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annotate src/Grids/mapped_grid.jl @ 1799:8583f6379bd8 feature/grids/curvilinear

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Fix signature of normal(g,b,i...)
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 01 Oct 2024 11:52:38 +0200
parents 25dbb1c02ddc
children 2b5f81e288f1 34ddb953a986
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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
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96 """
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97 mapped_grid(x, J, size::Vararg{Int})
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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...)
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106 return mapped_grid(lg, x, J)
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107 end
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108
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109 """
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110 mapped_grid(lg::Grid, x, J)
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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(lg::Grid, x, J)
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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 metric_tensor(g::MappedGrid)
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125
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126 The metric tensor of `g` as a grid function.
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127 """
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128 function metric_tensor(g::MappedGrid)
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129 return map(jacobian(g)) do ∂x∂ξ
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130 ∂x∂ξ'*∂x∂ξ
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131 end
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132 end
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133
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134 function min_spacing(g::MappedGrid{T,1} where T)
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135 n, = size(g)
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136
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137 ms = Inf
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138 for i ∈ 1:n-1
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139 ms = min(ms, norm(g[i+1]-g[i]))
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140 end
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141
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142 return ms
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143 end
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144
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145 function min_spacing(g::MappedGrid{T,2} where T)
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146 n, m = size(g)
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147
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148 ms = Inf
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149 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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150
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151 ms = min(
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152 ms,
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153 norm(g[i+1,j]-g[i,j]),
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154 norm(g[i,j+1]-g[i,j]),
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155
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156 norm(g[i+1,j]-g[i+1,j+1]),
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157 norm(g[i,j+1]-g[i+1,j+1]),
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158
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159 norm(g[i+1,j+1]-g[i,j]),
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160 norm(g[i+1,j]-g[i,j+1]),
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161 )
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162 # NOTE: This could be optimized to avoid checking all interior edges twice.
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163 end
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164
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165 return ms
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166 end
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167
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168 """
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169 normal(g::MappedGrid, boundary)
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170
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171 The outward pointing normal as a grid function on the corresponding boundary grid.
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172 """
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173 function normal(g::MappedGrid, boundary)
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174 b_indices = boundary_indices(g, boundary)
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175 σ = _boundary_sign(component_type(g), boundary)
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176 return map(jacobian(g)[b_indices...]) do ∂x∂ξ
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177 ∂ξ∂x = inv(∂x∂ξ)
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178 k = grid_id(boundary)
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179 σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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180 end
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181 end
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182
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183 function normal(g::MappedGrid, boundary, i...)
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184 σ = _boundary_sign(component_type(g), boundary)
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185 ∂ξ∂x = inv(jacobian(g)[i...])
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186
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187 k = grid_id(boundary)
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188 return σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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189 end
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190
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191
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192 function _boundary_sign(T, boundary)
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193 if boundary_id(boundary) == UpperBoundary()
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194 return one(T)
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195 elseif boundary_id(boundary) == LowerBoundary()
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196 return -one(T)
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197 else
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198 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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199 end
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200 end