Mercurial > repos > public > sbplib_julia
annotate test/Grids/mapped_grid_test.jl @ 1742:c9c601678a14 feature/grids/curvilinear
Add test for construction of Rn->Rm grid
author | Jonatan Werpers <jonatan@werpers.com> |
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date | Wed, 11 Sep 2024 12:09:59 +0200 |
parents | 248304f88e49 |
children | 49bd573ab07f |
rev | line source |
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1736 | 1 using Diffinitive.Grids |
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 |
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34 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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35 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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36 mg = MappedGrid(lg, x̄, J) |
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37 |
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38 @test mg isa Grid{SVector{2, Float64},2} |
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39 @test jacobian(mg) isa Array{<:AbstractMatrix} |
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40 @test logicalgrid(mg) isa Grid |
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41 |
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42 @test collect(mg) == x̄ |
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43 @test jacobian(mg) == J |
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44 @test logicalgrid(mg) == lg |
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45 |
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46 |
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47 x̄ = map(ξ̄ -> @SVector[ξ̄[1],ξ̄[2], ξ̄[1] + ξ̄[2]], lg) |
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48 J = map(ξ̄ -> @SMatrix[1 0; 0 1; 1 1], lg) |
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49 mg = MappedGrid(lg, x̄, J) |
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50 |
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51 @test mg isa Grid{SVector{3, Float64},2} |
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52 @test jacobian(mg) isa Array{<:AbstractMatrix} |
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53 @test logicalgrid(mg) isa Grid |
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54 |
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55 @test collect(mg) == x̄ |
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56 @test jacobian(mg) == J |
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57 @test logicalgrid(mg) == lg |
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58 |
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59 # TODO: Test that the element types agree |
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61 @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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63 | |
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64 end |
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65 |
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66 @testset "Indexing Interface" begin |
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67 lg = equidistant_grid((0,0), (1,1), 11, 21) |
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68 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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69 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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70 mg = MappedGrid(lg, x̄, J) |
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71 @test mg[1,1] == [0.0, 0.0] |
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72 @test mg[4,2] == [0.6, 0.1] |
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73 @test mg[6,10] == [1., 0.9] |
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74 |
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75 @test mg[begin, begin] == [0.0, 0.0] |
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76 @test mg[end,end] == [2.0, 2.0] |
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77 @test mg[begin,end] == [0., 2.] |
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78 |
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79 @test axes(mg) == (1:11, 1:21) |
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80 |
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81 @testset "cartesian indexing" begin |
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82 cases = [ |
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83 (1,1) , |
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84 (3,5) , |
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85 (10,6), |
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86 (1,1) , |
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87 (3,2) , |
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88 ] |
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89 |
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90 @testset "i = $is" for (lg, is) ∈ cases |
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91 @test mg[CartesianIndex(is...)] == mg[is...] |
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92 end |
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93 end |
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94 |
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95 @testset "eachindex" begin |
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96 @test eachindex(mg) == CartesianIndices((11,21)) |
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97 end |
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98 |
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99 @testset "firstindex" begin |
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100 @test firstindex(mg, 1) == 1 |
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101 @test firstindex(mg, 2) == 1 |
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102 end |
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103 |
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104 @testset "lastindex" begin |
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105 @test lastindex(mg, 1) == 11 |
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106 @test lastindex(mg, 2) == 21 |
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107 end |
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108 end |
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109 |
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110 @testset "Iterator interface" begin |
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111 lg = equidistant_grid((0,0), (1,1), 11, 21) |
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112 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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113 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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114 mg = MappedGrid(lg, x̄, J) |
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115 |
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116 sg = MappedGrid( |
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117 equidistant_grid((0,0), (1,1), 15, 11), |
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118 map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg), rand(SMatrix{2,3,Float64},15,11) |
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119 ) |
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120 |
