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annotate test/SimpleTimeSteppers/SimpleTimeSteppers_test.jl @ 862:a382942e5437 feature/subpackage_simple_timesteppers

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Add a few simple timesteppers
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 18 Jan 2022 15:29:54 +0100
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1 using Test
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2 using Sbplib.SimpleTimeSteppers
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3
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4
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5 @testset "rk4" begin
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6 ode_solutions = @NamedTuple{F,v}.([
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7 ((v,t) -> 0., (v₀,t₀,t) -> v₀),
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8 ((v,t) -> 1., (v₀,t₀,t) -> v₀+t-t₀),
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9 ((v,t) -> t, (v₀,t₀,t) -> v₀+(t^2-t₀^2)/2),
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10 ((v,t) -> v, (v₀,t₀,t) -> v₀*exp(t-t₀)),
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11 ((v,t) -> t*v, (v₀,t₀,t) -> v₀*exp((t^2-t₀^2)/2)),
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12 ])
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13
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14 @testset "Exact" begin
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15 @testset for i ∈ eachindex(ode_solutions[1:3])
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16 F, v = ode_solutions[i]
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17 cases = @NamedTuple{v₀,t₀}.([
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18 (0.,0.),
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19 (0.,1.),
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20 (1.,0.),
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21 (1.,1.),
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22 (2.,0.),
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23 (0.,2.),
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24 (2.,2.),
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25 ])
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26
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27 @testset for (v₀,t₀) ∈ cases
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28 @testset for Δt ∈ [0., 1., .5, 2.]
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29 @test rk4(F, v₀, t₀, Δt) == v(v₀, t₀, t₀+Δt)
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30 end
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31 end
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32 end
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33 end
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34
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35 @testset "Approximate" begin
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36 @testset for i ∈ eachindex(ode_solutions)
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37 F, v = ode_solutions[i]
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38
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39 @testset for v₀ ∈ [1., .5] ,t₀ ∈ [0., 1.]
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40 Δt = 0.1
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41 @test rk4(F, v₀, t₀, Δt) ≈ v(v₀, t₀, t₀+Δt) rtol=1e-6
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42 end
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43 end
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44 end
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45 end
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46
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47 @testset "rkn4" begin
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48
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49 function damped_oscillator(v₀, v̇₀,t₀,t; ζ)
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50 ω = sqrt(1-ζ^2)
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51
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52 C = v̇₀ + ζ*v₀
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53
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54 V = v₀*cos(ω*(t-t₀)) + C*sin(ω*(t-t₀))
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55 V̇ = C*cos(ω*(t-t₀)) - v₀*sin(ω*(t-t₀))
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56 v = exp(-ζ*(t-t₀))*V
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57 v̇ = -ζ*exp(-ζ*(t-t₀))*V + exp(-ζ*(t-t₀))*V̇
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58 return v, v̇
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59 end
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60
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61 ode_solutions = @NamedTuple{F,vv̇}.([
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62 ((v,v̇,t) -> 0., (v₀,v̇₀,t₀,t) -> (v₀ + (t-t₀)*v̇₀, v̇₀)),
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63 ((v,v̇,t) -> 1., (v₀,v̇₀,t₀,t) -> (v₀ + (t-t₀)*v̇₀ + (t-t₀)^2/2, v̇₀ + t - t₀)),
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64 ((v,v̇,t) -> t, (v₀,v̇₀,t₀,t) -> (v₀ + (t-t₀)*v̇₀ + (t-t₀)^3/6+ t₀/2*(t-t₀)^2, v̇₀ + (t^2-t₀^2)/2)),
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65 ((v,v̇,t) -> -v, (v₀,v̇₀,t₀,t) -> (v₀*cos(t-t₀) + v̇₀*sin(t-t₀), v̇₀*cos(t-t₀) - v₀*sin(t-t₀))),
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66 ((v,v̇,t) -> -v-6/5*v̇, (v₀,v̇₀,t₀,t) -> damped_oscillator(v₀,v̇₀,t₀,t; ζ=3/5)),
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67 ])
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68
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69 @testset "Exact" begin
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70 @testset for i ∈ eachindex(ode_solutions[1:3])
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71 F, vv̇ = ode_solutions[i]
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72 @testset for v₀ ∈ [0., 1., 2.], v̇₀ ∈ [0., 1.], t₀ ∈ [0.,1.,2.]
