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comparison test/SbpOperators/volumeops/laplace/laplace_test.jl @ 728:45966c77cb20 feature/selectable_tests

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Split tests for SbpOperators over several files
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 17 Mar 2021 20:34:40 +0100
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children 6114274447f5
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727:95b207729b7a 728:45966c77cb20
1 using Test
2
3 using Sbplib.SbpOperators
4 using Sbplib.Grids
5
6 @testset "Laplace" begin
7 g_1D = EquidistantGrid(101, 0.0, 1.)
8 g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.))
9 @testset "Constructors" begin
10 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
11 @testset "1D" begin
12 L = laplace(g_1D, op.innerStencil, op.closureStencils)
13 @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils)
14 @test L isa TensorMapping{T,1,1} where T
15 end
16 @testset "3D" begin
17 L = laplace(g_3D, op.innerStencil, op.closureStencils)
18 @test L isa TensorMapping{T,3,3} where T
19 Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1)
20 Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2)
21 Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,3)
22 @test L == Dxx + Dyy + Dzz
23 end
24 end
25
26 # Exact differentiation is measured point-wise. In other cases
27 # the error is measured in the l2-norm.
28 @testset "Accuracy" begin
29 l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2));
30 polynomials = ()
31 maxOrder = 4;
32 for i = 0:maxOrder-1
33 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
34 polynomials = (polynomials...,evalOn(g_3D,f_i))
35 end
36 v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
37 Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
38
39 # 2nd order interior stencil, 1st order boundary stencil,
40 # implies that L*v should be exact for binomials up to order 2.
41 @testset "2nd order" begin
42 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
43 L = laplace(g_3D,op.innerStencil,op.closureStencils)
44 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
45 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
46 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
47 @test L*v ≈ Δv rtol = 5e-2 norm = l2
48 end
49
50 # 4th order interior stencil, 2nd order boundary stencil,
51 # implies that L*v should be exact for binomials up to order 3.
52 @testset "4th order" begin
53 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
54 L = laplace(g_3D,op.innerStencil,op.closureStencils)
55 # NOTE: high tolerances for checking the "exact" differentiation
56 # due to accumulation of round-off errors/cancellation errors?
57 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
58 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
59 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
60 @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9
61 @test L*v ≈ Δv rtol = 5e-4 norm = l2
62 end
63 end
64 end