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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 1203:254934aac3f8 feature/dissipation_operators

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Change name and clarify docs
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 03 Feb 2023 10:05:52 +0100
parents c94a12327737
children 7d52c4835d15
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1 using Test
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2
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3 using Sbplib.SbpOperators
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4 using Sbplib.Grids
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5 using Sbplib.LazyTensors
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6
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7 import Sbplib.SbpOperators.VolumeOperator
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8
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9 # TODO: Refactor these test to look more like the tests in first_derivative_test.jl.
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10
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11 @testset "SecondDerivative" begin
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12 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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13 stencil_set = read_stencil_set(operator_path; order=4)
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14 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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15 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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16 Lx = 3.5
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17 Ly = 3.
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18 g_1D = EquidistantGrid(121, 0.0, Lx)
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19 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
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20
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21 @testset "Constructors" begin
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22 @testset "1D" begin
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23 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils,1)
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24 @test Dₓₓ == second_derivative(g_1D,inner_stencil,closure_stencils)
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25 @test Dₓₓ == second_derivative(g_1D,stencil_set,1)
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26 @test Dₓₓ == second_derivative(g_1D,stencil_set)
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27 @test Dₓₓ isa VolumeOperator
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28 end
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29 @testset "2D" begin
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30 Dₓₓ = second_derivative(g_2D,inner_stencil,closure_stencils,1)
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31 D2 = second_derivative(g_1D,inner_stencil,closure_stencils,1)
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32 I = IdentityTensor{Float64}(size(g_2D)[2])
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33 @test Dₓₓ == D2⊗I
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34 @test Dₓₓ == second_derivative(g_2D,stencil_set,1)
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35 @test Dₓₓ isa LazyTensor{T,2,2} where T
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36 end
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37 end
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38
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39 # Exact differentiation is measured point-wise. In other cases
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40 # the error is measured in the l2-norm.
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41 @testset "Accuracy" begin
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42 @testset "1D" begin
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43 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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44 monomials = ()
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45 maxOrder = 4;
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46 for i = 0:maxOrder-1
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47 f_i(x) = 1/factorial(i)*x^i
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48 monomials = (monomials...,evalOn(g_1D,f_i))
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49 end
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50 v = evalOn(g_1D,x -> sin(x))
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51 vₓₓ = evalOn(g_1D,x -> -sin(x))
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52
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53 # 2nd order interior stencil, 1nd order boundary stencil,
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54 # implies that L*v should be exact for monomials up to order 2.
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55 @testset "2nd order" begin
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56 stencil_set = read_stencil_set(operator_path; order=2)
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57 Dₓₓ = second_derivative(g_1D,stencil_set)
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58 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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59 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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60 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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61 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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62 end
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63
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64 # 4th order interior stencil, 2nd order boundary stencil,
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65 # implies that L*v should be exact for monomials up to order 3.
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66 @testset "4th order" begin
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67 stencil_set = read_stencil_set(operator_path; order=4)
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68 Dₓₓ = second_derivative(g_1D,stencil_set)
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69 # NOTE: high tolerances for checking the "exact" differentiation
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70 # due to accumulation of round-off errors/cancellation errors?
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71 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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72 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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73 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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74 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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75 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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76 end
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77 end
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78
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79 @testset "2D" begin
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80 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
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81 binomials = ()
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82 maxOrder = 4;
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83 for i = 0:maxOrder-1
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84 f_i(x,y) = 1/factorial(i)*y^i + x^i
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85 binomials = (binomials...,evalOn(g_2D,f_i))
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86 end
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87 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
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88 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
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89
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90 # 2nd order interior stencil, 1st order boundary stencil,
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91 # implies that L*v should be exact for binomials up to order 2.
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92 @testset "2nd order" begin
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93 stencil_set = read_stencil_set(operator_path; order=2)
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94 Dyy = second_derivative(g_2D,stencil_set,2)
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95 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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96 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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97 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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98 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
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99 end
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100
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101 # 4th order interior stencil, 2nd order boundary stencil,
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102 # implies that L*v should be exact for binomials up to order 3.
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103 @testset "4th order" begin
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104 stencil_set = read_stencil_set(operator_path; order=4)
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105 Dyy = second_derivative(g_2D,stencil_set,2)
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106 # NOTE: high tolerances for checking the "exact" differentiation
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107 # due to accumulation of round-off errors/cancellation errors?
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108 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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109 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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110 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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111 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
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112 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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113 end
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114 end
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115 end
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116 end