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comparison test/SbpOperators/volumeops/derivatives/secondderivative_test.jl @ 769:0158c3fd521c operator_storage_array_of_table

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Merge in default
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 15 Jul 2021 00:06:16 +0200
parents 6114274447f5
children
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768:7c87a33963c5 769:0158c3fd521c
1 using Test
2
3 using Sbplib.SbpOperators
4 using Sbplib.Grids
5 using Sbplib.LazyTensors
6
7 import Sbplib.SbpOperators.VolumeOperator
8
9 @testset "SecondDerivative" begin
10 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
11 Lx = 3.5
12 Ly = 3.
13 g_1D = EquidistantGrid(121, 0.0, Lx)
14 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
15
16 @testset "Constructors" begin
17 @testset "1D" begin
18 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
19 @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1)
20 @test Dₓₓ isa VolumeOperator
21 end
22 @testset "2D" begin
23 Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1)
24 D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils)
25 I = IdentityMapping{Float64}(size(g_2D)[2])
26 @test Dₓₓ == D2⊗I
27 @test Dₓₓ isa TensorMapping{T,2,2} where T
28 end
29 end
30
31 # Exact differentiation is measured point-wise. In other cases
32 # the error is measured in the l2-norm.
33 @testset "Accuracy" begin
34 @testset "1D" begin
35 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
36 monomials = ()
37 maxOrder = 4;
38 for i = 0:maxOrder-1
39 f_i(x) = 1/factorial(i)*x^i
40 monomials = (monomials...,evalOn(g_1D,f_i))
41 end
42 v = evalOn(g_1D,x -> sin(x))
43 vₓₓ = evalOn(g_1D,x -> -sin(x))
44
45 # 2nd order interior stencil, 1nd order boundary stencil,
46 # implies that L*v should be exact for monomials up to order 2.
47 @testset "2nd order" begin
48 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
49 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
50 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
51 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
52 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
53 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
54 end
55
56 # 4th order interior stencil, 2nd order boundary stencil,
57 # implies that L*v should be exact for monomials up to order 3.
58 @testset "4th order" begin
59 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
60 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
61 # NOTE: high tolerances for checking the "exact" differentiation
62 # due to accumulation of round-off errors/cancellation errors?
63 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
64 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
65 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
66 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
67 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
68 end
69 end
70
71 @testset "2D" begin
72 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
73 binomials = ()
74 maxOrder = 4;
75 for i = 0:maxOrder-1
76 f_i(x,y) = 1/factorial(i)*y^i + x^i
77 binomials = (binomials...,evalOn(g_2D,f_i))
78 end
79 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
80 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
81
82 # 2nd order interior stencil, 1st order boundary stencil,
83 # implies that L*v should be exact for binomials up to order 2.
84 @testset "2nd order" begin
85 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
86 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
87 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
88 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
89 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
90 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
91 end
92
93 # 4th order interior stencil, 2nd order boundary stencil,
94 # implies that L*v should be exact for binomials up to order 3.
95 @testset "4th order" begin
96 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
97 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
98 # NOTE: high tolerances for checking the "exact" differentiation
99 # due to accumulation of round-off errors/cancellation errors?
100 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
101 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
102 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
103 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
104 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
105 end
106 end
107 end
108 end