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annotate src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl @ 2002:4300c59bbeff feature/grids/geometry_functions

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Merge feature/grids/manifolds
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 29 Apr 2025 09:00:42 +0200
parents e9dfc1998d31
children 3684db043add
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1 """
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2 second_derivative_variable(g, coeff ..., [direction])
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3
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4 The variable second derivative operator as a `LazyTensor` on the given grid.
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5 `coeff` is a grid function of the variable coefficient.
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6
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7 Approximates the d/dξ c d/dξ on `g` along the coordinate dimension specified
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8 by `direction`.
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9 """
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10 function second_derivative_variable end
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11
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12 function second_derivative_variable(g::TensorGrid, coeff, stencil_set, dir::Int)
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13 inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"])
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14 closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"])
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15
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16 return second_derivative_variable(g, coeff, inner_stencil, closure_stencils, dir)
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17 end
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18
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19 function second_derivative_variable(g::EquidistantGrid, coeff, stencil_set)
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20 return second_derivative_variable(TensorGrid(g), coeff, stencil_set, 1)
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21 end
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22
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23 function second_derivative_variable(g::TensorGrid, coeff, inner_stencil::NestedStencil, closure_stencils, dir)
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24 check_coefficient(g, coeff)
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25
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26 Δxᵢ = spacing(g.grids[dir])
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27 scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2)
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28 scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2)
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29 return SecondDerivativeVariable(coeff, scaled_inner_stencil, scaled_closure_stencils, dir)
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30 end
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31
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32 function check_coefficient(g, coeff)
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33 if ndims(g) != ndims(coeff)
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34 throw(ArgumentError("The coefficient has dimension $(ndims(coeff)) while the grid is dimension $(ndims(g))"))
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35 end
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36
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37 if size(g) != size(coeff)
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38 throw(DimensionMismatch("the size $(size(coeff)) of the coefficient does not match the size $(size(g)) of the grid"))
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39 end
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40 end
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41
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42
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43 """
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44 SecondDerivativeVariable{Dir,T,D,...} <: LazyTensor{T,D,D}
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45
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46 A second derivative operator in direction `Dir` with a variable coefficient.
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47 """
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48 struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: LazyTensor{T,D,D}
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49 inner_stencil::IStencil
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50 closure_stencils::NTuple{M,CStencil}
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51 coefficient::TArray
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52
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53 function SecondDerivativeVariable(coefficient::AbstractArray, inner_stencil::NestedStencil{T}, closure_stencils::NTuple{M,NestedStencil{T}}, dir) where {T,M}
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54 D = ndims(coefficient)
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55 IStencil = typeof(inner_stencil)
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56 CStencil = eltype(closure_stencils)
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57 TArray = typeof(coefficient)
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58 return new{dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil, closure_stencils, coefficient)
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59 end
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60 end
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61
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62 derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir
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63
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64 closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils)
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65
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66 LazyTensors.range_size(op::SecondDerivativeVariable) = size(op.coefficient)
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67 LazyTensors.domain_size(op::SecondDerivativeVariable) = size(op.coefficient)
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68
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69
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70 function derivative_view(op, a, I)
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71 d = derivative_direction(op)
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72
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73 Iview = Base.setindex(I,:,d)
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74 return @view a[Iview...]
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75 end
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76
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77 function apply_lower(op::SecondDerivativeVariable, v, I...)
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78 ṽ = derivative_view(op, v, I)
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79 c̃ = derivative_view(op, op.coefficient, I)
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80
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81 i = I[derivative_direction(op)]
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82 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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83 end
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84
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85 function apply_interior(op::SecondDerivativeVariable, v, I...)
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86 ṽ = derivative_view(op, v, I)
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87 c̃ = derivative_view(op, op.coefficient, I)
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88
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89 i = I[derivative_direction(op)]
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90 return apply_stencil(op.inner_stencil, c̃, ṽ, i)
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91 end
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92
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93 function apply_upper(op::SecondDerivativeVariable, v, I...)
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94 ṽ = derivative_view(op, v, I)
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95 c̃ = derivative_view(op, op.coefficient, I)
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96
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97 i = I[derivative_direction(op)]
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98 sz = domain_size(op)[derivative_direction(op)]
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99 stencil = op.closure_stencils[sz-i+1]
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100 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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101 end
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102
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103 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index})
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104 if I[derivative_direction(op)] isa Index{Lower}
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105 return apply_lower(op, v, Int.(I)...)
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106 elseif I[derivative_direction(op)] isa Index{Upper}
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107 return apply_upper(op, v, Int.(I)...)
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108 elseif I[derivative_direction(op)] isa Index{Interior}
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109 return apply_interior(op, v, Int.(I)...)
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110 else
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111 error("Invalid region")
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112 end
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113 end
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114
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115 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...)
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116 dir = derivative_direction(op)
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117 sz = domain_size(op)[dir]
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118
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119 i = I[dir]
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120
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121 I = map(i->Index(i, Interior), I)
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122 if 0 < i <= closure_size(op)
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123 I = Base.setindex(I, Index(i, Lower), dir)
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124 return LazyTensors.apply(op, v, I...)
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125 elseif closure_size(op) < i <= sz-closure_size(op)
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126 I = Base.setindex(I, Index(i, Interior), dir)
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127 return LazyTensors.apply(op, v, I...)
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128 elseif sz-closure_size(op) < i <= sz
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129 I = Base.setindex(I, Index(i, Upper), dir)
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130 return LazyTensors.apply(op, v, I...)
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131 else
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132 error("Bounds error") # This should be `throw(BoundsError())` but the type inference is so fragile that it doesn't work. Needs investigation. / Jonatan 2023-06-08
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133 end
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134 end
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135
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136
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137 # 2D Specific implementations to avoid type instability
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138 # TBD: Can this be solved by fixing the general methods instead?
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139
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140
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141 ## x-direction
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142 function apply_lower(op::SecondDerivativeVariable{1}, v, i, j)
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143 ṽ = @view v[:,j]
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144 c̃ = @view op.coefficient[:,j]
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145
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146 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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147 end
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148
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149 function apply_interior(op::SecondDerivativeVariable{1}, v, i, j)
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150 ṽ = @view v[:,j]
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151 c̃ = @view op.coefficient[:,j]
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152
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153 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, i)
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154 end
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155
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156 function apply_upper(op::SecondDerivativeVariable{1}, v, i, j)
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157 ṽ = @view v[:,j]
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158 c̃ = @view op.coefficient[:,j]
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159
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160 sz = domain_size(op)[derivative_direction(op)]
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161 stencil = op.closure_stencils[sz-i+1]
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162 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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163 end
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164
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165
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166 ## y-direction
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167 function apply_lower(op::SecondDerivativeVariable{2}, v, i, j)
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168 ṽ = @view v[i,:]
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169 c̃ = @view op.coefficient[i,:]
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170
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171 return @inbounds apply_stencil(op.closure_stencils[j], c̃, ṽ, j)
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172 end
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173
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174 function apply_interior(op::SecondDerivativeVariable{2}, v, i, j)
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175 ṽ = @view v[i,:]
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176 c̃ = @view op.coefficient[i,:]
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177
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178 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, j)
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179 end
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180
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181 function apply_upper(op::SecondDerivativeVariable{2}, v, i, j)
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182 ṽ = @view v[i,:]
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183 c̃ = @view op.coefficient[i,:]
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184
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185 sz = domain_size(op)[derivative_direction(op)]
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186 stencil = op.closure_stencils[sz-j+1]
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187 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, j)
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188 end