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annotate +time/CdiffImplicit.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents d5bce13ece23
children d6ede7f5cbf9
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef CdiffImplicit < time.Timestepper
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2 properties
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3 A, B, C, G
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4 AA, BB, CC
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5 k
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6 t
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7 v, v_prev
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8 n
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9
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10 % LU factorization
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11 L,U,p,q
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12 end
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13
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14 methods
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15 % Solves
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16 % A*u_tt + B*u + C*v_t = G(t)
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17 % u(t0) = f1
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18 % u_t(t0) = f2
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19 % starting at time t0 with timestep k
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20 function obj = CdiffImplicit(A, B, C, G, f1, f2, k, t0)
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21 default_arg('A', []);
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22 default_arg('C', []);
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23 default_arg('G', []);
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24 default_arg('f1', 0);
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25 default_arg('f2', 0);
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26 default_arg('t0', 0);
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27
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28 m = size(B,1);
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29
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30 if isempty(A)
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31 A = speye(m);
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32 end
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33
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34 if isempty(C)
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35 C = sparse(m,m);
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36 end
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37
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38 if isempty(G)
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39 G = @(t) sparse(m,1);
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40 end
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41
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42 if isempty(f1)
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43 f1 = sparse(m,1);
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44 end
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45
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46 if isempty(f2)
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47 f2 = sparse(m,1);
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48 end
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49
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50 obj.A = A;
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51 obj.B = B;
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52 obj.C = C;
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53 obj.G = G;
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54
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55 AA = 1/k^2*A + 1/2*B + 1/(2*k)*C;
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56 BB = -2/k^2*A;
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57 CC = 1/k^2*A + 1/2*B - 1/(2*k)*C;
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58 % AA*v_next + BB*v + CC*v_prev == G(t_n)
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59
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60 obj.AA = AA;
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61 obj.BB = BB;
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62 obj.CC = CC;
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63
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64 v_prev = f1;
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65 I = speye(m);
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66 % v = (1/k^2*A)\((1/k^2*A - 1/2*B)*f1 + (1/k*I - 1/2*C)*f2 + 1/2*G(0));
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67 v = f1 + k*f2;
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68
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69
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70 if ~issparse(A) || ~issparse(B) || ~issparse(C)
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71 error('LU factorization with full pivoting only works for sparse matrices.')
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72 end
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73
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74 [L,U,p,q] = lu(AA,'vector');
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75
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76 obj.L = L;
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77 obj.U = U;
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78 obj.p = p;
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79 obj.q = q;
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80
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81
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82 obj.k = k;
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83 obj.t = t0+k;
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84 obj.n = 1;
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85 obj.v = v;
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86 obj.v_prev = v_prev;
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87 end
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88
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89 function [v,t] = getV(obj)
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90 v = obj.v;
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91 t = obj.t;
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92 end
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93
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94 function [vt,t] = getVt(obj)
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95 % Calculate next time step to be able to do centered diff.
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96 v_next = zeros(size(obj.v));
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97 b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev;
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98
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99 y = obj.L\b(obj.p);
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100 z = obj.U\y;
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101 v_next(obj.q) = z;
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102
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103
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104 vt = (v_next-obj.v_prev)/(2*obj.k);
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105 t = obj.t;
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106 end
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107
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108 function obj = step(obj)
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109 b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev;
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110 obj.v_prev = obj.v;
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111
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112 % % Backslash
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113 % obj.v = obj.AA\b;
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114
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115 % LU with column pivot
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116 y = obj.L\b(obj.p);
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117 z = obj.U\y;
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118 obj.v(obj.q) = z;
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119
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120 % Update time
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121 obj.t = obj.t + obj.k;
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122 obj.n = obj.n + 1;
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123 end
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124 end
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125 end
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126
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127
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128
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130
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131 %%% Derivation
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132 % syms A B C G
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133 % syms n k
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134 % syms f1 f2
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135
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136 % v = symfun(sym('v(n)'),n);
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137
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138
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139 % d = A/k^2 * (v(n+1) - 2*v(n) +v(n-1)) + B/2*(v(n+1)+v(n-1)) + C/(2*k)*(v(n+1) - v(n-1)) == G
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140 % ic1 = v(0) == f1
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141 % ic2 = A/k*(v(1)-f1) + k/2*(B*f1 + C*f2 - G) - f2 == 0
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142
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143 % c = collect(d, [v(n) v(n-1) v(n+1)]) % (-(2*A)/k^2)*v(n) + (B/2 + A/k^2 - C/(2*k))*v(n - 1) + (B/2 + A/k^2 + C/(2*k))*v(n + 1) == G
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144 % syms AA BB CC
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145 % % AA = B/2 + A/k^2 + C/(2*k)
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146 % % BB = -(2*A)/k^2
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147 % % CC = B/2 + A/k^2 - C/(2*k)
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148 % s = subs(c, [B/2 + A/k^2 + C/(2*k), -(2*A)/k^2, B/2 + A/k^2 - C/(2*k)], [AA, BB, CC])
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
149
ca73ee0623e5 Added an implicit central time stepping scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
150
ca73ee0623e5 Added an implicit central time stepping scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
151 % ic2_a = collect(ic2, [v(1) f1 f2]) % (A/k)*v(1) + ((B*k)/2 - A/k)*f1 + ((C*k)/2 - 1)*f2 - (G*k)/2 == 0
ca73ee0623e5 Added an implicit central time stepping scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
152