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121 @test eltype(mg) == SVector{2,Float64} |
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122 @test eltype(sg) == SVector{3,Float64} |
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123 |
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124 @test eltype(typeof(mg)) == SVector{2,Float64} |
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125 @test eltype(typeof(sg)) == SVector{3,Float64} |
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126 |
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127 @test size(mg) == (11,21) |
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128 @test size(sg) == (15,11) |
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129 |
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130 @test size(mg,2) == 21 |
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131 @test size(sg,2) == 11 |
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132 |
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133 @test length(mg) == 231 |
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134 @test length(sg) == 165 |
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135 |
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136 @test Base.IteratorSize(mg) == Base.HasShape{2}() |
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137 @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}() |
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138 |
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139 @test Base.IteratorSize(sg) == Base.HasShape{2}() |
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140 @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}() |
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141 |
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142 element, state = iterate(mg) |
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143 @test element == lg[1,1].*2 |
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144 element, _ = iterate(mg, state) |
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145 @test element == lg[2,1].*2 |
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146 |
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147 element, state = iterate(sg) |
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148 @test element == sg.physicalcoordinates[1,1] |
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149 element, _ = iterate(sg, state) |
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150 @test element == sg.physicalcoordinates[2,1] |
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151 |
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152 @test collect(mg) == 2 .* lg |
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153 end |
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154 |
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155 @testset "Base" begin |
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156 lg = equidistant_grid((0,0), (1,1), 11, 21) |
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157 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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158 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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159 mg = MappedGrid(lg, x̄, J) |
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160 |
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161 @test ndims(mg) == 2 |
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162 end |
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163 |
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164 @testset "==" begin |
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165 sz = (15,11) |
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166 lg = equidistant_grid((0,0), (1,1), sz...) |
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167 x = rand(SVector{3,Float64}, sz...) |
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168 J = rand(SMatrix{2,3,Float64}, sz...) |
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169 |
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170 sg = MappedGrid(lg, x, J) |
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171 |
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172 sg1 = MappedGrid(equidistant_grid((0,0), (1,1), sz...), copy(x), copy(J)) |
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173 |
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174 sz2 = (15,12) |
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175 lg2 = equidistant_grid((0,0), (1,1), sz2...) |
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176 x2 = rand(SVector{3,Float64}, sz2...) |
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177 J2 = rand(SMatrix{2,3,Float64}, sz2...) |
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178 sg2 = MappedGrid(lg2, x2, J2) |
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179 |
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180 sg3 = MappedGrid(lg, rand(SVector{3,Float64}, sz...), J) |
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181 sg4 = MappedGrid(lg, x, rand(SMatrix{2,3,Float64}, sz...)) |
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182 |
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183 @test sg == sg1 |
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184 @test sg != sg2 # Different size |
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185 @test sg != sg3 # Different coordinates |
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186 @test sg != sg4 # Different jacobian |
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187 end |
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188 |
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189 @testset "boundary_identifiers" begin |
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190 lg = equidistant_grid((0,0), (1,1), 11, 15) |
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191 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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192 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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193 mg = MappedGrid(lg, x̄, J) |
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194 @test boundary_identifiers(mg) == boundary_identifiers(lg) |
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195 end |
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196 |
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197 @testset "boundary_indices" begin |
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198 lg = equidistant_grid((0,0), (1,1), 11, 15) |
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199 x̄ = map(ξ̄ -> 2ξ̄, lg) |
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200 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg) |
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201 mg = MappedGrid(lg, x̄, J) |
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202 |
1736 | 203 @test boundary_indices(mg, CartesianBoundary{1,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{1,LowerBoundary}()) |
204 @test boundary_indices(mg, CartesianBoundary{2,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{2,LowerBoundary}()) | |
205 @test boundary_indices(mg, CartesianBoundary{1,UpperBoundary}()) == boundary_indices(lg,CartesianBoundary{1,UpperBoundary}()) | |
