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annotate +time/ExplicitRungeKuttaSecondOrderDiscreteData.m @ 1334:df8c71b80c33 feature/D2_boundary_opt

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Use the logic grid associated with a CurvilinearGrid instead of creating a new one
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 07 May 2022 10:40:47 +0200
parents 335b8b1366d4
children
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1 classdef ExplicitRungeKuttaSecondOrderDiscreteData < time.Timestepper
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2 properties
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3 k
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Martin Almquist <malmquist@stanford.edu>
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4 t
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Martin Almquist <malmquist@stanford.edu>
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5 w
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Martin Almquist <malmquist@stanford.edu>
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6 m
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Martin Almquist <malmquist@stanford.edu>
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7 D
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Martin Almquist <malmquist@stanford.edu>
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8 E
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9 M
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10 C_cont % Continuous part (function handle) of forcing on first order form.
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11 C_discr% Discrete part (matrix) of forcing on first order form.
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12 n
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13 order
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14 tsImplementation % Time stepper object, RK first order form,
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15 % which this wraps around.
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16 end
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17
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18
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19 methods
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20 % Solves u_tt = Du + Eu_t + S by
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21 % Rewriting on first order form:
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22 % w_t = M*w + C(t)
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23 % where
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24 % M = [
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25 % 0, I;
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26 % D, E;
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27 % ]
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28 % and
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29 % C(t) = [
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30 % 0;
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31 % S(t)
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32 % ]
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33 % D, E, should be matrices (or empty for zero)
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34 % They can also be omitted by setting them equal to the empty matrix.
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35 % S = S_cont + S_discr, where S_cont is a function handle
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36 % S_discr a matrix of data vectors, one column per stage.
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37 function obj = ExplicitRungeKuttaSecondOrderDiscreteData(D, E, S_cont, S_discr, k, t0, v0, v0t, order)
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38 default_arg('order', 4);
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39 default_arg('S_cont', []);
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40 default_arg('S_discr', []);
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41 obj.D = D;
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42 obj.E = E;
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43 obj.m = length(v0);
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44 obj.n = 0;
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45
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46 default_arg('D', sparse(obj.m, obj.m) );
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47 default_arg('E', sparse(obj.m, obj.m) );
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48
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49 obj.k = k;
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50 obj.t = t0;
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51 obj.w = [v0; v0t];
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52
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53 I = speye(obj.m);
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54 O = sparse(obj.m,obj.m);
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55
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56 obj.M = [
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57 O, I;
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58 D, E;
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59 ];
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60
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61 % Build C_cont
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62 if ~isempty(S_cont)
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63 obj.C_cont = @(t)[
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64 sparse(obj.m,1);
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65 S_cont(t)
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66 ];
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67 else
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68 obj.C_cont = [];
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69 end
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70
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71 % Build C_discr
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72 if ~isempty(S_discr)
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73 [~, nt] = size(S_discr);
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74 obj.C_discr = [sparse(obj.m, nt);
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75 S_discr
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76 ];
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77 else
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78 obj.C_discr = [];
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79 end
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80 obj.tsImplementation = time.ExplicitRungeKuttaDiscreteData(obj.M, obj.C_cont, obj.C_discr,...
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81 k, obj.t, obj.w, order);
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82 end
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83
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84 function [v,t,U,T,K] = getV(obj)
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85 [w,t,U,T,K] = obj.tsImplementation.getV();
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86
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87 v = w(1:end/2);
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88 U = U(1:end/2, :); % Stage approximations in previous time step.
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89 K = K(1:end/2, :); % Stage rates in previous time step.
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90 % T: Stage times in previous time step.
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91 end
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92
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93 function [vt,t,U,T,K] = getVt(obj)
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94 [w,t,U,T,K] = obj.tsImplementation.getV();
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95
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96 vt = w(end/2+1:end);
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97 U = U(end/2+1:end, :); % Stage approximations in previous time step.
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98 K = K(end/2+1:end, :); % Stage rates in previous time step.
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99 % T: Stage times in previous time step.
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100 end
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101
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102 function [a,b,c,s] = getTableau(obj)
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103 [a,b,c,s] = obj.tsImplementation.getTableau();
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104 end
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105
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106 % Returns quadrature weights for stages in one time step
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107 function quadWeights = getTimeStepQuadrature(obj)
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108 [~, b] = obj.getTableau();
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109 quadWeights = obj.k*b;
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110 end
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111
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112 % Use RK for first order form to step
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113 function obj = step(obj)
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114 obj.tsImplementation.step();
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115 [v, t] = obj.tsImplementation.getV();
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116 obj.w = v;
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117 obj.t = t;
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118 obj.n = obj.n + 1;
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119 end
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120 end
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121
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122 methods (Static)
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123 function k = getTimeStep(lambda, order)
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124 default_arg('order', 4);
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125 k = obj.tsImplementation.getTimeStep(lambda, order);
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126 end
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127 end
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128
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129 end