m);
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
513 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
514 end
e8fc3aa1faf6 Rename elastic scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
515 end