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annotate src/Grids/mapped_grid.jl @ 1902:f93ba5832146 feature/grids/parameter_spaces

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Copy changes related to ParameterSpace from feature/grids/manifolds
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 01 Feb 2025 22:12:53 +0100
parents 516eaabf1169
children 04c251bccbd4 dcbe8119fb0a
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1 """
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2 MappedGrid{T,D} <: Grid{T,D}
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3
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4 A grid defined by a coordinate mapping from a logical grid to some physical
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5 coordinates. The physical coordinates and the Jacobian are stored as grid
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6 functions corresponding to the logical grid.
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7
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8 See also: [`logical_grid`](@ref), [`jacobian`](@ref), [`metric_tensor`](@ref).
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9 """
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10 struct MappedGrid{T,D, GT<:Grid{<:Any,D}, CT<:AbstractArray{T,D}, JT<:AbstractArray{<:AbstractMatrix{<:Any}, D}} <: Grid{T,D}
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11 logical_grid::GT
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12 physicalcoordinates::CT
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13 jacobian::JT
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14
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15 """
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16 MappedGrid(logical_grid, physicalcoordinates, jacobian)
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17
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18 A MappedGrid with the given physical coordinates and jacobian.
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19 """
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20 function MappedGrid(logical_grid::GT, physicalcoordinates::CT, jacobian::JT) where {T,D, GT<:Grid{<:Any,D}, CT<:AbstractArray{T,D}, JT<:AbstractArray{<:AbstractMatrix{<:Any}, D}}
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21 if !(size(logical_grid) == size(physicalcoordinates) == size(jacobian))
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22 throw(ArgumentError("Sizes must match"))
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23 end
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24
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25 if size(first(jacobian)) != (length(first(physicalcoordinates)),D)
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26 throw(ArgumentError("The size of the jacobian must match the dimensions of the grid and coordinates"))
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27 end
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28
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29 return new{T,D,GT,CT,JT}(logical_grid, physicalcoordinates, jacobian)
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30 end
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31 end
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32
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33 function Base.:(==)(a::MappedGrid, b::MappedGrid)
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34 same_logical_grid = logical_grid(a) == logical_grid(b)
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35 same_coordinates = collect(a) == collect(b)
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36 same_jacobian = jacobian(a) == jacobian(b)
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37
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38 return same_logical_grid && same_coordinates && same_jacobian
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39 end
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40
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41 """
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42 logical_grid(g::MappedGrid)
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43
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44 The logical grid of `g`.
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45 """
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46 logical_grid(g::MappedGrid) = g.logical_grid
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47
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48 """
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49 jacobian(g::MappedGrid)
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50
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51 The Jacobian matrix of `g` as a grid function.
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52 """
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53 jacobian(g::MappedGrid) = g.jacobian
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54
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55
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56 # Indexing interface
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57 Base.getindex(g::MappedGrid, I::Vararg{Int}) = g.physicalcoordinates[I...]
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58 Base.eachindex(g::MappedGrid) = eachindex(g.logical_grid)
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59
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60 Base.firstindex(g::MappedGrid, d) = firstindex(g.logical_grid, d)
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61 Base.lastindex(g::MappedGrid, d) = lastindex(g.logical_grid, d)
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62
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63 # Iteration interface
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64 Base.iterate(g::MappedGrid) = iterate(g.physicalcoordinates)
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65 Base.iterate(g::MappedGrid, state) = iterate(g.physicalcoordinates, state)
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66
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67 Base.IteratorSize(::Type{<:MappedGrid{<:Any, D}}) where D = Base.HasShape{D}()
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68 Base.length(g::MappedGrid) = length(g.logical_grid)
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69 Base.size(g::MappedGrid) = size(g.logical_grid)
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70 Base.size(g::MappedGrid, d) = size(g.logical_grid, d)
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71
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72 boundary_identifiers(g::MappedGrid) = boundary_identifiers(g.logical_grid)
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73 boundary_indices(g::MappedGrid, id::TensorGridBoundary) = boundary_indices(g.logical_grid, id)
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74
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75 function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
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76 b_indices = boundary_indices(g.logical_grid, id)
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77
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78 # Calculate indices of needed jacobian components
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79 D = ndims(g)
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80 all_indices = SVector{D}(1:D)
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81 free_variable_indices = deleteat(all_indices, grid_id(id))
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82 jacobian_components = (:, free_variable_indices)
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83
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84 # Create grid function for boundary grid jacobian
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85 boundary_jacobian = componentview((@view g.jacobian[b_indices]) , jacobian_components...)