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206 end |
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207 |
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208 @testset "boundary_grid" begin |
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209 x̄, J = _partially_curved_mapping() |
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210 mg = mapped_grid(x̄, J, 10, 11) |
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211 J1((ξ, η)) = @SMatrix[ |
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212 1 ; |
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213 η*(2ξ-1); |
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214 ] |
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215 J2((ξ, η)) = @SMatrix[ |
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216 0; |
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217 1+ξ*(ξ-1); |
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218 ] |
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219 |
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220 function expected_bg(mg, bId, Jb) |
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221 lg = logicalgrid(mg) |
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222 return MappedGrid( |
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223 boundary_grid(lg, bId), |
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224 map(x̄, boundary_grid(lg, bId)), |
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225 map(Jb, boundary_grid(lg, bId)), |
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226 ) |
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227 end |
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228 |
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229 let bid = TensorGridBoundary{1, LowerBoundary}() |
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230 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2) |
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231 end |
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232 |
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233 let bid = TensorGridBoundary{1, UpperBoundary}() |
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234 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2) |
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235 end |
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236 |
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237 let bid = TensorGridBoundary{2, LowerBoundary}() |
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238 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1) |
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239 end |
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240 |
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241 let bid = TensorGridBoundary{2, UpperBoundary}() |
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242 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1) |
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243 end |
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244 end |
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245 end |
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246 |
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247 @testset "mapped_grid" begin |
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248 x̄, J = _partially_curved_mapping() |
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249 mg = mapped_grid(x̄, J, 10, 11) |
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250 @test mg isa MappedGrid{SVector{2,Float64}, 2} |
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251 |
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252 lg = equidistant_grid((0,0), (1,1), 10, 11) |
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253 @test logicalgrid(mg) == lg |
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254 @test collect(mg) == map(x̄, lg) |
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255 |
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256 @test mapped_grid(lg, x̄, J) == mg |
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257 end |
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258 |
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259 @testset "jacobian_determinant" begin |
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260 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2] |
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261 J((ξ, η)) = @SMatrix[ |
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262 η ξ; |
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263 1 2η; |
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264 ] |
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265 |
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266 g = mapped_grid(x̄, J, 10, 11) |
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267 J = map(logicalgrid(g)) do (ξ,η) |
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268 2η^2 - ξ |
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269 end |
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270 @test jacobian_determinant(g) ≈ J |
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271 |
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272 |
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273 lg = equidistant_grid((0,0), (1,1), 11, 21) |
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274 x̄ = map(ξ̄ -> @SVector[ξ̄[1],ξ̄[2], ξ̄[1] + ξ̄[2]], lg) |
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275 J = map(ξ̄ -> @SMatrix[1 0; 0 1; 1 1], lg) |
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276 mg = MappedGrid(lg, x̄, J) |
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277 |
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278 @test_broken jacobian(mg) isa AbstractArray{2,Float64} |
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279 end |
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280 |
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281 @testset "metric_tensor" begin |
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282 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2] |
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283 J((ξ, η)) = @SMatrix[ |
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284 η ξ; |
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285 1 2η; |
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286 ] |
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287 |
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288 g = mapped_grid(x̄, J, 10, 11) |
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289 G = map(logicalgrid(g)) do (ξ,η) |
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290 @SMatrix[ |
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291 1+η^2 ξ*η+2η; |
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292 ξ*η+2η ξ^2 + 4η^2; |
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293 ] |
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294 end |
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295 @test metric_tensor(g) ≈ G |
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296 end |
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297 |
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298 @testset "metric_tensor_inverse" begin |
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299 x̄((ξ, η)) = @SVector[ξ + ξ^2/2, η + η^2 + ξ^2/2] |
