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annotate src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl @ 1368:26ad90b42efd feature/variable_derivatives

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Remove export of SecondDerivativeVariable
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 26 May 2023 14:54:00 +0200
parents 71e89507dd9a
children 4ef8fb75d144
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1 # REVIEW: Fixa docs
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2 """
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3 SecondDerivativeVariable{Dir,T,D,...} <: LazyTensor{T,D,D}
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4
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5 A second derivative operator in direction `Dir` with a variable coefficient.
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6 """
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7 struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: LazyTensor{T,D,D}
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8 inner_stencil::IStencil
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9 closure_stencils::NTuple{M,CStencil}
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10 coefficient::TArray
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11
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12 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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13 IStencil = typeof(inner_stencil)
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14 CStencil = eltype(closure_stencils)
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15 TArray = typeof(coefficient)
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16 return new{Dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil, closure_stencils, coefficient)
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17 end
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18 end
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19
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20 function SecondDerivativeVariable(g::TensorGrid, coeff::AbstractArray, inner_stencil::NestedStencil, closure_stencils, dir)
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21 check_coefficient(g, coeff)
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22
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23 Δxᵢ = spacing(g.grids[dir])
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24 scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2)
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25 scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2)
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26 return SecondDerivativeVariable{dir, ndims(g)}(scaled_inner_stencil, scaled_closure_stencils, coeff)
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27 end
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28
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29 function SecondDerivativeVariable(g::EquidistantGrid, coeff::AbstractVector, inner_stencil::NestedStencil, closure_stencils)
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30 return SecondDerivativeVariable(TensorGrid(g), coeff, inner_stencil, closure_stencils, 1)
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31 end
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32
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33 @doc raw"""
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34 SecondDerivativeVariable(g::EquidistantGrid, coeff::AbstractArray, stencil_set, dir)
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35
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36 Create a `LazyTensor` for the second derivative with a variable coefficient
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37 `coeff` on `grid` from the stencils in `stencil_set`. The direction is
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38 determined by `dir`.
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39
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40 `coeff` is a grid function on `grid`.
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41
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42 # Example
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43 With
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44 ```
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45 D = SecondDerivativeVariable(g, c, stencil_set, 2)
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46 ```
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47 then `D*u` approximates
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48 ```math
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49 \frac{\partial}{\partial y} c(x,y) \frac{\partial u}{\partial y},
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50 ```
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51 on ``(0,1)⨯(0,1)`` represented by `g`.
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52 """
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53 function SecondDerivativeVariable(g::TensorGrid, coeff::AbstractArray, stencil_set, dir::Int)
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54 inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"])
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55 closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"])
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56
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57 return SecondDerivativeVariable(g, coeff, inner_stencil, closure_stencils, dir)
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58 end
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59
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60 function SecondDerivativeVariable(g::EquidistantGrid, coeff::AbstractArray, stencil_set)
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61 return SecondDerivativeVariable(TensorGrid(g), coeff, stencil_set, 1)
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62 end
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63
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64 function check_coefficient(g, coeff)
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65 if ndims(g) != ndims(coeff)
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66 throw(ArgumentError("The coefficient has dimension $(ndims(coeff)) while the grid is dimension $(ndims(g))"))
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67 end
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68
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69 if size(g) != size(coeff)
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70 throw(DimensionMismatch("the size $(size(coeff)) of the coefficient does not match the size $(size(g)) of the grid"))
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71 end
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72 end
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73
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74 derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir
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75
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76 closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils)
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77
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78 LazyTensors.range_size(op::SecondDerivativeVariable) = size(op.coefficient)
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79 LazyTensors.domain_size(op::SecondDerivativeVariable) = size(op.coefficient)
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80
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81
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82 function derivative_view(op, a, I)
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83 d = derivative_direction(op)
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84
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85 Iview = Base.setindex(I,:,d)
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86 return @view a[Iview...]
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87 end
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88
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89 function apply_lower(op::SecondDerivativeVariable, v, I...)
