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annotate +time/+rk/General.m @ 995:10c5eda235b7 feature/timesteppers

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Full use of butcher tableau in time.rk.General. Inline rungekutta step methods
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 09 Jan 2019 22:57:13 +0100
parents 44e7e497c3b7
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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bbd165cc585c Move time.Rungekutta to time.rk.General
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1 classdef General < time.Timestepper
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2 properties
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3 F % RHS of the ODE
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4 dt % Time step
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5 t % Time point
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6 v % Solution vector
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7 n % Time level
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8 scheme % The scheme used for the time stepping, e.g rk4, rk6 etc.
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9 bt
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10 V % All stage approximations in most recent time step
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11 K % All stage rates in most recent time step
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12 end
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13
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14
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15 methods
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16 % Timesteps v_t = F(t,v), using the specified ButcherTableau
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17 % from t = t0 with timestep dt and initial conditions v(0) = v0
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18 function obj = General(F, dt, t0, v0, bt)
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19 assertType(bt, 'time.rk.ButcherTableau')
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20 obj.F = F;
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21 obj.dt = dt;
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22 obj.t = t0;
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23 obj.v = v0;
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24 obj.n = 0;
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25
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26 assert(bt.isExplicit())
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27 obj.bt = bt;
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28 end
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29
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30 % v: Current solution
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31 % t: Current time
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32 % V: All stage approximations in most recent time step
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33 % K: All stage rates in most recent time step
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34 % T: Time points (corresponding to V and K) in most recent time step
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35 function [v,t] = getV(obj)
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36 v = obj.v;
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37 t = obj.t;
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38 end
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39
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40 function obj = step(obj)
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41 s = obj.bt.nStages();
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42 a = obj.bt.a;
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43 b = obj.bt.b;
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44 c = obj.bt.c;
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45
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46 % Compute rates K
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47 K = zeros(length(v), s);
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48 for i = 1:s
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49 V_i = obj.v;
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50 for j = 1:i-1
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51 V_i = V_i + dt*a(i,j)*K(:,j);
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52 end
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53 K(:,i) = F(t+dt*c(i), V_i);
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54 end
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55
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56 % Compute updated solution
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57 v_next = v;
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58 for i = 1:s
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59 v_next = v_next + dt*b(i)*K(:,i);
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60 end
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61
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62 obj.v = v_next;
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63 obj.t = obj.t + obj.dt;
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64 obj.n = obj.n + 1;
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65 end
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66
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67 % TBD: Method name
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68 % TBD: Parameter name
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69 %
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70 % Takes a regular step but with discreteRates(:,i) added to RHS for stage i.
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71 % v_t = F(t,v) + discreteRates(:, ...)
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72 %
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73 % Also returns the stage approximations (V) and stage rates (K).
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74 function [v,t, V, K] = stepWithDiscreteData(obj, discreteRates)
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75 s = obj.bt.nStages();
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76 a = obj.bt.a;
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77 b = obj.bt.b;
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78 c = obj.bt.c;
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79
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80 % Compute rates K and stage approximations V
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81 K = zeros(length(v), s);
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82 V = zeros(length(v), s);
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83 for i = 1:s
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84 V_i = obj.v;
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85 for j = 1:i-1
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86 V_i = V_i + dt*a(i,j)*K(:,j);
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87 end
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88
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89 K_i = F(t+dt*c(i), V_i);
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90 K_i = K_i + discreteRates(:,i);
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91
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92 V(:,i) = V_i;
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93 K(:,i) = K_i;
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94 end
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95
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96 % Compute updated updated solution
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97 v_next = v;
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98 for i = 1:s
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99 v_next = v_next + dt*b(i)*K(:,i);
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100 end
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101
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102 obj.v = v_next;
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103 obj.t = obj.t + obj.dt;
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104 obj.n = obj.n + 1;
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105 end
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106
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107 % Returns a vector of time points, including substage points,
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108 % in the time interval [t0, tEnd].
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109 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
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110 function tvec = timePoints(obj, t0, tEnd)
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111 % TBD: Should this be implemented here or somewhere else?
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112 N = round( (tEnd-t0)/obj.dt );
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113 tvec = zeros(N*obj.s, 1);
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114 s = obj.coeffs.s;
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115 c = obj.coeffs.c;
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116 for i = 1:N
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117 ind = (i-1)*s+1 : i*s;
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118 tvec(ind) = ((i-1) + c')*obj.dt;
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119 end
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120 end
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121
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122 % Returns a vector of quadrature weights corresponding to grid points
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123 % in time interval [t0, tEnd], substage points included.
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124 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
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125 function weights = quadWeights(obj, t0, tEnd)
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126 % TBD: Should this be implemented here or somewhere else?
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127 N = round( (tEnd-t0)/obj.dt );
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128 b = obj.coeffs.b;
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129 weights = repmat(b', N, 1);
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130 end
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131 end
993
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132
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133 methods(Static)
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134 % TBD: Function name
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135 function ts = methodFromStr(F, dt, t0, v0, methodStr, discreteData)
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136 default_arg('discreteData', []);
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137
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138 try
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139 bt = time.rk.ButcherTableau.(method);
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140 catch
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141 error('Runge-Kutta method ''%s'' is not implemented', methodStr)
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142 end
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143
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144 ts = time.rk.General(F, dt, t0, v0, bt, discreteData);
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145 end
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146 end
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147 end