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73 @testset for Δt ∈ [0., 1., .5, 2.]
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74 V,V̇ = rkn4(F, v₀, v̇₀, t₀, Δt)
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75 v,v̇ = vv̇(v₀, v̇₀, t₀, t₀+Δt)
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76 @test V ≈ v rtol=1e-15
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77 @test V̇ ≈ v̇ rtol=1e-15
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78 end
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79 end
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80 end
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81 end
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82
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83 @testset "Approximate" begin
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84 @testset for i ∈ eachindex(ode_solutions)
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85 F, vv̇ = ode_solutions[i]
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86 @testset for v̇₀ ∈ [0., 0.5], v₀ ∈ [1., 0.5], t₀∈[0.,1.]
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87 Δt = 0.1
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88 V,V̇ = rkn4(F, v₀, v̇₀, t₀, Δt)
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89 v,v̇ = vv̇(v₀, v̇₀, t₀, t₀+Δt)
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90
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91 if i != 5
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92 @test V ≈ v rtol=1e-6
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93 @test V̇ ≈ v̇ rtol=1e-6
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94 else
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95 # TODO: Is this a bug or reasonable?
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96 @test_broken V ≈ v rtol=1e-6
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97 @test_broken V̇ ≈ v̇ rtol=1e-6
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98 end
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99 end
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100 end
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101 end
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102 end
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103
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104 @testset "cdiff" begin
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105 ode_solutions = @NamedTuple{F,vv̇}.([
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106 ((v,t) -> 0., (v₀,v̇₀,t₀,t) -> v₀ + (t-t₀)*v̇₀),
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107 ((v,t) -> 1., (v₀,v̇₀,t₀,t) -> v₀ + (t-t₀)*v̇₀ + (t-t₀)^2/2),
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108 ((v,t) -> t, (v₀,v̇₀,t₀,t) -> v₀ + (t-t₀)*v̇₀ + (t-t₀)^3/6+ t₀/2*(t-t₀)^2),
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109 ((v,t) -> -v, (v₀,v̇₀,t₀,t) -> v₀*cos(t-t₀) + v̇₀*sin(t-t₀)),
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110 ])
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111
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112 @testset "Exact" begin
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113 @testset for i ∈ eachindex(ode_solutions[1:3])
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114 F, v = ode_solutions[i]
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115 @testset for v₀ ∈ [1., 2.], v̇₀ ∈ [0., 1.], t₀ ∈ [0.,1.,2.]
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116 @testset for Δt ∈ [0., 1., .5]
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117 v₋₁ = v(v₀, v̇₀, t₀, t₀-Δt)
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118 v₁ = v(v₀, v̇₀, t₀, t₀+Δt)
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119
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120 V₁, V₀ = centered_2nd_order_fd(F, v₀, v₋₁, t₀, Δt)
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121
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122 @test V₁ ≈ v₁ rtol=1e-15
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123 @test V₀ ≈ v₀ rtol=1e-15
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124 end
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125 end
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126 end
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127 end
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128
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129 @testset "Approximate" begin
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130 @testset for i ∈ eachindex(ode_solutions)
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131 F, v = ode_solutions[i]
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132 @testset for v̇₀ ∈ [0., 0.5], v₀ ∈ [1., 0.5], t₀ ∈ [0.,1.]
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133 Δt = 0.1
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134 v₋₁ = v(v₀, v̇₀, t₀, t₀-Δt)
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135 v₁ = v(v₀, v̇₀, t₀, t₀+Δt)
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136
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137 V₁, V₀ = centered_2nd_order_fd(F, v₀, v₋₁, t₀, Δt)
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138
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139
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140 @test V₁ ≈ v₁ rtol=1e-5
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141 @test V₀ ≈ v₀ rtol=1e-5
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142 end
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143 end
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144 end
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145 end