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annotate src/Grids/mapped_grid.jl @ 1745:2f7974367cd3 feature/grids/curvilinear

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Add TBD
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 11 Sep 2024 14:11:11 +0200
parents c38eead8be17
children 44faa334adc6
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1 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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2 logicalgrid::GT
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3 physicalcoordinates::CT
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4 jacobian::JT
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5
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6 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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7 if !(size(logicalgrid) == size(physicalcoordinates) == size(jacobian))
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8 throw(ArgumentError("Sizes must match"))
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9 end
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10
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11 if size(first(jacobian)) != (length(first(physicalcoordinates)),D)
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12 @show size(first(jacobian))
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13 @show (length(first(physicalcoordinates)),D)
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14 throw(ArgumentError("The size of the jacobian must match the dimensions of the grid and coordinates"))
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15 end
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16
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17 return new{T,D,GT,CT,JT}(logicalgrid, physicalcoordinates, jacobian)
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18 end
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19 end
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20
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21 function Base.:(==)(a::MappedGrid, b::MappedGrid)
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22 same_logicalgrid = logicalgrid(a) == logicalgrid(b)
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23 same_coordinates = collect(a) == collect(b)
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24 same_jacobian = jacobian(a) == jacobian(b)
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25
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26 return same_logicalgrid && same_coordinates && same_jacobian
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27 end
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28
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29 jacobian(g::MappedGrid) = g.jacobian
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30 logicalgrid(g::MappedGrid) = g.logicalgrid
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31
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32
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33 # Indexing interface
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34 Base.getindex(g::MappedGrid, I::Vararg{Int}) = g.physicalcoordinates[I...]
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35 Base.eachindex(g::MappedGrid) = eachindex(g.logicalgrid)
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36
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37 Base.firstindex(g::MappedGrid, d) = firstindex(g.logicalgrid, d)
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38 Base.lastindex(g::MappedGrid, d) = lastindex(g.logicalgrid, d)
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39
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40 # Iteration interface
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41 Base.iterate(g::MappedGrid) = iterate(g.physicalcoordinates)
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42 Base.iterate(g::MappedGrid, state) = iterate(g.physicalcoordinates, state)
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43
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44 Base.IteratorSize(::Type{<:MappedGrid{<:Any, D}}) where D = Base.HasShape{D}()
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45 Base.length(g::MappedGrid) = length(g.logicalgrid)
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46 Base.size(g::MappedGrid) = size(g.logicalgrid)
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47 Base.size(g::MappedGrid, d) = size(g.logicalgrid, d)
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48
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49 boundary_identifiers(g::MappedGrid) = boundary_identifiers(g.logicalgrid)
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50 boundary_indices(g::MappedGrid, id::TensorGridBoundary) = boundary_indices(g.logicalgrid, id)
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51
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52 function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
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53 b_indices = boundary_indices(g.logicalgrid, id)
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54
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55 # Calculate indices of needed jacobian components
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56 D = ndims(g)
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57 all_indices = SVector{D}(1:D)
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58 free_variable_indices = deleteat(all_indices, grid_id(id))
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59 jacobian_components = (:, free_variable_indices)
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60
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61 # Create grid function for boundary grid jacobian
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62 boundary_jacobian = componentview((@view g.jacobian[b_indices...]) , jacobian_components...)
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63 boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices...]
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64
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65 return MappedGrid(
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66 boundary_grid(g.logicalgrid, id),
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67 boundary_physicalcoordinates,
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68 boundary_jacobian,
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69 )
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70 end
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71
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72 # TBD: refine and coarsen could be implemented once we have a simple manifold implementation.
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73 # Before we do, we should consider the overhead of including such a field in the mapped grid struct.
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74
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75 function mapped_grid(x, J, size::Vararg{Int})
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76 D = length(size)
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77 lg = equidistant_grid(ntuple(i->0., D), ntuple(i->1., D), size...)
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78 return mapped_grid(lg, x, J)
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79 end
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80
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81 function mapped_grid(lg::Grid, x, J)
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82 return MappedGrid(
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83 lg,
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84 map(x,lg),
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85 map(J,lg),
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86 )
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87 end
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88
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89 function jacobian_determinant(g::MappedGrid)
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90 return map(jacobian(g)) do ∂x∂ξ
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91 det(∂x∂ξ)
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92 end
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93 end
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94 # TBD: Should this be changed to calculate sqrt(g) instead?
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95 # This would make it well defined also for n-dim grids embedded in higher dimensions.
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96 # TBD: Is there a better name? metric_determinant?
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97 # TBD: Is the best option to delete it?
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98
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99 function metric_tensor(g::MappedGrid)
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100 return map(jacobian(g)) do ∂x∂ξ
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101 ∂x∂ξ'*∂x∂ξ
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102 end
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103 end
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104
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105 function metric_tensor_inverse(g::MappedGrid)
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106 return map(jacobian(g)) do ∂x∂ξ
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107 inv(∂x∂ξ'*∂x∂ξ)
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108 end
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109 end
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110
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111 function min_spacing(g::MappedGrid{T,1} where T)
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112 n, = size(g)
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113
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114 ms = Inf
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115 for i ∈ 1:n-1
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116 ms = min(ms, norm(g[i+1]-g[i]))
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117 end
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118
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119 return ms
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120 end
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121
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122 function min_spacing(g::MappedGrid{T,2} where T)
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123 n, m = size(g)
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124
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125 ms = Inf
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126 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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127
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128 ms = min(
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129 ms,
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130 norm(g[i+1,j]-g[i,j]),
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131 norm(g[i,j+1]-g[i,j]),
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132
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133 norm(g[i+1,j]-g[i+1,j+1]),
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134 norm(g[i,j+1]-g[i+1,j+1]),
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135
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136 norm(g[i+1,j+1]-g[i,j]),
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137 norm(g[i+1,j]-g[i,j+1]),
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138 )
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139 # NOTE: This could be optimized to avoid checking all interior edges twice.
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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 """
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146 normal(g::MappedGrid, boundary)
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147
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148 The outward pointing normal as a grid function on the boundary
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149 """
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150 function normal(g::MappedGrid, boundary)
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151 b_indices = boundary_indices(g, boundary)
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152 σ =_boundary_sign(component_type(g), boundary)
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153 return map(jacobian(g)[b_indices...]) do ∂x∂ξ
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154 ∂ξ∂x = inv(∂x∂ξ)
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155 k = grid_id(boundary)
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156 σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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157 end
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158 end
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159
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160 function _boundary_sign(T, boundary)
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161 if boundary_id(boundary) == UpperBoundary()
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162 return one(T)
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163 elseif boundary_id(boundary) == LowerBoundary()
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164 return -one(T)
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165 else
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166 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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167 end
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168 end