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annotate test/Grids/mapped_grid_test.jl @ 1739:e1ae5d8e30c3 feature/grids/curvilinear

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Add tests for jacobian_determinant, metric_tensor, and metric_tensor_inverse
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 11 Sep 2024 08:59:03 +0200
parents 7573c9244e47
children 9f2bc8ea6a07
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1 using Diffinitive.Grids
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2 using Diffinitive.RegionIndices
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3 using Test
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4 using StaticArrays
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5 using LinearAlgebra
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6
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7
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8 _skew_mapping(a,b) = (ξ̄->ξ̄[1]*a + ξ̄[2]*b, ξ̄->[a b])
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9
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10 function _partially_curved_mapping()
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11 x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
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12 J((ξ, η)) = @SMatrix[
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13 1 0;
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14 η*(2ξ-1) 1+ξ*(ξ-1);
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15 ]
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16
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17 return x̄, J
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18 end
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19
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20 function _fully_curved_mapping()
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21 x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
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22 J((ξ, η)) = @SMatrix[
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23 2 1-2η;
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24 (2+η)*ξ 3+1/2*ξ^2;
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25 ]
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26
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27 return x̄, J
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28 end
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29
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30 @testset "MappedGrid" begin
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31 @testset "Constructor" begin
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32 lg = equidistant_grid((0,0), (1,1), 11, 21)
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33 x̄ = map(ξ̄ -> 2ξ̄, lg)
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34 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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35 mg = MappedGrid(lg, x̄, J)
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36
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37 # TODO: Test constructor for different dims of range and domain for the coordinates
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38 # TODO: Test constructor with different type than TensorGrid. a dummy type?
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39 # TODO: Test that the element types agree
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40
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41 @test_broken false # @test_throws ArgumentError("Sizes must match") MappedGrid(lg, map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg), rand(SMatrix{2,3,Float64},15,11))
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42
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43
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44 @test mg isa Grid{SVector{2, Float64},2}
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45
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46 @test jacobian(mg) isa Array{<:AbstractMatrix}
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47 @test logicalgrid(mg) isa Grid
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48 end
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49
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50 @testset "Indexing Interface" begin
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51 lg = equidistant_grid((0,0), (1,1), 11, 21)
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52 x̄ = map(ξ̄ -> 2ξ̄, lg)
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53 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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54 mg = MappedGrid(lg, x̄, J)
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55 @test mg[1,1] == [0.0, 0.0]
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56 @test mg[4,2] == [0.6, 0.1]
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57 @test mg[6,10] == [1., 0.9]
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58
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59 @test mg[begin, begin] == [0.0, 0.0]
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60 @test mg[end,end] == [2.0, 2.0]
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61 @test mg[begin,end] == [0., 2.]
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62
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63 @test axes(mg) == (1:11, 1:21)
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64
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65 @testset "cartesian indexing" begin
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66 cases = [
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67 (1,1) ,
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68 (3,5) ,
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69 (10,6),
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70 (1,1) ,
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71 (3,2) ,
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72 ]
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73
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74 @testset "i = $is" for (lg, is) ∈ cases
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75 @test mg[CartesianIndex(is...)] == mg[is...]
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76 end
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77 end
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78
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79 @testset "eachindex" begin
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80 @test eachindex(mg) == CartesianIndices((11,21))
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81 end
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82
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83 @testset "firstindex" begin
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84 @test firstindex(mg, 1) == 1
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85 @test firstindex(mg, 2) == 1
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86 end
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87
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88 @testset "lastindex" begin
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89 @test lastindex(mg, 1) == 11
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90 @test lastindex(mg, 2) == 21
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91 end
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92 end
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93
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94 @testset "Iterator interface" begin
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95 lg = equidistant_grid((0,0), (1,1), 11, 21)
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96 x̄ = map(ξ̄ -> 2ξ̄, lg)
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97 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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98 mg = MappedGrid(lg, x̄, J)
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99
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100 sg = MappedGrid(
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101 equidistant_grid((0,0), (1,1), 15, 11),
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102 map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg), rand(SMatrix{2,3,Float64},15,11)
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103 )
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104
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105 @test eltype(mg) == SVector{2,Float64}
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106 @test eltype(sg) == SVector{3,Float64}
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107
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108 @test eltype(typeof(mg)) == SVector{2,Float64}
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109 @test eltype(typeof(sg)) == SVector{3,Float64}
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110
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111 @test size(mg) == (11,21)
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112 @test size(sg) == (15,11)
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113
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114 @test size(mg,2) == 21
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115 @test size(sg,2) == 11
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116
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117 @test length(mg) == 231
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118 @test length(sg) == 165
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119
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120 @test Base.IteratorSize(mg) == Base.HasShape{2}()
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121 @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}()
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122
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123 @test Base.IteratorSize(sg) == Base.HasShape{2}()
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124 @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}()
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125
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126 element, state = iterate(mg)
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127 @test element == lg[1,1].*2
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128 element, _ = iterate(mg, state)
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129 @test element == lg[2,1].*2
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130
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131 element, state = iterate(sg)
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132 @test element == sg.physicalcoordinates[1,1]
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133 element, _ = iterate(sg, state)
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134 @test element == sg.physicalcoordinates[2,1]
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135
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136 @test collect(mg) == 2 .* lg
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137 end
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138
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139 @testset "Base" begin
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140 lg = equidistant_grid((0,0), (1,1), 11, 21)
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141 x̄ = map(ξ̄ -> 2ξ̄, lg)
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142 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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143 mg = MappedGrid(lg, x̄, J)
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144
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145 @test ndims(mg) == 2
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146 end
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147
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148 @testset "==" begin
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149 sz = (15,11)
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150 lg = equidistant_grid((0,0), (1,1), sz...)
