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annotate src/Grids/mapped_grid.jl @ 1746:44faa334adc6 feature/grids/curvilinear

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Add docs
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 11 Sep 2024 14:41:14 +0200
parents 2f7974367cd3
children 03894fd7b132 e4353d5e8fc3
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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: [`logicalgrid`](@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{<:AbstractArray{<:Any, 2}, D}} <: Grid{T,D}
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11 logicalgrid::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(logicalgrid, 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(logicalgrid::GT, physicalcoordinates::CT, jacobian::JT) where {T,D, GT<:Grid{<:Any,D}, CT<:AbstractArray{T,D}, JT<:AbstractArray{<:AbstractArray{<:Any, 2}, D}}
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21 if !(size(logicalgrid) == 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 @show size(first(jacobian))
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27 @show (length(first(physicalcoordinates)),D)
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28 throw(ArgumentError("The size of the jacobian must match the dimensions of the grid and coordinates"))
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29 end
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30
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31 return new{T,D,GT,CT,JT}(logicalgrid, physicalcoordinates, jacobian)
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32 end
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33 end
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34
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35 function Base.:(==)(a::MappedGrid, b::MappedGrid)
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36 same_logicalgrid = logicalgrid(a) == logicalgrid(b)
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37 same_coordinates = collect(a) == collect(b)
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38 same_jacobian = jacobian(a) == jacobian(b)
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39
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40 return same_logicalgrid && same_coordinates && same_jacobian
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41 end
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42
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43 """
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44 logicalgrid(g::MappedGrid)
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45
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46 The logical grid of `g`.
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47 """
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48 logicalgrid(g::MappedGrid) = g.logicalgrid
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49
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50 """
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51 jacobian(g::MappedGrid)
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52
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53 The Jacobian matrix of `g` as a grid function.
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54 """
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55 jacobian(g::MappedGrid) = g.jacobian
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56
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57
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58 # Indexing interface
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59 Base.getindex(g::MappedGrid, I::Vararg{Int}) = g.physicalcoordinates[I...]
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60 Base.eachindex(g::MappedGrid) = eachindex(g.logicalgrid)
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61
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62 Base.firstindex(g::MappedGrid, d) = firstindex(g.logicalgrid, d)
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63 Base.lastindex(g::MappedGrid, d) = lastindex(g.logicalgrid, d)
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64
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65 # Iteration interface
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66 Base.iterate(g::MappedGrid) = iterate(g.physicalcoordinates)
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67 Base.iterate(g::MappedGrid, state) = iterate(g.physicalcoordinates, state)
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68
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69 Base.IteratorSize(::Type{<:MappedGrid{<:Any, D}}) where D = Base.HasShape{D}()
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70 Base.length(g::MappedGrid) = length(g.logicalgrid)
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71 Base.size(g::MappedGrid) = size(g.logicalgrid)
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72 Base.size(g::MappedGrid, d) = size(g.logicalgrid, d)
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73
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74 boundary_identifiers(g::MappedGrid) = boundary_identifiers(g.logicalgrid)
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75 boundary_indices(g::MappedGrid, id::TensorGridBoundary) = boundary_indices(g.logicalgrid, id)
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76
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77 function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
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78 b_indices = boundary_indices(g.logicalgrid, id)
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79
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80 # Calculate indices of needed jacobian components
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81 D = ndims(g)
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82 all_indices = SVector{D}(1:D)
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83 free_variable_indices = deleteat(all_indices, grid_id(id))
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84 jacobian_components = (:, free_variable_indices)
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85
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86 # Create grid function for boundary grid jacobian
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87 boundary_jacobian = componentview((@view g.jacobian[b_indices...]) , jacobian_components...)
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88 boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices...]
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89
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90 return MappedGrid(
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91 boundary_grid(g.logicalgrid, id),
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92 boundary_physicalcoordinates,
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93 boundary_jacobian,
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94 )
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95 end
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96
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97
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98 """
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99 mapped_grid(x, J, size::Vararg{Int})
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100
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101 A `MappedGrid` with a default logical grid on a unit hyper box. `x` and `J`
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102 are functions to be evaluated on the logical grid and `size` determines the
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103 size of the logical grid.
