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annotate +time/SBPInTimeImplicitFormulation.m @ 460:e0caae9ef6ed feature/grids

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Add SBPinTime for linear DAE formulations (BUGS!)
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 19 Jun 2017 16:50:13 +0200
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children 0b010f8de7cb
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460
e0caae9ef6ed Add SBPinTime for linear DAE formulations (BUGS!)
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1 classdef SBPInTimeImplicitFormulation < time.Timestepper
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2 % The SBP in time method.
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3 % Implemented for A*v_t = B*v + f(t), v(0) = v0
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4 properties
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5 A,B
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6 f
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7
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8 k % total time step.
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9
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10 blockSize % number of points in each block
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11 N % Number of components
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12
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13 order
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14 nodes
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15
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16 M,K % System matrices
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17 L,U,p,q % LU factorization of M
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18 e_T
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19
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20 % Time state
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21 t
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22 v
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23 n
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24 end
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25
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26 methods
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27 function obj = SBPInTimeImplicitFormulation(A, B, f, k, t0, v0, TYPE, order, blockSize)
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28
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29 default_arg('TYPE','gauss');
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30
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31 if(strcmp(TYPE,'gauss'))
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32 default_arg('order',4)
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33 default_arg('blockSize',4)
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34 else
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35 default_arg('order', 8);
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36 default_arg('blockSize',time.SBPInTimeImplicitFormulation.smallestBlockSize(order,TYPE));
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37 end
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38
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39 obj.A = A;
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40 obj.B = B;
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41 obj.f = f;
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42
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43 obj.k = k;
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44 obj.blockSize = blockSize;
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45 obj.N = length(v0);
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46
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47 obj.n = 0;
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48 obj.t = t0;
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49
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50 %==== Build the time discretization matrix =====%
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51 switch TYPE
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52 case 'equidistant'
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53 ops = sbp.D2Standard(blockSize,{0,obj.k},order);
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54 case 'optimal'
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55 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order);
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56 case 'minimal'
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57 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order,'minimal');
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58 case 'gauss'
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59 ops = sbp.D1Gauss(blockSize,{0,obj.k});
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60 end
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61
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62 I = speye(size(A));
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63 I_t = speye(blockSize,blockSize);
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64
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65 D1 = kron(ops.D1, I);
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66 HI = kron(ops.HI, I);
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67 e_0 = kron(ops.e_l, I);
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68 e_T = kron(ops.e_r, I);
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69 obj.nodes = ops.x;
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70
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71 % Convert to form M*w = K*v0 + f(t)
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72 tau = kron(I_t, A) * e_0;
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73 M = kron(I_t, A)*D1 + HI*tau*e_0' - kron(I_t, B);
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74
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75 K = HI*tau;
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76
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77 obj.M = M;
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78 obj.K = K;
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79 obj.e_T = e_T;
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80
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81 % LU factorization
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82 [obj.L,obj.U,obj.p,obj.q] = lu(obj.M, 'vector');
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83
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84 obj.v = v0;
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85 end
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86
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87 function [v,t] = getV(obj)
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88 v = obj.v;
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89 t = obj.t;
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90 end
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91
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92 function obj = step(obj)
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93 RHS = zeros(obj.blockSize*obj.N,1);
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94
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95 for i = 1:length(obj.blockSize)
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96 RHS((1 + (i-1)*obj.N):(i*obj.N)) = obj.f(obj.nodes(i));
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97 end
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98
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99 RHS = RHS + obj.K*obj.v;
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100
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101 y = obj.L\RHS(obj.p);
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102 z = obj.U\y;
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103
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104 w = zeros(size(z));
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105 w(obj.q) = z;
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106
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107 obj.v = obj.e_T'*w;
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108
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109 obj.t = obj.t + obj.k;
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110 obj.n = obj.n + 1;
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111 end
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112 end
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113
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114 methods(Static)
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115 function N = smallestBlockSize(order,TYPE)
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116 default_arg('TYPE','gauss')
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117
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118 switch TYPE
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119 case 'gauss'
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120 N = 4;
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121 end
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122 end
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123 end
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124 end