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90 ṽ = derivative_view(op, v, I)
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91 c̃ = derivative_view(op, op.coefficient, I)
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92
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93 i = I[derivative_direction(op)]
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94 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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95 end
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96
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97 function apply_interior(op::SecondDerivativeVariable, v, I...)
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98 ṽ = derivative_view(op, v, I)
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99 c̃ = derivative_view(op, op.coefficient, I)
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100
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101 i = I[derivative_direction(op)]
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102 return apply_stencil(op.inner_stencil, c̃, ṽ, i)
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103 end
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104
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105 function apply_upper(op::SecondDerivativeVariable, v, I...)
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106 ṽ = derivative_view(op, v, I)
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107 c̃ = derivative_view(op, op.coefficient, I)
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108
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109 i = I[derivative_direction(op)]
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110 sz = domain_size(op)[derivative_direction(op)]
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111 stencil = op.closure_stencils[sz-i+1]
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112 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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113 end
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114
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115 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index})
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116 if I[derivative_direction(op)] isa Index{Lower}
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117 return apply_lower(op, v, Int.(I)...)
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118 elseif I[derivative_direction(op)] isa Index{Upper}
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119 return apply_upper(op, v, Int.(I)...)
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120 elseif I[derivative_direction(op)] isa Index{Interior}
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121 return apply_interior(op, v, Int.(I)...)
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122 else
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123 error("Invalid region")
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124 end
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125 end
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126
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127 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...)
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128 dir = derivative_direction(op)
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129 sz = domain_size(op)[dir]
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130
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131 i = I[dir]
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132
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133 I = map(i->Index(i, Interior), I)
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134 if 0 < i <= closure_size(op)
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135 I = Base.setindex(I, Index(i, Lower), dir)
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136 return LazyTensors.apply(op, v, I...)
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137 elseif closure_size(op) < i <= sz-closure_size(op)
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138 I = Base.setindex(I, Index(i, Interior), dir)
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139 return LazyTensors.apply(op, v, I...)
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140 elseif sz-closure_size(op) < i <= sz
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141 I = Base.setindex(I, Index(i, Upper), dir)
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142 return LazyTensors.apply(op, v, I...)
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143 else
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144 error("Bounds error") # TODO: Make this more standard
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145 end
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146 end
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147
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148
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149 ## 2D Specific implementations to avoid instability
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150 ## TODO: Should really be solved by fixing the general methods instead
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151
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152
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153 ## x-direction
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154 function apply_lower(op::SecondDerivativeVariable{1}, v, i, j)
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155 ṽ = @view v[:,j]
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156 c̃ = @view op.coefficient[:,j]
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157
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158 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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159 end
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160
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161 function apply_interior(op::SecondDerivativeVariable{1}, v, i, j)
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162 ṽ = @view v[:,j]
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163 c̃ = @view op.coefficient[:,j]
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164
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165 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, i)
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166 end
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167
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168 function apply_upper(op::SecondDerivativeVariable{1}, v, i, j)
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169 ṽ = @view v[:,j]
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170 c̃ = @view op.coefficient[:,j]
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171
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172 sz = domain_size(op)[derivative_direction(op)]
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173 stencil = op.closure_stencils[sz-i+1]
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174 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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175 end
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176
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177
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178 ## y-direction
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179 function apply_lower(op::SecondDerivativeVariable{2}, v, i, j)
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180 ṽ = @view v[i,:]
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181 c̃ = @view op.coefficient[i,:]
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182
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183 return @inbounds apply_stencil(op.closure_stencils[j], c̃, ṽ, j)
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184 end
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185
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186 function apply_interior(op::SecondDerivativeVariable{2}, v, i, j)
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187 ṽ = @view v[i,:]
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188 c̃ = @view op.coefficient[i,:]
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189
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190 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, j)
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191 end
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192
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193 function apply_upper(op::SecondDerivativeVariable{2}, v, i, j)
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194 ṽ = @view v[i,:]
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195 c̃ = @view op.coefficient[i,:]
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196
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197 sz = domain_size(op)[derivative_direction(op)]
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198 stencil = op.closure_stencils[sz-j+1]
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199 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, j)
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200 end