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annotate +time/Rungekutta4SecondOrder.m @ 1344:b4e5e45bd239 feature/D2_boundary_opt

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Remove round off zeros from D2Nonequidistant operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 15 Oct 2022 15:48:20 +0200
parents 74eec7e69b63
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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0
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1 classdef Rungekutta4SecondOrder < time.Timestepper
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2 properties
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3 F
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4 k
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5 t
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6 w
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7 m
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8 D
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9 E
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10 S
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11 M
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12 C
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13 n
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14 end
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15
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16
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17 methods
549
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18 % Solves u_tt = Du + Eu_t + S by
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19 % Rewriting on first order form:
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20 % w_t = M*w + C(t)
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21 % where
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22 % M = [
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23 % 0, I;
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24 % D, E;
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25 % ]
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26 % and
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27 % C(t) = [
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28 % 0;
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29 % S(t)
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30 % ]
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31 % D, E, S can either all be constants or all be function handles,
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32 % They can also be omitted by setting them equal to the empty matrix.
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33 function obj = Rungekutta4SecondOrder(D, E, S, k, t0, v0, v0t)
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34 obj.D = D;
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35 obj.E = E;
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36 obj.S = S;
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37 obj.m = length(v0);
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38 obj.n = 0;
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39
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40 % Construct RHS system on first order form.
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41 % 3 different setups are handeled:
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42 % If none of D, E, S are time-dependent (e.g function_handles)
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43 % then a complete matrix of the RHS is constructed.
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44 % If the source term S is time-depdentent, then the first order system matrix M
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45 % is formed via D and E, while S is kept as a function handle
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46 % If D or E are time-dependent, then all terns are treated as function handles.
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47 if ~isa(D, 'function_handle') && ~isa(E, 'function_handle') && isa(S, 'function_handle')
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48 default_arg('D', sparse(obj.m, obj.m));
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49 default_arg('E', sparse(obj.m, obj.m));
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50 default_arg('S', @(t)sparse(obj.m, 1));
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51
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52 I = speye(obj.m);
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53 O = sparse(obj.m,obj.m);
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54
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55 obj.M = [
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56 O, I;
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57 D, E;
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58 ];
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59
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60 obj.k = k;
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61 obj.t = t0;
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62 obj.w = [v0; v0t];
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63 obj.F = @(w,t)obj.rhsTimeDepS(w,t,obj.M,S,obj.m);
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64 elseif isa(D, 'function_handle') || isa(E, 'function_handle')
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65 default_arg('D', @(t)sparse(obj.m, obj.m));
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66 default_arg('E', @(t)sparse(obj.m, obj.m));
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67 default_arg('S', @(t)sparse(obj.m, 1) );
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68
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69 if ~isa(D, 'function_handle')
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70 D = @(t)D;
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71 end
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72 if ~isa(E, 'function_handle')
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73 E = @(t)E;
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74 end
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75 if ~isa(S, 'function_handle')
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76 S = @(t)S;
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77 end
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78
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79 obj.k = k;
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80 obj.t = t0;
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81 obj.w = [v0; v0t];
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82
549
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83 % Avoid matrix formulation because it is VERY slow
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84 obj.F = @(w,t)[
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85 w(obj.m+1:end);
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86 D(t)*w(1:obj.m) + E(t)*w(obj.m+1:end) + S(t);
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87 ];
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88 else
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89 default_arg('D', sparse(obj.m, obj.m));
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90 default_arg('E', sparse(obj.m, obj.m));
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91 default_arg('S', sparse(obj.m, 1) );
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92
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93 I = speye(obj.m);
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94 O = sparse(obj.m,obj.m);
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95
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96 obj.M = [
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97 O, I;
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98 D, E;
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99 ];
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100 obj.C = [
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101 zeros(obj.m,1);
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102 S;
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103 ];
0
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104
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105 obj.k = k;
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106 obj.t = t0;
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107 obj.w = [v0; v0t];
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108
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109 obj.F = @(w,t)(obj.M*w + obj.C);
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110 end
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111 end
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112
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113 function [v,t] = getV(obj)
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114 v = obj.w(1:end/2);
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115 t = obj.t;
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116 end
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117
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118 function [vt,t] = getVt(obj)
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119 vt = obj.w(end/2+1:end);
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120 t = obj.t;
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121 end
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122
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123 function obj = step(obj)
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124 obj.w = time.rk4.rungekutta_4(obj.w, obj.t, obj.k, obj.F);
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125 obj.t = obj.t + obj.k;
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126 obj.n = obj.n + 1;
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127 end
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128 end
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129
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130
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131 methods (Static)
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132 function k = getTimeStep(lambda)
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133 k = rk4.get_rk4_time_step(lambda);
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134 end
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135
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136 function F = rhsTimeDepS(w,t,M,S,m)
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137 F = M*w;
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138 F(m+1:end) = F(m+1:end) + S(t);
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139 end
0
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140 end
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141
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142 end