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86 boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices]
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87
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88 return MappedGrid(
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89 boundary_grid(g.logical_grid, id),
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90 boundary_physicalcoordinates,
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91 boundary_jacobian,
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92 )
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93 end
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94
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95 # TODO: Make sure all methods of `mapped_grid` are implemented correctly and tested.
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96 """
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97 mapped_grid(x, J, size...)
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98
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99 A `MappedGrid` with a default logical grid on the D-dimensional unit hyper
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100 box [0,1]ᴰ. `x` and `J` are functions to be evaluated on the logical grid
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101 and `size` determines the size of the logical grid.
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102 """
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103 function mapped_grid(x, J, size::Vararg{Int})
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104 D = length(size)
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105 lg = equidistant_grid(ntuple(i->0., D), ntuple(i->1., D), size...) # TODO: Clean this up with ParamaterSpace once feature/grids/manifolds is merged
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106 return mapped_grid(x, J, lg)
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107 end
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108
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109 """
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110 mapped_grid(x, J, lg::Grid)
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111
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112 A `MappedGrid` with logical grid `lg`. Physical coordinates and Jacobian are
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113 determined by the functions `x` and `J`.
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114 """
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115 function mapped_grid(x, J, lg::Grid)
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116 return MappedGrid(
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117 lg,
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118 map(x,lg),
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119 map(J,lg),
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120 )
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121 end
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122
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123 """
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124 mapped_grid(x, J, ps::ParameterSpace, size...)
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125
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126 A `MappedGrid` with logical grid `lg`. Physical coordinates and Jacobian are
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127 determined by the functions `x` and `J`.
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128 """
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129 function mapped_grid(x, J, ps::ParameterSpace, size::Vararg{Int})
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130 lg = equidistant_grid(ps, size...)
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131 return mapped_grid(x, J, lg)
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132 end
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133
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134 """
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135 metric_tensor(g::MappedGrid)
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136
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137 The metric tensor of `g` as a grid function.
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138 """
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139 function metric_tensor(g::MappedGrid)
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140 return map(jacobian(g)) do ∂x∂ξ
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141 ∂x∂ξ'*∂x∂ξ
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142 end
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143 end
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144
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145 function min_spacing(g::MappedGrid{T,1} where T)
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146 n, = size(g)
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147
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148 ms = Inf
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149 for i ∈ 1:n-1
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150 ms = min(ms, norm(g[i+1]-g[i]))
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151 end
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152
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153 return ms
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154 end
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155
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156 function min_spacing(g::MappedGrid{T,2} where T)
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157 n, m = size(g)
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158
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159 ms = Inf
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160 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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161
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162 ms = min(
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163 ms,
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164 norm(g[i+1,j]-g[i,j]),
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165 norm(g[i,j+1]-g[i,j]),
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166
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167 norm(g[i+1,j]-g[i+1,j+1]),
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168 norm(g[i,j+1]-g[i+1,j+1]),
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169
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170 norm(g[i+1,j+1]-g[i,j]),
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171 norm(g[i+1,j]-g[i,j+1]),
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172 )
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173 # NOTE: This could be optimized to avoid checking all interior edges twice.
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174 end
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175
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176 return ms
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177 end
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178
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179 """
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180 normal(g::MappedGrid, boundary)
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181
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182 The outward pointing normal as a grid function on the corresponding boundary grid.
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183 """
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184 function normal(g::MappedGrid, boundary)
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185 return map(boundary_indices(g, boundary)) do I
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186 normal(g, boundary, Tuple(I)...)
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187 end
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188 end
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189
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190 """
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191 normal(g::MappedGrid, boundary, i...)
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192
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193 The outward pointing normal to the specified boundary in grid point `i`.
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194 """
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195 function normal(g::MappedGrid, boundary, i...)
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196 σ = _boundary_sign(component_type(g), boundary)
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197 ∂ξ∂x = inv(jacobian(g)[i...])
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198
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199 k = grid_id(boundary)
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200 return σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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201 end
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202
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203
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204 function _boundary_sign(T, boundary)
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205 if boundary_id(boundary) == UpperBoundary()
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206 return one(T)
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207 elseif boundary_id(boundary) == LowerBoundary()
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208 return -one(T)
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209 else
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210 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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211 end
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212 end