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comparison test/SbpOperators/volumeops/derivatives/first_derivative_test.jl @ 985:1b4f31ae114f

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Merge feature/first_derivative
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 16 Mar 2022 18:32:59 +0100
parents 5bfc03cf3ba7
children 7bf3121c6864 1ba8a398af9c e00eb000346e
comparison
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970:a52bd2f1126c 985:1b4f31ae114f
1 using Test
2
3
4 using Sbplib.SbpOperators
5 using Sbplib.Grids
6 using Sbplib.LazyTensors
7
8 using Sbplib.SbpOperators: closure_size, Stencil, VolumeOperator
9
10 """
11 monomial(x,k)
12
13 Evaluates ``x^k/k!` with the convetion that it is ``0`` for all ``k<0``.
14 Has the property that ``d/dx monomial(x,k) = monomial(x,k-1)``
15 """
16 function monomial(x,k)
17 if k < 0
18 return zero(x)
19 end
20 x^k/factorial(k)
21 end
22
23 @testset "first_derivative" begin
24 @testset "Constructors" begin
25 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
26
27 g₁ = EquidistantGrid(11, 0., 1.)
28 g₂ = EquidistantGrid((11,14), (0.,1.), (1.,3.))
29
30 @test first_derivative(g₁, stencil_set, 1) isa TensorMapping{Float64,1,1}
31 @test first_derivative(g₂, stencil_set, 2) isa TensorMapping{Float64,2,2}
32
33 interior_stencil = CenteredStencil(-1,0,1)
34 closure_stencils = [Stencil(-1,1, center=1)]
35
36 @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa TensorMapping{Float64,1,1}
37 @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa VolumeOperator
38 @test first_derivative(g₂, interior_stencil, closure_stencils, 2) isa TensorMapping{Float64,2,2}
39 end
40
41 @testset "Accuracy conditions" begin
42 N = 20
43 g = EquidistantGrid(N, 0//1,2//1)
44 @testset for order ∈ [2,4]
45 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order)
46 D₁ = first_derivative(g, stencil_set, 1)
47
48 @testset "boundary x^$k" for k ∈ 0:order÷2
49 v = evalOn(g, x->monomial(x,k))
50
51 @testset for i ∈ 1:closure_size(D₁)
52 x, = points(g)[i]
53 @test (D₁*v)[i] == monomial(x,k-1)
54 end
55
56 @testset for i ∈ (N-closure_size(D₁)+1):N
57 x, = points(g)[i]
58 @test (D₁*v)[i] == monomial(x,k-1)
59 end
60 end
61
62 @testset "interior x^$k" for k ∈ 0:order
63 v = evalOn(g, x->monomial(x,k))
64
65 x, = points(g)[10]
66 @test (D₁*v)[10] == monomial(x,k-1)
67 end
68 end
69 end
70
71 @testset "Accuracy on function" begin
72 g = EquidistantGrid(30, 0.,1.)
73 v = evalOn(g, x->exp(x))
74 @testset for (order, tol) ∈ [(2, 6e-3),(4, 2e-4)]
75 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order)
76 D₁ = first_derivative(g, stencil_set, 1)
77
78 @test D₁*v ≈ v rtol=tol
79 end
80 end
81 end
82