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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 964:2ae62dbaf839 feature/laplace_opset

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Add method for creating second derivative from a stencil set.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 14 Mar 2022 10:43:11 +0100
parents d2f4ac2be47f
children 7bf3121c6864 1ba8a398af9c
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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 @testset "SecondDerivative" begin
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10 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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11 stencil_set = read_stencil_set(operator_path; order=4)
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12 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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13 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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14 Lx = 3.5
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15 Ly = 3.
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16 g_1D = EquidistantGrid(121, 0.0, Lx)
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17 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
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18
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19 @testset "Constructors" begin
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20 @testset "1D" begin
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21 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils,1)
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22 @test Dₓₓ == second_derivative(g_1D,inner_stencil,closure_stencils)
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23 @test Dₓₓ == second_derivative(g_1D,stencil_set,1)
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24 @test Dₓₓ isa VolumeOperator
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25 end
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26 @testset "2D" begin
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27 Dₓₓ = second_derivative(g_2D,inner_stencil,closure_stencils,1)
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28 D2 = second_derivative(g_1D,inner_stencil,closure_stencils)
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29 I = IdentityMapping{Float64}(size(g_2D)[2])
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30 @test Dₓₓ == D2⊗I
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31 @test Dₓₓ == second_derivative(g_2D,stencil_set,1)
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32 @test Dₓₓ isa TensorMapping{T,2,2} where T
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33 end
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34 end
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35
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36 # Exact differentiation is measured point-wise. In other cases
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37 # the error is measured in the l2-norm.
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38 @testset "Accuracy" begin
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39 @testset "1D" begin
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40 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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41 monomials = ()
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42 maxOrder = 4;
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43 for i = 0:maxOrder-1
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44 f_i(x) = 1/factorial(i)*x^i
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45 monomials = (monomials...,evalOn(g_1D,f_i))
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46 end
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47 v = evalOn(g_1D,x -> sin(x))
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48 vₓₓ = evalOn(g_1D,x -> -sin(x))
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49
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50 # 2nd order interior stencil, 1nd order boundary stencil,
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51 # implies that L*v should be exact for monomials up to order 2.
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52 @testset "2nd order" begin
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53 stencil_set = read_stencil_set(operator_path; order=2)
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54 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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55 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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56 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils)
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57 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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58 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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59 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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60 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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61 end
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62
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63 # 4th order interior stencil, 2nd order boundary stencil,
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64 # implies that L*v should be exact for monomials up to order 3.
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65 @testset "4th order" begin
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66 stencil_set = read_stencil_set(operator_path; order=4)
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67 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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68 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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69 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils)
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70 # NOTE: high tolerances for checking the "exact" differentiation
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71 # due to accumulation of round-off errors/cancellation errors?
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72 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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73 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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74 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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75 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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76 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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77 end
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78 end
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79
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80 @testset "2D" begin
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81 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
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82 binomials = ()
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83 maxOrder = 4;
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84 for i = 0:maxOrder-1
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85 f_i(x,y) = 1/factorial(i)*y^i + x^i
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86 binomials = (binomials...,evalOn(g_2D,f_i))
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87 end
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88 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
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89 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
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90
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91 # 2nd order interior stencil, 1st order boundary stencil,
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92 # implies that L*v should be exact for binomials up to order 2.
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93 @testset "2nd order" begin
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94 stencil_set = read_stencil_set(operator_path; order=2)
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95 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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96 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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97 Dyy = second_derivative(g_2D,inner_stencil,closure_stencils,2)
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98 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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99 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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100 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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101 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
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102 end
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103
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104 # 4th order interior stencil, 2nd order boundary stencil,
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105 # implies that L*v should be exact for binomials up to order 3.
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106 @testset "4th order" begin
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107 stencil_set = read_stencil_set(operator_path; order=4)
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108 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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109 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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110 Dyy = second_derivative(g_2D,inner_stencil,closure_stencils,2)
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111 # NOTE: high tolerances for checking the "exact" differentiation
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112 # due to accumulation of round-off errors/cancellation errors?
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113 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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114 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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115 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
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116 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
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117 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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118 end
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119 end
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120 end
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121 end