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104 """
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105 function mapped_grid(x, J, size::Vararg{Int})
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106 D = length(size)
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107 lg = equidistant_grid(ntuple(i->0., D), ntuple(i->1., D), size...)
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108 return mapped_grid(lg, x, J)
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109 end
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110
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111 """
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112 mapped_grid(lg::Grid, x, J)
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113
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114 A `MappedGrid` with logical grid `lg`. Physical coordinates and Jacobian are
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115 determined by the functions `x` and `J`.
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116 """
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117 function mapped_grid(lg::Grid, x, J)
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118 return MappedGrid(
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119 lg,
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120 map(x,lg),
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121 map(J,lg),
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122 )
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123 end
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124
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125 """
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126 jacobian_determinant(g::MappedGrid)
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127
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128 The jacobian determinant of `g` as a grid function.
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129 """
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130 function jacobian_determinant(g::MappedGrid)
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131 return map(jacobian(g)) do ∂x∂ξ
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132 det(∂x∂ξ)
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133 end
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134 end
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135 # TBD: Should this be changed to calculate sqrt(g) instead?
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136 # This would make it well defined also for n-dim grids embedded in higher dimensions.
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137 # TBD: Is there a better name? metric_determinant?
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138 # TBD: Is the best option to delete it?
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139
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140 """
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141 metric_tensor(g::MappedGrid)
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142
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143 The metric tensor of `g` as a grid function.
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144 """
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145 function metric_tensor(g::MappedGrid)
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146 return map(jacobian(g)) do ∂x∂ξ
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147 ∂x∂ξ'*∂x∂ξ
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148 end
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149 end
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150
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151 """
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152 metric_tensor_inverse(g::MappedGrid)
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153
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154 The inverse of the metric tensor of `g` as a grid function.
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155 """
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156 function metric_tensor_inverse(g::MappedGrid)
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157 return map(jacobian(g)) do ∂x∂ξ
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158 inv(∂x∂ξ'*∂x∂ξ)
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159 end
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160 end
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161
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162 function min_spacing(g::MappedGrid{T,1} where T)
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163 n, = size(g)
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164
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165 ms = Inf
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166 for i ∈ 1:n-1
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167 ms = min(ms, norm(g[i+1]-g[i]))
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168 end
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169
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170 return ms
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171 end
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172
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173 function min_spacing(g::MappedGrid{T,2} where T)
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174 n, m = size(g)
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175
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176 ms = Inf
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177 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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178
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179 ms = min(
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180 ms,
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181 norm(g[i+1,j]-g[i,j]),
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182 norm(g[i,j+1]-g[i,j]),
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183
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184 norm(g[i+1,j]-g[i+1,j+1]),
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185 norm(g[i,j+1]-g[i+1,j+1]),
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186
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187 norm(g[i+1,j+1]-g[i,j]),
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188 norm(g[i+1,j]-g[i,j+1]),
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189 )
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190 # NOTE: This could be optimized to avoid checking all interior edges twice.
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191 end
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192
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193 return ms
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194 end
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195
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196 """
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197 normal(g::MappedGrid, boundary)
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198
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199 The outward pointing normal as a grid function on the corresponding boundary grid.
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200 """
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201 function normal(g::MappedGrid, boundary)
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202 b_indices = boundary_indices(g, boundary)
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203 σ =_boundary_sign(component_type(g), boundary)
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204 return map(jacobian(g)[b_indices...]) do ∂x∂ξ
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205 ∂ξ∂x = inv(∂x∂ξ)
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206 k = grid_id(boundary)
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207 σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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208 end
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209 end
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210
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211 function _boundary_sign(T, boundary)
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212 if boundary_id(boundary) == UpperBoundary()
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213 return one(T)
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214 elseif boundary_id(boundary) == LowerBoundary()
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215 return -one(T)
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216 else
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217 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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218 end
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219 end