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annotate src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl @ 1370:4ef8fb75d144 feature/variable_derivatives

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Start splitting out a second_derivative_variable function
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 26 May 2023 21:39:08 +0200
parents 26ad90b42efd
children d0e48c2e6aad
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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
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13 function second_derivative_variable(g::TensorGrid, coeff::AbstractArray, inner_stencil::NestedStencil, closure_stencils, dir)
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14 check_coefficient(g, coeff)
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15
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16 Δxᵢ = spacing(g.grids[dir])
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17 scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2)
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18 scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2)
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19 return SecondDerivativeVariable{dir, ndims(g)}(scaled_inner_stencil, scaled_closure_stencils, coeff)
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20 end
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21
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22 function second_derivative_variable(g::EquidistantGrid, coeff::AbstractVector, inner_stencil::NestedStencil, closure_stencils)
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23 return second_derivative_variable(TensorGrid(g), coeff, inner_stencil, closure_stencils, 1)
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24 end
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25
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26 function second_derivative_variable(g::TensorGrid, coeff::AbstractArray, stencil_set, dir::Int)
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27 inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"])
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28 closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"])
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29
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30 return second_derivative_variable(g, coeff, inner_stencil, closure_stencils, dir)
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31 end
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32
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33 function second_derivative_variable(g::EquidistantGrid, coeff::AbstractArray, stencil_set)
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34 return second_derivative_variable(TensorGrid(g), coeff, stencil_set, 1)
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35 end
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36
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37
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38 function check_coefficient(g, coeff)
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39 if ndims(g) != ndims(coeff)
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40 throw(ArgumentError("The coefficient has dimension $(ndims(coeff)) while the grid is dimension $(ndims(g))"))
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41 end
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42
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43 if size(g) != size(coeff)
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44 throw(DimensionMismatch("the size $(size(coeff)) of the coefficient does not match the size $(size(g)) of the grid"))
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45 end
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46 end
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47
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48
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49 # REVIEW: Fixa docs
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50 """
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51 SecondDerivativeVariable{Dir,T,D,...} <: LazyTensor{T,D,D}
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52
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53 A second derivative operator in direction `Dir` with a variable coefficient.
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54 """
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55 struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: LazyTensor{T,D,D}
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56 inner_stencil::IStencil
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57 closure_stencils::NTuple{M,CStencil}
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58 coefficient::TArray
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59
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60 function SecondDerivativeVariable{Dir, D}(inner_stencil::NestedStencil{T}, closure_stencils::NTuple{M,NestedStencil{T}}, coefficient::AbstractArray) where {Dir,T,D,M}
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61 IStencil = typeof(inner_stencil)
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62 CStencil = eltype(closure_stencils)
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63 TArray = typeof(coefficient)
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64 return new{Dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil, closure_stencils, coefficient)
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65 end
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66 end
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67
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68 derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir
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69
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70 closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils)
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71
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72 LazyTensors.range_size(op::SecondDerivativeVariable) = size(op.coefficient)
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73 LazyTensors.domain_size(op::SecondDerivativeVariable) = size(op.coefficient)
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74
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75
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76 function derivative_view(op, a, I)
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77 d = derivative_direction(op)
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78
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79 Iview = Base.setindex(I,:,d)
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80 return @view a[Iview...]
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81 end
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82
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83 function apply_lower(op::SecondDerivativeVariable, v, I...)
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84 ṽ = derivative_view(op, v, I)
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85 c̃ = derivative_view(op, op.coefficient, I)
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86
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87 i = I[derivative_direction(op)]
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88 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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89 end
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90
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91 function apply_interior(op::SecondDerivativeVariable, v, I...)
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92 ṽ = derivative_view(op, v, I)
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93 c̃ = derivative_view(op, op.coefficient, I)
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94
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95 i = I[derivative_direction(op)]
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96 return apply_stencil(op.inner_stencil, c̃, ṽ, i)
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97 end
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98
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99 function apply_upper(op::SecondDerivativeVariable, v, I...)
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100 ṽ = derivative_view(op, v, I)
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101 c̃ = derivative_view(op, op.coefficient, I)
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102
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103 i = I[derivative_direction(op)]
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104 sz = domain_size(op)[derivative_direction(op)]
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105 stencil = op.closure_stencils[sz-i+1]
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106 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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107 end
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108
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109 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index})
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110 if I[derivative_direction(op)] isa Index{Lower}
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111 return apply_lower(op, v, Int.(I)...)
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112 elseif I[derivative_direction(op)] isa Index{Upper}
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113 return apply_upper(op, v, Int.(I)...)
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114 elseif I[derivative_direction(op)] isa Index{Interior}
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115 return apply_interior(op, v, Int.(I)...)
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116 else
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117 error("Invalid region")
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118 end
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119 end
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120
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121 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...)
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122 dir = derivative_direction(op)
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123 sz = domain_size(op)[dir]
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124
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125 i = I[dir]
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126
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127 I = map(i->Index(i, Interior), I)
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128 if 0 < i <= closure_size(op)
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129 I = Base.setindex(I, Index(i, Lower), dir)
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130 return LazyTensors.apply(op, v, I...)
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131 elseif closure_size(op) < i <= sz-closure_size(op)
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132 I = Base.setindex(I, Index(i, Interior), dir)
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133 return LazyTensors.apply(op, v, I...)
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134 elseif sz-closure_size(op) < i <= sz
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135 I = Base.setindex(I, Index(i, Upper), dir)
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136 return LazyTensors.apply(op, v, I...)
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137 else
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138 error("Bounds error") # TODO: Make this more standard
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139 end
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140 end
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141
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142
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143 ## 2D Specific implementations to avoid instability
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144 ## TODO: Should really be solved by fixing the general methods instead
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145
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146
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147 ## x-direction
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148 function apply_lower(op::SecondDerivativeVariable{1}, v, i, j)
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149 ṽ = @view v[:,j]
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150 c̃ = @view op.coefficient[:,j]
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151
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152 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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153 end
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154
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155 function apply_interior(op::SecondDerivativeVariable{1}, v, i, j)
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156 ṽ = @view v[:,j]
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157 c̃ = @view op.coefficient[:,j]
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158
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159 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, i)
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160 end
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161
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162 function apply_upper(op::SecondDerivativeVariable{1}, v, i, j)
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163 ṽ = @view v[:,j]
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164 c̃ = @view op.coefficient[:,j]
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165
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166 sz = domain_size(op)[derivative_direction(op)]
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167 stencil = op.closure_stencils[sz-i+1]
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168 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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169 end
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170
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171
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172 ## y-direction
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173 function apply_lower(op::SecondDerivativeVariable{2}, v, i, j)
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174 ṽ = @view v[i,:]
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175 c̃ = @view op.coefficient[i,:]
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176
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177 return @inbounds apply_stencil(op.closure_stencils[j], c̃, ṽ, j)
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178 end
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179
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180 function apply_interior(op::SecondDerivativeVariable{2}, v, i, j)
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181 ṽ = @view v[i,:]
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182 c̃ = @view op.coefficient[i,:]
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183
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184 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, j)
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185 end
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186
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187 function apply_upper(op::SecondDerivativeVariable{2}, v, i, j)
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188 ṽ = @view v[i,:]
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189 c̃ = @view op.coefficient[i,:]
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190
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191 sz = domain_size(op)[derivative_direction(op)]
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192 stencil = op.closure_stencils[sz-j+1]
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193 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, j)
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194 end