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151 x = rand(SVector{3,Float64}, sz...)
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152 J = rand(SMatrix{2,3,Float64}, sz...)
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153
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154 sg = MappedGrid(lg, x, J)
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155
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156 sg1 = MappedGrid(equidistant_grid((0,0), (1,1), sz...), copy(x), copy(J))
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157
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158 sz2 = (15,12)
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159 lg2 = equidistant_grid((0,0), (1,1), sz2...)
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160 x2 = rand(SVector{3,Float64}, sz2...)
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161 J2 = rand(SMatrix{2,3,Float64}, sz2...)
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162 sg2 = MappedGrid(lg2, x2, J2)
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163
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164 sg3 = MappedGrid(lg, rand(SVector{3,Float64}, sz...), J)
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165 sg4 = MappedGrid(lg, x, rand(SMatrix{2,3,Float64}, sz...))
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166
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167 @test sg == sg1
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168 @test sg != sg2 # Different size
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169 @test sg != sg3 # Different coordinates
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170 @test sg != sg4 # Different jacobian
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171 end
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172
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173 @testset "boundary_identifiers" begin
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174 lg = equidistant_grid((0,0), (1,1), 11, 15)
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175 x̄ = map(ξ̄ -> 2ξ̄, lg)
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176 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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177 mg = MappedGrid(lg, x̄, J)
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178 @test boundary_identifiers(mg) == boundary_identifiers(lg)
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179 end
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180
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181 @testset "boundary_indices" begin
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182 lg = equidistant_grid((0,0), (1,1), 11, 15)
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183 x̄ = map(ξ̄ -> 2ξ̄, lg)
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184 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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185 mg = MappedGrid(lg, x̄, J)
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186
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187 @test boundary_indices(mg, CartesianBoundary{1,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{1,LowerBoundary}())
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188 @test boundary_indices(mg, CartesianBoundary{2,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{2,LowerBoundary}())
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189 @test boundary_indices(mg, CartesianBoundary{1,UpperBoundary}()) == boundary_indices(lg,CartesianBoundary{1,UpperBoundary}())
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190 end
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191
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192 @testset "boundary_grid" begin
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193 x̄, J = _partially_curved_mapping()
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194 mg = mapped_grid(x̄, J, 10, 11)
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195 J1((ξ, η)) = @SMatrix[
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196 1 ;
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197 η*(2ξ-1);
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198 ]
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199 J2((ξ, η)) = @SMatrix[
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200 0;
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201 1+ξ*(ξ-1);
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202 ]
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203
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204 function expected_bg(mg, bId, Jb)
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205 lg = logicalgrid(mg)
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206 return MappedGrid(
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207 boundary_grid(lg, bId),
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208 map(x̄, boundary_grid(lg, bId)),
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209 map(Jb, boundary_grid(lg, bId)),
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210 )
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211 end
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212
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213 let bid = TensorGridBoundary{1, LowerBoundary}()
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214 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
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215 end
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216
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217 let bid = TensorGridBoundary{1, UpperBoundary}()
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218 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
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219 end
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220
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221 let bid = TensorGridBoundary{2, LowerBoundary}()
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222 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
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223 end
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224
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225 let bid = TensorGridBoundary{2, UpperBoundary}()
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226 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
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227 end
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228 end
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229 end
1502
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230
1506
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231 @testset "mapped_grid" begin
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232 x̄, J = _partially_curved_mapping()
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233 mg = mapped_grid(x̄, J, 10, 11)
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234 @test mg isa MappedGrid{SVector{2,Float64}, 2}
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235
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diff changeset
236 lg = equidistant_grid((0,0), (1,1), 10, 11)
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diff changeset
237 @test logicalgrid(mg) == lg
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diff changeset
238 @test collect(mg) == map(x̄, lg)
1704
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239
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diff changeset
240 @test mapped_grid(lg, x̄, J) == mg
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241 end
1659
3bbcd496e021 Add function for computing the normal at the boundary of a mapped grid as a grid function
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diff changeset
242
1690
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diff changeset
243 @testset "jacobian_determinant" begin
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diff changeset
244 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2]
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245 J((ξ, η)) = @SMatrix[
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diff changeset
246 η ξ;
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247 1 2η;
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248 ]
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249
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250 g = mapped_grid(x̄, J, 10, 11)
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251 J = map(logicalgrid(g)) do (ξ,η)
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252 2η^2 - ξ
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253 end
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254 @test jacobian_determinant(g) ≈ J
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255 end
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256
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diff changeset
257 @testset "metric_tensor" begin
1739
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258 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2]
