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annotate src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl @ 2096:5af7534e5b3c feature/sbp_operators/laplace_curvilinear tip

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Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 02 Mar 2026 15:58:27 +0100
parents 3684db043add e21c295fb2da
children
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1 """
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2 second_derivative_variable(g, coeff, ..., [dim])
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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 `dim`.
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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, dim::Int)
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13 if dim ∉ 1:ndims(g)
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14 throw(DomainError(dim, "Derivative direction must be in 1:$(ndims(g))."))
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15 end
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16 inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"])
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17 closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"])
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18
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19 return second_derivative_variable(g, coeff, inner_stencil, closure_stencils, dim)
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20 end
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21
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22 function second_derivative_variable(g::EquidistantGrid, coeff, stencil_set)
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23 return second_derivative_variable(TensorGrid(g), coeff, stencil_set, 1)
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24 end
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25
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26 function second_derivative_variable(g::EquidistantGrid, coeff, stencil_set, dim)
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27 if dim != 1
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28 throw(DomainError(dim, "Derivative direction must be 1."))
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29 end
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30 return second_derivative_variable(g, coeff, stencil_set)
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31 end
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32
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33 function second_derivative_variable(g::TensorGrid, coeff, inner_stencil::NestedStencil, closure_stencils, dim)
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34 check_coefficient(g, coeff)
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35
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36 Δxᵢ = spacing(g.grids[dim])
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37 scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2)
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38 scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2)
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39 return SecondDerivativeVariable(coeff, scaled_inner_stencil, scaled_closure_stencils, dim)
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40 end
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41
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42 function check_coefficient(g, coeff)
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43 if ndims(g) != ndims(coeff)
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44 throw(ArgumentError("The coefficient has dimension $(ndims(coeff)) while the grid is dimension $(ndims(g))"))
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45 end
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46
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47 if size(g) != size(coeff)
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48 throw(DimensionMismatch("the size $(size(coeff)) of the coefficient does not match the size $(size(g)) of the grid"))
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49 end
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50 end
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51
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52
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53 """
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54 SecondDerivativeVariable{Dir,T,D,...} <: LazyTensor{T,D,D}
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55
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56 A second derivative operator in direction `Dir` with a variable coefficient.
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57 """
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58 struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: LazyTensor{T,D,D}
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59 inner_stencil::IStencil
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60 closure_stencils::NTuple{M,CStencil}
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61 coefficient::TArray
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62
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63 function SecondDerivativeVariable(coefficient::AbstractArray, inner_stencil::NestedStencil{T}, closure_stencils::NTuple{M,NestedStencil{T}}, dir) where {T,M}
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64 D = ndims(coefficient)
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65 IStencil = typeof(inner_stencil)
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66 CStencil = eltype(closure_stencils)
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67 TArray = typeof(coefficient)
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68 return new{dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil, closure_stencils, coefficient)
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69 end
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70 end
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71
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72 derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir
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73
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74 closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils)
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75
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76 LazyTensors.range_size(op::SecondDerivativeVariable) = size(op.coefficient)
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77 LazyTensors.domain_size(op::SecondDerivativeVariable) = size(op.coefficient)
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78
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79
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80 function derivative_view(op, a, I)
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81 d = derivative_direction(op)
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82
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83 Iview = Base.setindex(I,:,d)
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84 return @view a[Iview...]
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85 end
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86
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87 function apply_lower(op::SecondDerivativeVariable, v, I...)
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88 ṽ = derivative_view(op, v, I)
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89 c̃ = derivative_view(op, op.coefficient, I)
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90
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91 i = I[derivative_direction(op)]
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92 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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93 end
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94
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95 function apply_interior(op::SecondDerivativeVariable, v, I...)
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96 ṽ = derivative_view(op, v, I)
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97 c̃ = derivative_view(op, op.coefficient, I)
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98
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99 i = I[derivative_direction(op)]
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100 return apply_stencil(op.inner_stencil, c̃, ṽ, i)
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101 end
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102
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103 function apply_upper(op::SecondDerivativeVariable, v, I...)
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104 ṽ = derivative_view(op, v, I)
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105 c̃ = derivative_view(op, op.coefficient, I)
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106
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107 i = I[derivative_direction(op)]
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108 sz = domain_size(op)[derivative_direction(op)]
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109 stencil = op.closure_stencils[sz-i+1]
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110 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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111 end
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112
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113 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index})
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114 if I[derivative_direction(op)] isa Index{Lower}
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115 return apply_lower(op, v, Int.(I)...)
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116 elseif I[derivative_direction(op)] isa Index{Upper}
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117 return apply_upper(op, v, Int.(I)...)
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118 elseif I[derivative_direction(op)] isa Index{Interior}
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119 return apply_interior(op, v, Int.(I)...)
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120 else
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121 error("Invalid region")
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122 end
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123 end
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124
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125 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...)
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126 dir = derivative_direction(op)
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127 sz = domain_size(op)[dir]
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128
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129 i = I[dir]
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130
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131 I = map(i->Index(i, Interior), I)
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132 if 0 < i <= closure_size(op)
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133 I = Base.setindex(I, Index(i, Lower), dir)
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134 return LazyTensors.apply(op, v, I...)
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135 elseif closure_size(op) < i <= sz-closure_size(op)
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136 I = Base.setindex(I, Index(i, Interior), dir)
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137 return LazyTensors.apply(op, v, I...)
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138 elseif sz-closure_size(op) < i <= sz
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139 I = Base.setindex(I, Index(i, Upper), dir)
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140 return LazyTensors.apply(op, v, I...)
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141 else
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142 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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143 end
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144 end
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145
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146
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147 # 2D Specific implementations to avoid type instability
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148 # TBD: Can this be solved by fixing the general methods instead?
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149
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150
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151 ## x-direction
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152 function apply_lower(op::SecondDerivativeVariable{1}, v, i, j)
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153 Base.@constprop :aggressive
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154 ṽ = @view v[:,j]
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155 c̃ = @view op.coefficient[:,j]
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156
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157 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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158 end
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159
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160 function apply_interior(op::SecondDerivativeVariable{1}, v, i, j)
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161 Base.@constprop :aggressive
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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 Base.@constprop :aggressive
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170 ṽ = @view v[:,j]
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171 c̃ = @view op.coefficient[:,j]
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172
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173 sz = domain_size(op)[derivative_direction(op)]
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174 stencil = op.closure_stencils[sz-i+1]
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175 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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176 end
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177
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178
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179 ## y-direction
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180 function apply_lower(op::SecondDerivativeVariable{2}, v, i, j)
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181 Base.@constprop :aggressive
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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 return @inbounds apply_stencil(op.closure_stencils[j], c̃, ṽ, j)
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186 end
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187
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188 function apply_interior(op::SecondDerivativeVariable{2}, v, i, j)
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189 Base.@constprop :aggressive
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190 ṽ = @view v[i,:]
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191 c̃ = @view op.coefficient[i,:]
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192
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193 return @inbounds apply_stencil(op.inner_stencil, c̃, ṽ, j)
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194 end
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195
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196 function apply_upper(op::SecondDerivativeVariable{2}, v, i, j)
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197 Base.@constprop :aggressive
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198 ṽ = @view v[i,:]
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199 c̃ = @view op.coefficient[i,:]
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200
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201 sz = domain_size(op)[derivative_direction(op)]
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202 stencil = op.closure_stencils[sz-j+1]
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203 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, j)
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204 end