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annotate test/SbpOperators/volumeops/derivatives/first_derivative_test.jl @ 995:1ba8a398af9c refactor/lazy_tensors

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Rename types
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 18 Mar 2022 21:14:47 +0100
parents 5bfc03cf3ba7
children 7fc8df5157a7 05a25a5063bb
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1 using Test
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2
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3
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4 using Sbplib.SbpOperators
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5 using Sbplib.Grids
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6 using Sbplib.LazyTensors
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8 using Sbplib.SbpOperators: closure_size, Stencil, VolumeOperator
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9
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10 """
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11 monomial(x,k)
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12
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13 Evaluates ``x^k/k!` with the convetion that it is ``0`` for all ``k<0``.
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14 Has the property that ``d/dx monomial(x,k) = monomial(x,k-1)``
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15 """
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16 function monomial(x,k)
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17 if k < 0
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18 return zero(x)
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19 end
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20 x^k/factorial(k)
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21 end
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22
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23 @testset "first_derivative" begin
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24 @testset "Constructors" begin
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25 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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26
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27 g₁ = EquidistantGrid(11, 0., 1.)
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28 g₂ = EquidistantGrid((11,14), (0.,1.), (1.,3.))
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29
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30 @test first_derivative(g₁, stencil_set, 1) isa LazyTensor{Float64,1,1}
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31 @test first_derivative(g₂, stencil_set, 2) isa LazyTensor{Float64,2,2}
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32
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33 interior_stencil = CenteredStencil(-1,0,1)
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34 closure_stencils = [Stencil(-1,1, center=1)]
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35
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36 @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa LazyTensor{Float64,1,1}
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37 @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa VolumeOperator
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38 @test first_derivative(g₂, interior_stencil, closure_stencils, 2) isa LazyTensor{Float64,2,2}
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39 end
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40
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41 @testset "Accuracy conditions" begin
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42 N = 20
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43 g = EquidistantGrid(N, 0//1,2//1)
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44 @testset for order ∈ [2,4]
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45 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order)
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46 D₁ = first_derivative(g, stencil_set, 1)
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47
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48 @testset "boundary x^$k" for k ∈ 0:order÷2
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49 v = evalOn(g, x->monomial(x,k))
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50
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51 @testset for i ∈ 1:closure_size(D₁)
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52 x, = points(g)[i]
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53 @test (D₁*v)[i] == monomial(x,k-1)
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54 end
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55
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56 @testset for i ∈ (N-closure_size(D₁)+1):N
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57 x, = points(g)[i]
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58 @test (D₁*v)[i] == monomial(x,k-1)
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59 end
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60 end
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61
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62 @testset "interior x^$k" for k ∈ 0:order
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63 v = evalOn(g, x->monomial(x,k))
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64
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65 x, = points(g)[10]
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66 @test (D₁*v)[10] == monomial(x,k-1)
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67 end
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68 end
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69 end
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71 @testset "Accuracy on function" begin
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72 g = EquidistantGrid(30, 0.,1.)
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73 v = evalOn(g, x->exp(x))
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74 @testset for (order, tol) ∈ [(2, 6e-3),(4, 2e-4)]
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75 stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order)
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76 D₁ = first_derivative(g, stencil_set, 1)
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77
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78 @test D₁*v ≈ v rtol=tol
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79 end
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80 end
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81 end
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82