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annotate test/SbpOperators/volumeops/derivatives/second_derivative_test.jl @ 2080:0f949681d3d3 refactor/sbp_operators/direction_check tip

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Check that direction of first/second derivative operators is within the dimension of the grid. Add 1D functions for first/second derivative operators that take a direction.
author Vidar Stiernström <vidar.stiernstrom@gmail.com>
date Fri, 20 Feb 2026 12:01:05 +0100
parents 471a948cd2b2
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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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, stencil_set, 1)
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25 @test Dₓₓ == second_derivative(g_1D, inner_stencil, closure_stencils)
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26 @test Dₓₓ isa LazyTensor{Float64,1,1}
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0f949681d3d3 Check that direction of first/second derivative operators is within the dimension of the grid. Add 1D functions for first/second derivative operators that take a direction.
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28 @test_throws DomainError(3, "Direction must be inside [0, 1].") second_derivative(g_1D, stencil_set, 3)
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29 end
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30 @testset "2D" begin
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31 Dₓₓ = second_derivative(g_2D,stencil_set,1)
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32 @test Dₓₓ isa LazyTensor{Float64,2,2}
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33 end
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34 end
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36 # Exact differentiation is measured point-wise. In other cases
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37 # the error is measured in the l2-norm.
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38 @testset "Accuracy" begin
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39 @testset "1D" begin
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40 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
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41 monomials = ()
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42 maxOrder = 4;
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43 for i = 0:maxOrder-1
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44 f_i(x) = 1/factorial(i)*x^i
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45 monomials = (monomials...,eval_on(g_1D,f_i))
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46 end
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47 v = eval_on(g_1D,x -> sin(x))
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48 vₓₓ = eval_on(g_1D,x -> -sin(x))
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50 # 2nd order interior stencil, 1nd order boundary stencil,
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51 # implies that L*v should be exact for monomials up to order 2.
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52 @testset "2nd order" begin
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53 stencil_set = read_stencil_set(operator_path; order=2)
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54 Dₓₓ = second_derivative(g_1D,stencil_set)
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55 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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56 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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57 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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58 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
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59 end
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60
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61 # 4th order interior stencil, 2nd order boundary stencil,
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62 # implies that L*v should be exact for monomials up to order 3.
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63 @testset "4th order" begin
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64 stencil_set = read_stencil_set(operator_path; order=4)
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65 Dₓₓ = second_derivative(g_1D,stencil_set)
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66 # NOTE: high tolerances for checking the "exact" differentiation
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67 # due to accumulation of round-off errors/cancellation errors?
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68 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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69 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
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70 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
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71 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
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72 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
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73 end
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74 end
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75
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76 @testset "2D" begin
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77 l2(v) = sqrt(prod(spacing.(g_2D.grids))*sum(v.^2));
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78 binomials = ()
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79 maxOrder = 4;
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80 for i = 0:maxOrder-1
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81 f_i(x,y) = 1/factorial(i)*y^i + x^i
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82 binomials = (binomials...,eval_on(g_2D,f_i))
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83 end
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84 v = eval_on(g_2D, (x,y) -> sin(x)+cos(y))
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85 v_yy = eval_on(g_2D,(x,y) -> -cos(y))
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86
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87 # 2nd order interior stencil, 1st order boundary stencil,
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88 # implies that L*v should be exact for binomials up to order 2.
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89 @testset "2nd order" begin
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90 stencil_set = read_stencil_set(operator_path; order=2)
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91 Dyy = second_derivative(g_2D,stencil_set,2)
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92 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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93 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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94 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
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95 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
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96 end
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97
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98 # 4th order interior stencil, 2nd order boundary stencil,
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99 # implies that L*v should be exact for binomials up to order 3.
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100 @testset "4th order" begin
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101 stencil_set = read_stencil_set(operator_path; order=4)
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102 Dyy = second_derivative(g_2D,stencil_set,2)
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103 # NOTE: high tolerances for checking the "exact" differentiation
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104 # due to accumulation of round-off errors/cancellation errors?
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105 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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106 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
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107 @test Dyy*binomials[3] ≈ eval_on(g_2D,(x,y)->1.) atol = 5e-9
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108 @test Dyy*binomials[4] ≈ eval_on(g_2D,(x,y)->y) atol = 5e-9
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109 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
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110 end
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111 end
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112 end
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113 end