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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 877:dd2ab001a7b6 feature/equidistant_grid/refine

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Implement refine function, move exports to the top of the file, change location of constuctors. The constructors were changed have only one inner constructor and simpler outer constructors.
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 14 Feb 2022 09:39:58 +0100
parents d2f4ac2be47f
children 2ae62dbaf839
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45966c77cb20 Split tests for SbpOperators over several files
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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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7 import Sbplib.SbpOperators.VolumeOperator
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8
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9 @testset "SecondDerivative" begin
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10 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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11 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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12 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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13 Lx = 3.5
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14 Ly = 3.
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15 g_1D = EquidistantGrid(121, 0.0, Lx)
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16 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
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17
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18 @testset "Constructors" begin
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19 @testset "1D" begin
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20 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils)
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21 @test Dₓₓ == second_derivative(g_1D,inner_stencil,closure_stencils,1)
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22 @test Dₓₓ isa VolumeOperator
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23 end
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24 @testset "2D" begin
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25 Dₓₓ = second_derivative(g_2D,inner_stencil,closure_stencils,1)
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26 D2 = second_derivative(g_1D,inner_stencil,closure_stencils)
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27 I = IdentityMapping{Float64}(size(g_2D)[2])
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28 @test Dₓₓ == D2⊗I
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29 @test Dₓₓ isa TensorMapping{T,2,2} where T
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30 end
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31 end
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32
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33 # Exact differentiation is measured point-wise. In other cases
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34 # the error is measured in the l2-norm.
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35 @testset "Accuracy" begin
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36 @testset "1D" begin
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37 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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38 monomials = ()
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39 maxOrder = 4;
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40 for i = 0:maxOrder-1
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41 f_i(x) = 1/factorial(i)*x^i
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42 monomials = (monomials...,evalOn(g_1D,f_i))
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43 end
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44 v = evalOn(g_1D,x -> sin(x))
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45 vₓₓ = evalOn(g_1D,x -> -sin(x))
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46
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47 # 2nd order interior stencil, 1nd order boundary stencil,
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48 # implies that L*v should be exact for monomials up to order 2.
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49 @testset "2nd order" begin
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50 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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51 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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52 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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53 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils)
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54 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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55 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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56 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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57 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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58 end
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59
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60 # 4th order interior stencil, 2nd order boundary stencil,
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61 # implies that L*v should be exact for monomials up to order 3.
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62 @testset "4th order" begin
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63 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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64 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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65 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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66 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils)
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67 # NOTE: high tolerances for checking the "exact" differentiation
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68 # due to accumulation of round-off errors/cancellation errors?
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69 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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70 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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71 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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72 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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73 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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74 end
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75 end
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76
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77 @testset "2D" begin
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78 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
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79 binomials = ()
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80 maxOrder = 4;
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81 for i = 0:maxOrder-1
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82 f_i(x,y) = 1/factorial(i)*y^i + x^i
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83 binomials = (binomials...,evalOn(g_2D,f_i))
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84 end
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85 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
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86 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
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87
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88 # 2nd order interior stencil, 1st order boundary stencil,
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89 # implies that L*v should be exact for binomials up to order 2.
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90 @testset "2nd order" begin
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91 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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92 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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93 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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94 Dyy = second_derivative(g_2D,inner_stencil,closure_stencils,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(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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105 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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106 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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107 Dyy = second_derivative(g_2D,inner_stencil,closure_stencils,2)
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108 # NOTE: high tolerances for checking the "exact" differentiation
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109 # due to accumulation of round-off errors/cancellation errors?
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110 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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111 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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112 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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113 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
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114 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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115 end
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116 end
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117 end
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118 end