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300 J((ξ, η)) = @SMatrix[ |
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301 1+ξ 0; |
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302 ξ 1+η; |
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303 ] |
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304 |
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305 g = mapped_grid(x̄, J, 10, 11) |
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306 G⁻¹ = map(logicalgrid(g)) do (ξ,η) |
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307 @SMatrix[ |
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308 (1+η)^2 -ξ*(1+η); |
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309 -ξ*(1+η) (1+ξ)^2+ξ^2; |
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310 ]/(((1+ξ)^2+ξ^2)*(1+η)^2 - ξ^2*(1+η)^2) |
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311 |
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312 end |
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313 |
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314 @test metric_tensor_inverse(g) ≈ G⁻¹ |
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315 end |
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316 |
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317 @testset "min_spacing" begin |
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318 let g = mapped_grid(identity, x->@SMatrix[1], 11) |
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319 @test min_spacing(g) ≈ 0.1 |
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320 end |
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321 |
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322 let g = mapped_grid(x->x+x.^2/2, x->@SMatrix[1 .+ x], 11) |
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323 @test min_spacing(g) ≈ 0.105 |
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324 end |
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325 |
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326 let g = mapped_grid(x->x + x.*(1 .- x)/2, x->@SMatrix[1.5 .- x], 11) |
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327 @test min_spacing(g) ≈ 0.055 |
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328 end |
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329 |
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330 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,11) |
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331 @test min_spacing(g) ≈ 0.1 |
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332 end |
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333 |
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334 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,21) |
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335 @test min_spacing(g) ≈ 0.05 |
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336 end |
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337 |
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338 |
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339 @testset let a = @SVector[1,0], b = @SVector[1,1]/√2 |
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340 g = mapped_grid(_skew_mapping(a,b)...,11,11) |
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341 |
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342 @test min_spacing(g) ≈ 0.1*norm(b-a) |
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343 end |
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344 |
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345 @testset let a = @SVector[1,0], b = @SVector[-1,1]/√2 |
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346 g = mapped_grid(_skew_mapping(a,b)...,11,11) |
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347 |
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348 @test min_spacing(g) ≈ 0.1*norm(a+b) |
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349 end |
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350 end |
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351 |
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352 @testset "normal" begin |
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353 g = mapped_grid(_partially_curved_mapping()...,10, 11) |
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354 |
1736 | 355 @test normal(g, CartesianBoundary{1,LowerBoundary}()) == fill(@SVector[-1,0], 11) |
356 @test normal(g, CartesianBoundary{1,UpperBoundary}()) == fill(@SVector[1,0], 11) | |
357 @test normal(g, CartesianBoundary{2,LowerBoundary}()) == fill(@SVector[0,-1], 10) | |
358 @test normal(g, CartesianBoundary{2,UpperBoundary}()) ≈ map(boundary_grid(g,CartesianBoundary{2,UpperBoundary}())|>logicalgrid) do ξ̄ | |
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359 α = 1-2ξ̄[1] |
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360 @SVector[α,1]/√(α^2 + 1) |
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361 end |
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362 |
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363 g = mapped_grid(_fully_curved_mapping()...,5,4) |
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364 |
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365 unit(v) = v/norm(v) |
1736 | 366 @testset let bId = CartesianBoundary{1,LowerBoundary}() |
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367 lbg = boundary_grid(logicalgrid(g), bId) |
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368 @test normal(g, bId) ≈ map(lbg) do (ξ, η) |
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369 -unit(@SVector[1/2, η/3-1/6]) |
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370 end |
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371 end |
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372 |
1736 | 373 @testset let bId = CartesianBoundary{1,UpperBoundary}() |
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374 lbg = boundary_grid(logicalgrid(g), bId) |
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375 @test normal(g, bId) ≈ map(lbg) do (ξ, η) |
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376 unit(@SVector[7/2, 2η-1]/(5 + 3η + 2η^2)) |
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377 end |
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378 end |
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379 |
1736 | 380 @testset let bId = CartesianBoundary{2,LowerBoundary}() |
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381 lbg = boundary_grid(logicalgrid(g), bId) |
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382 @test normal(g, bId) ≈ map(lbg) do (ξ, η) |
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383 -unit(@SVector[-2ξ, 2]/(6 + ξ^2 - 2ξ)) |
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384 end |
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385 end |
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386 |
1736 | 387 @testset let bId = CartesianBoundary{2,UpperBoundary}() |
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388 lbg = boundary_grid(logicalgrid(g), bId) |
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389 @test normal(g, bId) ≈ map(lbg) do (ξ, η) |
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390 unit(@SVector[-3ξ, 2]/(6 + ξ^2 + 3ξ)) |
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391 end |
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392 end |
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393 end |