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annotate src/Grids/mapped_grid.jl @ 1773:08e52f442872 feature/grids/curvilinear

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Replace AbstractArray{<:Any,2} with AbstractMatrix{<:Any}
author Jonatan Werpers <jonatan@werpers.com>
date Sun, 15 Sep 2024 18:00:40 +0200
parents 672897f64d58
children 035af82f559a
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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{<:AbstractMatrix{<:Any}, 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{<:AbstractMatrix{<:Any}, 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 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}(logicalgrid, 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_logicalgrid = logicalgrid(a) == logicalgrid(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_logicalgrid && same_coordinates && same_jacobian
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39 end
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40
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41 # Review: rename function logicalgrid to logical_grid
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42 # for consistency with mapped_grid.
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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 # Review: Error when calling plot(boundary_grid(g, id))
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78 # Currently need to collect first, i.e., plot(collect(boundary_grid(g, id)))
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79 function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
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80 b_indices = boundary_indices(g.logicalgrid, id)
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81
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82 # Calculate indices of needed jacobian components
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83 D = ndims(g)
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84 all_indices = SVector{D}(1:D)
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85 free_variable_indices = deleteat(all_indices, grid_id(id))
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86 jacobian_components = (:, free_variable_indices)
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87
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88 # Create grid function for boundary grid jacobian
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89 boundary_jacobian = componentview((@view g.jacobian[b_indices...]) , jacobian_components...)
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90 boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices...]
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91
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92 return MappedGrid(
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93 boundary_grid(g.logicalgrid, id),
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94 boundary_physicalcoordinates,
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95 boundary_jacobian,
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96 )
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97 end
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98
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99
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100 """
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101 mapped_grid(x, J, size::Vararg{Int})
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102
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103 A `MappedGrid` with a default logical grid on a unit hyper box. `x` and `J`
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104 are functions to be evaluated on the logical grid and `size` determines the
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105 size of the logical grid.
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106 """
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107 function mapped_grid(x, J, size::Vararg{Int})
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108 D = length(size)
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109 lg = equidistant_grid(ntuple(i->0., D), ntuple(i->1., D), size...)
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110 return mapped_grid(lg, x, J)
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111 end
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112
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113 """
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114 mapped_grid(lg::Grid, x, J)
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115
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116 A `MappedGrid` with logical grid `lg`. Physical coordinates and Jacobian are
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117 determined by the functions `x` and `J`.
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118 """
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119 function mapped_grid(lg::Grid, x, J)
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120 return MappedGrid(
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121 lg,
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122 map(x,lg),
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123 map(J,lg),
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124 )
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125 end
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126
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127 # Review: Error when calling jacobian_determinant(boundary_grid(g,id))
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128 """
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129 jacobian_determinant(g::MappedGrid)
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130
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131 The jacobian determinant of `g` as a grid function.
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132 """
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133 function jacobian_determinant(g::MappedGrid)
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134 return map(jacobian(g)) do ∂x∂ξ
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135 det(∂x∂ξ)
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136 end
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137 end
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138 # TBD: Should this be changed to calculate sqrt(g) instead?
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139 # This would make it well defined also for n-dim grids embedded in higher dimensions.
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140 # TBD: Is there a better name? metric_determinant?
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141 # TBD: Is the best option to delete it?
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142 # Review: I don't think we should delete it. Users building their own
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143 # curvilinear operators will need the functionality. Also the
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144 # determinant of the jacobian (and not its square root) is required
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145 # for quadratures on mapped grids right? For that reason I think we should
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146 # keep the function as is. We could provide a function for the square root
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147 # as well if we think it would be helpfull. Regarding naming, perhaps
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148 # metric_determinant is better?
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149
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150 """
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151 metric_tensor(g::MappedGrid)
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152
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153 The metric tensor of `g` as a grid function.
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154 """
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155 function metric_tensor(g::MappedGrid)
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156 return map(jacobian(g)) do ∂x∂ξ
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157 ∂x∂ξ'*∂x∂ξ
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158 end
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159 end
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160
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161 """
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162 metric_tensor_inverse(g::MappedGrid)
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163
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164 The inverse of the metric tensor of `g` as a grid function.
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165 """
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166 function metric_tensor_inverse(g::MappedGrid)
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167 return map(jacobian(g)) do ∂x∂ξ
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168 inv(∂x∂ξ'*∂x∂ξ)
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169 end
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170 end
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171
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172 function min_spacing(g::MappedGrid{T,1} where T)
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173 n, = size(g)
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174
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175 ms = Inf
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176 for i ∈ 1:n-1
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177 ms = min(ms, norm(g[i+1]-g[i]))
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178 end
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179
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180 return ms
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181 end
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182
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183 function min_spacing(g::MappedGrid{T,2} where T)
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184 n, m = size(g)
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185
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186 ms = Inf
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187 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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188
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189 ms = min(
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190 ms,
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191 norm(g[i+1,j]-g[i,j]),
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192 norm(g[i,j+1]-g[i,j]),
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193
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194 norm(g[i+1,j]-g[i+1,j+1]),
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195 norm(g[i,j+1]-g[i+1,j+1]),
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196
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197 norm(g[i+1,j+1]-g[i,j]),
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198 norm(g[i+1,j]-g[i,j+1]),
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199 )
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200 # NOTE: This could be optimized to avoid checking all interior edges twice.
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201 end
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202
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203 return ms
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204 end
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205
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206 # Review: I would implement the normal through Nansons formula
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207 # nⱼ = inv(Jᵧ)*J*Fⱼᵢ*νᵢ
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208 # where
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209 # Jᵧ boundary jacobian determiant
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210 # J is the volume jacobian determinant
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211 # Fⱼᵢ = dξᵢ/dxⱼ
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212 # νᵢ normal on logical grid
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213 # j: indices on physical grid
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214 # i: indices on logical grid
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215 # ξ: coordinate vector on logical grid
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216 # x: coordinate vector on logical grid
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217 # Perhaps the below is equivalent?
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218 """
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219 normal(g::MappedGrid, boundary)
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220
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221 The outward pointing normal as a grid function on the corresponding boundary grid.
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222 """
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223 function normal(g::MappedGrid, boundary)
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224 b_indices = boundary_indices(g, boundary)
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225 σ =_boundary_sign(component_type(g), boundary)
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226 return map(jacobian(g)[b_indices...]) do ∂x∂ξ
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227 ∂ξ∂x = inv(∂x∂ξ)
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228 k = grid_id(boundary)
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229 σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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230 end
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231 end
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232
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233 function _boundary_sign(T, boundary)
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234 if boundary_id(boundary) == UpperBoundary()
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235 return one(T)
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236 elseif boundary_id(boundary) == LowerBoundary()
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237 return -one(T)
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238 else
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239 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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240 end
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241 end