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annotate src/Grids/manifolds.jl @ 2015:5c2448d6a201 feature/grids/geometry_functions tip

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Structure tests a bit more
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 09 May 2025 15:57:38 +0200
parents a1b2453c02c9
children
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1 """
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2 Chart{D}
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3
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4 A parametrized description of a manifold or part of a manifold.
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5 """
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6 struct Chart{D, PST<:ParameterSpace{D}, MT}
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7 mapping::MT
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8 parameterspace::PST
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9 end
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10
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11 Base.ndims(::Chart{D}) where D = D
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12 parameterspace(c::Chart) = c.parameterspace
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13
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14 function (c::Chart)(ξ)
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15 if ξ ∉ parameterspace(c)
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16 throw(DomainError(ξ, "chart was called logical coordinates outside the parameterspace. If this was inteded, use the `mapping` field from the Chart struct instead."))
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17 end
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18 return c.mapping(ξ)
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19 end
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20
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21 """
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22 jacobian(c::Chart, ξ)
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23
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24 The jacobian of the mapping evaluated at `ξ`. This defers to the
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25 implementation of `jacobian` for the mapping itself. If no implementation is
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26 available one can easily be specified for either the mapping function or the
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27 chart itself.
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28 ```julia
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29 c = Chart(f, ps)
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30 jacobian(f::typeof(f), ξ) = f′(ξ)
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31 ```
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32 or
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33 ```julia
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34 c = Chart(f, ps)
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35 jacobian(c::typeof(c),ξ) = f′(ξ)
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36 ```
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37 which will both allow calling `jacobian(c,ξ)`.
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38 """
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39 function jacobian(c::Chart, ξ)
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40 if ξ ∉ parameterspace(c)
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41 throw(DomainError(ξ, "jacobian was called with logical coordinates outside the parameterspace of the chart. If this was inteded, use the `mapping` field from the Chart struct instead."))
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42 end
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43 return jacobian(c.mapping, ξ)
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44 end
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45
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46 boundary_identifiers(c::Chart) = boundary_identifiers(parameterspace(c))
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47
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48
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49 """
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50 Atlas
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51
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52 A collection of charts and their connections.
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53 Should implement methods for `charts` and `connections`.
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54 """
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55 abstract type Atlas end
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56
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57 """
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58 charts(::Atlas)
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59
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60 The colloction of charts in the atlas.
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61 """
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62 function charts end
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63
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64 """
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65 connections(::Atlas)
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66
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67 Collection of 2-tuples of multiblock boundary identifiers.
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68 """
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69 function connections end
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70
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72 """
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73 CartesianAtlas{D,C<:Chart,AT<:AbstractArray{C,D}} <: Atlas
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74
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75 An atlas where the charts are arranged and connected like an array.
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76 """
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77 struct CartesianAtlas{D,C<:Chart,AT<:AbstractArray{C,D}} <: Atlas
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78 charts::AT
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79 end
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80
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81 charts(a::CartesianAtlas) = a.charts
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82
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83 function connections(a::CartesianAtlas)
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84 c = Tuple{MultiBlockBoundary, MultiBlockBoundary}[]
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85
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86 for d ∈ 1:ndims(charts(a))
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87 Is = eachslice(CartesianIndices(charts(a)); dims=d)
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88 for i ∈ 1:length(Is)-1 # For each interface between slices
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89 for jk ∈ eachindex(Is[i]) # For each block in slice
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90 Iᵢⱼₖ = Tuple(Is[i][jk])
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91 Iᵢ₊₁ⱼₖ = Tuple(Is[i+1][jk])
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92 push!(c,
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93 (
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94 MultiBlockBoundary{Iᵢⱼₖ, CartesianBoundary{d,UpperBoundary}}(),
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95 MultiBlockBoundary{Iᵢ₊₁ⱼₖ, CartesianBoundary{d,LowerBoundary}}(),
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96 )
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97 )
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98 end
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99 end
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100 end
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101
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102 return c
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103 end
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104
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105 """
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106 boundary_identifiers(a::CartesianAtlas)
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107
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108 All non-connected boundaries of the charts of `a`.
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109 """
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110 function boundary_identifiers(a::CartesianAtlas)
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111 bs = MultiBlockBoundary[]
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112
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113 for d ∈ 1:ndims(charts(a))
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114 Is = eachslice(CartesianIndices(charts(a)); dims=d)
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115
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116 for (i,b) ∈ ((1,LowerBoundary),(length(Is),UpperBoundary)) # For first and last slice
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117 for jk ∈ eachindex(Is[i]) # For each block in slice
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118 Iᵢⱼₖ = Tuple(Is[i][jk])
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119 push!(bs,
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120 MultiBlockBoundary{Iᵢⱼₖ, CartesianBoundary{d,b}}(),
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121 )
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122 end
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123 end
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124 end
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125
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126 return bs
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127 end
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128
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129
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130 """
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131 UnstructuredAtlas{C<:Chart, CN<:Tuple{MultiBlockBoundary,MultiBlockBoundary}, ...} <: Atlas
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132
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133 An atlas with connections determined by a vector `MultiBlockBoundary` pairs.
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134 """
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135 struct UnstructuredAtlas{C<:Chart, CN<:Tuple{MultiBlockBoundary,MultiBlockBoundary}, CV<:AbstractVector{C}, CNV<:AbstractVector{CN}} <: Atlas
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136 charts::CV
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137 connections::CNV
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138 end
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139
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140 charts(a::UnstructuredAtlas) = a.charts
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141 connections(a::UnstructuredAtlas) = a.connections
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142
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143 """
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144 boundary_identifiers(a::UnstructuredAtlas)
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145
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146 All non-connected boundaries of the charts of `a`.
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147 """
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148 function boundary_identifiers(a::UnstructuredAtlas)
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149 bs = MultiBlockBoundary[]
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150
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151 for (i,c) ∈ enumerate(charts(a))
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152 for b ∈ boundary_identifiers(c)
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153 mbb = MultiBlockBoundary{i,typeof(b)}()
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154
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155 if !any(cn->mbb∈cn, connections(a))
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156 push!(bs, mbb)
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157 end
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158 end
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159 end
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160
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161 return bs
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162 end