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annotate test/SbpOperators/volumeops/laplace/laplace_test.jl @ 1594:d68d02dd882f feature/boundary_conditions

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Merge with default
author Vidar Stiernström <vidar.stiernstrom@gmail.com>
date Sat, 25 May 2024 16:07:10 -0700
parents e96ee7d7ac9c 43aaf710463e
children 19cdec9c21cb
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45966c77cb20 Split tests for SbpOperators over several files
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1 using Test
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2
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3 using Sbplib.SbpOperators
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4 using Sbplib.Grids
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5 using Sbplib.LazyTensors
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6 using Sbplib.BoundaryConditions
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7
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8 @testset "Laplace" begin
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9 # Default stencils (4th order)
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10 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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11 stencil_set = read_stencil_set(operator_path; order=4)
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12 g_1D = equidistant_grid(0.0, 1., 101)
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13 g_3D = equidistant_grid((0.0, -1.0, 0.0), (1., 1., 1.), 51, 101, 52)
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14
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15 @testset "Constructors" begin
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16 @testset "1D" begin
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17 @test Laplace(g_1D, stencil_set) == Laplace(laplace(g_1D, stencil_set), stencil_set)
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18 @test Laplace(g_1D, stencil_set) isa LazyTensor{Float64,1,1}
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19 end
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20 @testset "3D" begin
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21 @test Laplace(g_3D, stencil_set) == Laplace(laplace(g_3D, stencil_set),stencil_set)
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22 @test Laplace(g_3D, stencil_set) isa LazyTensor{Float64,3,3}
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23 end
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24 end
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25
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26 # Exact differentiation is measured point-wise. In other cases
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27 # the error is measured in the l2-norm.
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28 @testset "Accuracy" begin
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29 l2(v) = sqrt(prod(spacing.(g_3D.grids))*sum(v.^2));
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30 polynomials = ()
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31 maxOrder = 4;
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32 for i = 0:maxOrder-1
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33 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
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34 polynomials = (polynomials...,eval_on(g_3D,f_i))
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35 end
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36 # v = eval_on(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
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37 # Δv = eval_on(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
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38
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39 v = eval_on(g_3D, x̄ -> sin(x̄[1]) + cos(x̄[2]) + exp(x̄[3]))
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40 Δv = eval_on(g_3D, x̄ -> -sin(x̄[1]) - cos(x̄[2]) + exp(x̄[3]))
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41 @inferred v[1,2,3]
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42
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43 # 2nd order interior stencil, 1st order boundary stencil,
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44 # implies that L*v should be exact for binomials up to order 2.
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45 @testset "2nd order" begin
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46 stencil_set = read_stencil_set(operator_path; order=2)
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47 Δ = Laplace(g_3D, stencil_set)
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48 @test Δ*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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49 @test Δ*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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50 @test Δ*polynomials[3] ≈ polynomials[1] atol = 5e-9
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51 @test Δ*v ≈ Δv rtol = 5e-2 norm = l2
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52 end
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53
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54 # 4th order interior stencil, 2nd order boundary stencil,
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55 # implies that L*v should be exact for binomials up to order 3.
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56 @testset "4th order" begin
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57 stencil_set = read_stencil_set(operator_path; order=4)
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58 Δ = Laplace(g_3D, stencil_set)
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59 # NOTE: high tolerances for checking the "exact" differentiation
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60 # due to accumulation of round-off errors/cancellation errors?
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61 @test Δ*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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62 @test Δ*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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63 @test Δ*polynomials[3] ≈ polynomials[1] atol = 5e-9
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64 @test Δ*polynomials[4] ≈ polynomials[2] atol = 5e-9
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65 @test Δ*v ≈ Δv rtol = 5e-4 norm = l2
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66 end
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67 end
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68 end
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69
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70 @testset "laplace" begin
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71 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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72 stencil_set = read_stencil_set(operator_path; order=4)
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73 g_1D = equidistant_grid(0.0, 1., 101)
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74 g_3D = equidistant_grid((0.0, -1.0, 0.0), (1., 1., 1.), 51, 101, 52)
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75
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76 @testset "1D" begin
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77 Δ = laplace(g_1D, stencil_set)
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78 @test Δ == second_derivative(g_1D, stencil_set)
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79 @test Δ isa LazyTensor{Float64,1,1}
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80 end
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81 @testset "3D" begin
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82 Δ = laplace(g_3D, stencil_set)
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83 @test Δ isa LazyTensor{Float64,3,3}
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84 Dxx = second_derivative(g_3D, stencil_set, 1)
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85 Dyy = second_derivative(g_3D, stencil_set, 2)
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86 Dzz = second_derivative(g_3D, stencil_set, 3)
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87 @test Δ == Dxx + Dyy + Dzz
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88 @test Δ isa LazyTensor{Float64,3,3}
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89 end
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90 end
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91
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92 @testset "sat_tensors" begin
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93 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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94 stencil_set = read_stencil_set(operator_path; order=4)
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95 g = equidistant_grid((101,102), (-1.,-1.), (1.,1.))
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96 W,E,S,N = boundary_identifiers(g)
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97
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98 u = eval_on(g, (x,y) -> sin(x+y))
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99 uWx = eval_on(boundary_grid(g,W), (x,y) -> -cos(x+y))
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100 uEx = eval_on(boundary_grid(g,E), (x,y) -> cos(x+y))
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101 uSy = eval_on(boundary_grid(g,S), (x,y) -> -cos(x+y))
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102 uNy = eval_on(boundary_grid(g,N), (x,y) -> cos(x+y))
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103
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104
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105 v = eval_on(g, (x,y) -> cos(x+y))
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106 vW = eval_on(boundary_grid(g,W), (x,y) -> cos(x+y))
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107 vE = eval_on(boundary_grid(g,E), (x,y) -> cos(x+y))
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108 vS = eval_on(boundary_grid(g,S), (x,y) -> cos(x+y))
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109 vN = eval_on(boundary_grid(g,N), (x,y) -> cos(x+y))
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110
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111
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112 @testset "Neumann" begin
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113 Δ = Laplace(g, stencil_set)
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114 H = inner_product(g, stencil_set)
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115 HW = inner_product(boundary_grid(g,W), stencil_set)
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116 HE = inner_product(boundary_grid(g,E), stencil_set)
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117 HS = inner_product(boundary_grid(g,S), stencil_set)
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118 HN = inner_product(boundary_grid(g,N), stencil_set)
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119
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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120 ncW = NeumannCondition(0., W)
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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121 ncE = NeumannCondition(0., E)
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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122 ncS = NeumannCondition(0., S)
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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123 ncN = NeumannCondition(0., N)
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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124
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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125 SATW = foldl(∘,sat_tensors(Δ, g, ncW))
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
diff changeset
126 SATE = foldl(∘,sat_tensors(Δ, g, ncE))
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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127 SATS = foldl(∘,sat_tensors(Δ, g, ncS))
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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128 SATN = foldl(∘,sat_tensors(Δ, g, ncN))
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
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parents: 1291
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129
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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130
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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131 @test sum((H*SATW*u).*v) ≈ sum((HW*uWx).*vW) rtol = 1e-6
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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132 @test sum((H*SATE*u).*v) ≈ sum((HE*uEx).*vE) rtol = 1e-6
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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133 @test sum((H*SATS*u).*v) ≈ sum((HS*uSy).*vS) rtol = 1e-6
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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134 @test sum((H*SATN*u).*v) ≈ sum((HN*uNy).*vN) rtol = 1e-6
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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135 end
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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136 end
e96ee7d7ac9c Test sat_tensors for Laplace w. Neumann conditions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1291
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137