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comparison test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 1360:f59228534d3a tooling/benchmarks

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Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 20 May 2023 15:15:22 +0200
parents 356ec6a72974
children 43aaf710463e
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1321:42738616422e 1360:f59228534d3a
13 stencil_set = read_stencil_set(operator_path; order=4) 13 stencil_set = read_stencil_set(operator_path; order=4)
14 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"]) 14 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
15 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"]) 15 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
16 Lx = 3.5 16 Lx = 3.5
17 Ly = 3. 17 Ly = 3.
18 g_1D = EquidistantGrid(121, 0.0, Lx) 18 g_1D = equidistant_grid(121, 0.0, Lx)
19 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly)) 19 g_2D = equidistant_grid((121,123), (0.0, 0.0), (Lx, Ly))
20 20
21 @testset "Constructors" begin 21 @testset "Constructors" begin
22 @testset "1D" begin 22 @testset "1D" begin
23 Dₓₓ = second_derivative(g_1D,inner_stencil,closure_stencils,1) 23 Dₓₓ = second_derivative(g_1D, stencil_set)
24 @test Dₓₓ == second_derivative(g_1D,inner_stencil,closure_stencils) 24 @test Dₓₓ == second_derivative(g_1D, inner_stencil, closure_stencils)
25 @test Dₓₓ == second_derivative(g_1D,stencil_set,1) 25 @test Dₓₓ isa LazyTensor{Float64,1,1}
26 @test Dₓₓ == second_derivative(g_1D,stencil_set)
27 @test Dₓₓ isa VolumeOperator
28 end 26 end
29 @testset "2D" begin 27 @testset "2D" begin
30 Dₓₓ = second_derivative(g_2D,inner_stencil,closure_stencils,1) 28 Dₓₓ = second_derivative(g_2D,stencil_set,1)
31 D2 = second_derivative(g_1D,inner_stencil,closure_stencils,1) 29 @test Dₓₓ isa LazyTensor{Float64,2,2}
32 I = IdentityTensor{Float64}(size(g_2D)[2])
33 @test Dₓₓ == D2⊗I
34 @test Dₓₓ == second_derivative(g_2D,stencil_set,1)
35 @test Dₓₓ isa LazyTensor{T,2,2} where T
36 end 30 end
37 end 31 end
38 32
39 # Exact differentiation is measured point-wise. In other cases 33 # Exact differentiation is measured point-wise. In other cases
40 # the error is measured in the l2-norm. 34 # the error is measured in the l2-norm.
43 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2)); 37 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
44 monomials = () 38 monomials = ()
45 maxOrder = 4; 39 maxOrder = 4;
46 for i = 0:maxOrder-1 40 for i = 0:maxOrder-1
47 f_i(x) = 1/factorial(i)*x^i 41 f_i(x) = 1/factorial(i)*x^i
48 monomials = (monomials...,evalOn(g_1D,f_i)) 42 monomials = (monomials...,eval_on(g_1D,f_i))
49 end 43 end
50 v = evalOn(g_1D,x -> sin(x)) 44 v = eval_on(g_1D,x -> sin(x))
51 vₓₓ = evalOn(g_1D,x -> -sin(x)) 45 vₓₓ = eval_on(g_1D,x -> -sin(x))
52 46
53 # 2nd order interior stencil, 1nd order boundary stencil, 47 # 2nd order interior stencil, 1nd order boundary stencil,
54 # implies that L*v should be exact for monomials up to order 2. 48 # implies that L*v should be exact for monomials up to order 2.
55 @testset "2nd order" begin 49 @testset "2nd order" begin
56 stencil_set = read_stencil_set(operator_path; order=2) 50 stencil_set = read_stencil_set(operator_path; order=2)
75 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2 69 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
76 end 70 end
77 end 71 end
78 72
79 @testset "2D" begin 73 @testset "2D" begin
80 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2)); 74 l2(v) = sqrt(prod(spacing.(g_2D.grids))*sum(v.^2));
81 binomials = () 75 binomials = ()
82 maxOrder = 4; 76 maxOrder = 4;
83 for i = 0:maxOrder-1 77 for i = 0:maxOrder-1
84 f_i(x,y) = 1/factorial(i)*y^i + x^i 78 f_i(x,y) = 1/factorial(i)*y^i + x^i
85 binomials = (binomials...,evalOn(g_2D,f_i)) 79 binomials = (binomials...,eval_on(g_2D,f_i))
86 end 80 end
87 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y)) 81 v = eval_on(g_2D, (x,y) -> sin(x)+cos(y))
88 v_yy = evalOn(g_2D,(x,y) -> -cos(y)) 82 v_yy = eval_on(g_2D,(x,y) -> -cos(y))
89 83
90 # 2nd order interior stencil, 1st order boundary stencil, 84 # 2nd order interior stencil, 1st order boundary stencil,
91 # implies that L*v should be exact for binomials up to order 2. 85 # implies that L*v should be exact for binomials up to order 2.
92 @testset "2nd order" begin 86 @testset "2nd order" begin
93 stencil_set = read_stencil_set(operator_path; order=2) 87 stencil_set = read_stencil_set(operator_path; order=2)
94 Dyy = second_derivative(g_2D,stencil_set,2) 88 Dyy = second_derivative(g_2D,stencil_set,2)
95 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 89 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
96 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 90 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
97 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 91 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
98 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2 92 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
99 end 93 end
100 94
101 # 4th order interior stencil, 2nd order boundary stencil, 95 # 4th order interior stencil, 2nd order boundary stencil,
102 # implies that L*v should be exact for binomials up to order 3. 96 # implies that L*v should be exact for binomials up to order 3.
105 Dyy = second_derivative(g_2D,stencil_set,2) 99 Dyy = second_derivative(g_2D,stencil_set,2)
106 # NOTE: high tolerances for checking the "exact" differentiation 100 # NOTE: high tolerances for checking the "exact" differentiation
107 # due to accumulation of round-off errors/cancellation errors? 101 # due to accumulation of round-off errors/cancellation errors?
108 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 102 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
109 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 103 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
110 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 104 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
111 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9 105 @test Dyy*binomials[4] ≈ eval_on(g_2D,(x,y)->y) atol = 5e-9
112 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2 106 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
113 end 107 end
114 end 108 end
115 end 109 end
116 end 110 end