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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 1726:471a948cd2b2 rename_module

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Rename project from Sbplib to Diffinitive
author Vidar Stiernström <vidar.stiernstrom@gmail.com>
date Sat, 07 Sep 2024 12:11:53 -0700
parents 43aaf710463e
children
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1 using Test
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2
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3 using Diffinitive.SbpOperators
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4 using Diffinitive.Grids
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5 using Diffinitive.LazyTensors
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7 import Diffinitive.SbpOperators.VolumeOperator
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8
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9 # TODO: Refactor these test to look more like the tests in first_derivative_test.jl.
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10
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11 @testset "SecondDerivative" begin
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12 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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13 stencil_set = read_stencil_set(operator_path; order=4)
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14 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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15 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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16 Lx = 3.5
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17 Ly = 3.
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18 g_1D = equidistant_grid(0.0, Lx, 121)
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19 g_2D = equidistant_grid((0.0, 0.0), (Lx, Ly), 121, 123)
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21 @testset "Constructors" begin
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22 @testset "1D" begin
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23 Dₓₓ = second_derivative(g_1D, stencil_set)
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24 @test Dₓₓ == second_derivative(g_1D, inner_stencil, closure_stencils)
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25 @test Dₓₓ isa LazyTensor{Float64,1,1}
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26 end
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27 @testset "2D" begin
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28 Dₓₓ = second_derivative(g_2D,stencil_set,1)
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29 @test Dₓₓ isa LazyTensor{Float64,2,2}
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30 end
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31 end
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33 # Exact differentiation is measured point-wise. In other cases
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34 # the error is measured in the l2-norm.
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35 @testset "Accuracy" begin
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36 @testset "1D" begin
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37 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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38 monomials = ()
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39 maxOrder = 4;
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40 for i = 0:maxOrder-1
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41 f_i(x) = 1/factorial(i)*x^i
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42 monomials = (monomials...,eval_on(g_1D,f_i))
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43 end
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44 v = eval_on(g_1D,x -> sin(x))
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45 vₓₓ = eval_on(g_1D,x -> -sin(x))
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47 # 2nd order interior stencil, 1nd order boundary stencil,
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48 # implies that L*v should be exact for monomials up to order 2.
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49 @testset "2nd order" begin
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50 stencil_set = read_stencil_set(operator_path; order=2)
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51 Dₓₓ = second_derivative(g_1D,stencil_set)
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52 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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53 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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54 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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55 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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56 end
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57
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58 # 4th order interior stencil, 2nd order boundary stencil,
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59 # implies that L*v should be exact for monomials up to order 3.
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60 @testset "4th order" begin
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61 stencil_set = read_stencil_set(operator_path; order=4)
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62 Dₓₓ = second_derivative(g_1D,stencil_set)
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63 # NOTE: high tolerances for checking the "exact" differentiation
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64 # due to accumulation of round-off errors/cancellation errors?
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65 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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66 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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67 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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68 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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69 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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70 end
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71 end
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72
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73 @testset "2D" begin
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74 l2(v) = sqrt(prod(spacing.(g_2D.grids))*sum(v.^2));
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75 binomials = ()
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76 maxOrder = 4;
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77 for i = 0:maxOrder-1
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78 f_i(x,y) = 1/factorial(i)*y^i + x^i
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79 binomials = (binomials...,eval_on(g_2D,f_i))
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80 end
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81 v = eval_on(g_2D, (x,y) -> sin(x)+cos(y))
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82 v_yy = eval_on(g_2D,(x,y) -> -cos(y))
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83
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84 # 2nd order interior stencil, 1st order boundary stencil,
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85 # implies that L*v should be exact for binomials up to order 2.
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86 @testset "2nd order" begin
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87 stencil_set = read_stencil_set(operator_path; order=2)
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88 Dyy = second_derivative(g_2D,stencil_set,2)
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89 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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90 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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91 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
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92 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
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93 end
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94
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95 # 4th order interior stencil, 2nd order boundary stencil,
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96 # implies that L*v should be exact for binomials up to order 3.
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97 @testset "4th order" begin
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98 stencil_set = read_stencil_set(operator_path; order=4)
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99 Dyy = second_derivative(g_2D,stencil_set,2)
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100 # NOTE: high tolerances for checking the "exact" differentiation
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101 # due to accumulation of round-off errors/cancellation errors?
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102 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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103 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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104 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
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105 @test Dyy*binomials[4] ≈ eval_on(g_2D,(x,y)->y) atol = 5e-9
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106 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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107 end
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108 end
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109 end
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110 end