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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 776:6fb556b02f7c refactor/sbp_operators_method_signatures

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Rename secondderivative.jl to second_derivative.jl
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 17 Jul 2021 18:07:15 +0200
parents test/SbpOperators/volumeops/derivatives/secondderivative_test.jl@6114274447f5
children d2f4ac2be47f
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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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6114274447f5 Add missing using and imports in test files
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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 @testset "SecondDerivative" begin
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10 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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11 Lx = 3.5
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12 Ly = 3.
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13 g_1D = EquidistantGrid(121, 0.0, Lx)
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14 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
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15
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16 @testset "Constructors" begin
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17 @testset "1D" begin
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18 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
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19 @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1)
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20 @test Dₓₓ isa VolumeOperator
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21 end
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22 @testset "2D" begin
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23 Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1)
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24 D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils)
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25 I = IdentityMapping{Float64}(size(g_2D)[2])
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26 @test Dₓₓ == D2⊗I
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27 @test Dₓₓ isa TensorMapping{T,2,2} where T
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28 end
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29 end
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30
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31 # Exact differentiation is measured point-wise. In other cases
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32 # the error is measured in the l2-norm.
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33 @testset "Accuracy" begin
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34 @testset "1D" begin
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35 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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36 monomials = ()
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37 maxOrder = 4;
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38 for i = 0:maxOrder-1
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39 f_i(x) = 1/factorial(i)*x^i
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40 monomials = (monomials...,evalOn(g_1D,f_i))
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41 end
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42 v = evalOn(g_1D,x -> sin(x))
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43 vₓₓ = evalOn(g_1D,x -> -sin(x))
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44
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45 # 2nd order interior stencil, 1nd order boundary stencil,
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46 # implies that L*v should be exact for monomials up to order 2.
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47 @testset "2nd order" begin
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48 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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49 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
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50 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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51 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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52 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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53 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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54 end
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55
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56 # 4th order interior stencil, 2nd order boundary stencil,
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57 # implies that L*v should be exact for monomials up to order 3.
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58 @testset "4th order" begin
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59 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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60 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
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61 # NOTE: high tolerances for checking the "exact" differentiation
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62 # due to accumulation of round-off errors/cancellation errors?
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63 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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64 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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65 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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66 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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67 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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68 end
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69 end
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70
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71 @testset "2D" begin
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72 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
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73 binomials = ()
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74 maxOrder = 4;
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75 for i = 0:maxOrder-1
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76 f_i(x,y) = 1/factorial(i)*y^i + x^i
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77 binomials = (binomials...,evalOn(g_2D,f_i))
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78 end
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79 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
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80 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
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81
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82 # 2nd order interior stencil, 1st order boundary stencil,
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83 # implies that L*v should be exact for binomials up to order 2.
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84 @testset "2nd order" begin
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85 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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86 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
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87 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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88 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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89 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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90 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
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91 end
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92
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93 # 4th order interior stencil, 2nd order boundary stencil,
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94 # implies that L*v should be exact for binomials up to order 3.
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95 @testset "4th order" begin
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96 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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97 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
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98 # NOTE: high tolerances for checking the "exact" differentiation
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99 # due to accumulation of round-off errors/cancellation errors?
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100 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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101 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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102 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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103 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
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104 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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105 end
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106 end
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107 end
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108 end