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259 J((ξ, η)) = @SMatrix[
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diff changeset
260 η ξ;
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diff changeset
261 1 2η;
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diff changeset
262 ]
e1ae5d8e30c3 Add tests for jacobian_determinant, metric_tensor, and metric_tensor_inverse
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263
e1ae5d8e30c3 Add tests for jacobian_determinant, metric_tensor, and metric_tensor_inverse
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264 g = mapped_grid(x̄, J, 10, 11)
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diff changeset
265 G = map(logicalgrid(g)) do (ξ,η)
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266 @SMatrix[
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267 1+η^2 ξ*η+2η;
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268 ξ*η+2η ξ^2 + 4η^2;
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269 ]
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270 end
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271 @test metric_tensor(g) ≈ G
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272 end
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273
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274 @testset "metric_tensor_inverse" begin
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275 x̄((ξ, η)) = @SVector[ξ + ξ^2/2, η + η^2 + ξ^2/2]
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276 J((ξ, η)) = @SMatrix[
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277 1+ξ 0;
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278 ξ 1+η;
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279 ]
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280
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281 g = mapped_grid(x̄, J, 10, 11)
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282 G⁻¹ = map(logicalgrid(g)) do (ξ,η)
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283 @SMatrix[
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284 (1+η)^2 -ξ*(1+η);
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285 -ξ*(1+η) (1+ξ)^2+ξ^2;
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286 ]/(((1+ξ)^2+ξ^2)*(1+η)^2 - ξ^2*(1+η)^2)
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287
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288 end
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289
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290 @test metric_tensor_inverse(g) ≈ G⁻¹
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291 end
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292
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293 @testset "min_spacing" begin
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294 let g = mapped_grid(identity, x->@SMatrix[1], 11)
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295 @test min_spacing(g) ≈ 0.1
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296 end
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297
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298 let g = mapped_grid(x->x+x.^2/2, x->@SMatrix[1 .+ x], 11)
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299 @test min_spacing(g) ≈ 0.105
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300 end
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301
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302 let g = mapped_grid(x->x + x.*(1 .- x)/2, x->@SMatrix[1.5 .- x], 11)
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303 @test min_spacing(g) ≈ 0.055
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304 end
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305
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306 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,11)
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307 @test min_spacing(g) ≈ 0.1
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308 end
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309
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310 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,21)
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311 @test min_spacing(g) ≈ 0.05
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312 end
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313
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314
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315 @testset let a = @SVector[1,0], b = @SVector[1,1]/√2
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316 g = mapped_grid(_skew_mapping(a,b)...,11,11)
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317
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318 @test min_spacing(g) ≈ 0.1*norm(b-a)
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319 end
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320
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321 @testset let a = @SVector[1,0], b = @SVector[-1,1]/√2
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322 g = mapped_grid(_skew_mapping(a,b)...,11,11)
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323
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324 @test min_spacing(g) ≈ 0.1*norm(a+b)
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325 end
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326 end
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327
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328 @testset "normal" begin
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329 g = mapped_grid(_partially_curved_mapping()...,10, 11)
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330
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331 @test normal(g, CartesianBoundary{1,LowerBoundary}()) == fill(@SVector[-1,0], 11)
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332 @test normal(g, CartesianBoundary{1,UpperBoundary}()) == fill(@SVector[1,0], 11)
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333 @test normal(g, CartesianBoundary{2,LowerBoundary}()) == fill(@SVector[0,-1], 10)
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334 @test normal(g, CartesianBoundary{2,UpperBoundary}()) ≈ map(boundary_grid(g,CartesianBoundary{2,UpperBoundary}())|>logicalgrid) do ξ̄
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335 α = 1-2ξ̄[1]
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336 @SVector[α,1]/√(α^2 + 1)
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337 end
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338
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339 g = mapped_grid(_fully_curved_mapping()...,5,4)
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340
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341 unit(v) = v/norm(v)
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342 @testset let bId = CartesianBoundary{1,LowerBoundary}()
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343 lbg = boundary_grid(logicalgrid(g), bId)
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344 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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345 -unit(@SVector[1/2, η/3-1/6])
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346 end
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347 end
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348
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349 @testset let bId = CartesianBoundary{1,UpperBoundary}()
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350 lbg = boundary_grid(logicalgrid(g), bId)
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351 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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352 unit(@SVector[7/2, 2η-1]/(5 + 3η + 2η^2))
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353 end
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354 end
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355
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356 @testset let bId = CartesianBoundary{2,LowerBoundary}()
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357 lbg = boundary_grid(logicalgrid(g), bId)
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358 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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359 -unit(@SVector[-2ξ, 2]/(6 + ξ^2 - 2ξ))
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360 end
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361 end
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362
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363 @testset let bId = CartesianBoundary{2,UpperBoundary}()
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364 lbg = boundary_grid(logicalgrid(g), bId)
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365 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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366 unit(@SVector[-3ξ, 2]/(6 + ξ^2 + 3ξ))
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367 end
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368 end
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369 end