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annotate src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl @ 917:eb054537fc63 feature/variable_derivatives

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author Jonatan Werpers <jonatan@werpers.com>
date Fri, 18 Feb 2022 07:39:07 +0100
parents fc1f03fc8d65
children ba5f4a0ec879
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1 export SecondDerivativeVariable
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2
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3 # REVIEW: Fixa docs
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4 """
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5 SecondDerivativeVariable{Dir,T,D,...} <: TensorMapping{T,D,D}
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6
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7 A second derivative operator in direction `Dir` with a variable coefficient.
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8 """
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9 struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: TensorMapping{T,D,D}
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10 inner_stencil::IStencil
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11 closure_stencils::NTuple{M,CStencil}
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12 size::NTuple{D,Int}
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13 coefficient::TArray
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14
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15 function SecondDerivativeVariable{Dir, D}(inner_stencil::NestedStencil{T}, closure_stencils::NTuple{M,NestedStencil{T}}, size::NTuple{D,Int}, coefficient::AbstractArray) where {Dir,T,D,M}
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16 IStencil = typeof(inner_stencil)
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17 CStencil = eltype(closure_stencils)
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18 TArray = typeof(coefficient)
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19 return new{Dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil,closure_stencils,size, coefficient)
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20 end
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21 end
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22
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23 function SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, inner_stencil, closure_stencils, dir)
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24 Δxᵢ = spacing(grid)[dir]
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25 scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2)
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26 scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2)
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27 return SecondDerivativeVariable{dir, dimension(grid)}(scaled_inner_stencil, scaled_closure_stencils, size(grid), coeff)
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28 end
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29
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30 function SecondDerivativeVariable(grid::EquidistantGrid{1}, coeff::AbstractVector, inner_stencil, closure_stencils)
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31 return SecondDerivativeVariable(grid, coeff, inner_stencil, closure_stencils, 1)
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32 end
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33
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34 @doc raw"""
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35 SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, stencil_set, dir)
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36
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37 Create a `TensorMapping` for the second derivative with a variable coefficient
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38 `coeff` on `grid` from the stencils in `stencil_set`. The direction is
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39 determined by `dir`.
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40
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41 `coeff` is a grid function on `grid`.
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42
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43 # Example
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44 With
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45 ```
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46 D = SecondDerivativeVariable(g, c, stencil_set, 2)
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47 ```
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48 then `D*u` approximates
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49 ```math
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50 \frac{\partial}{\partial y} c(x,y) \frac{\partial u}{\partial y},
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51 ```
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52 on ``(0,1)⨯(0,1)`` represented by `g`.
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53 """
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54 function SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, stencil_set, dir)
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55 inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"])
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56 closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"])
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57
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58 return SecondDerivativeVariable(grid, coeff, inner_stencil, closure_stencils, dir)
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59 end
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60
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61 derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir
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62
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63 closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils)
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64
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65 LazyTensors.range_size(op::SecondDerivativeVariable) = op.size
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66 LazyTensors.domain_size(op::SecondDerivativeVariable) = op.size
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67
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68
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69 function derivative_view(op, a, I)
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70 d = derivative_direction(op)
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71
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72 Iview = Base.setindex(I,:,d)
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73 return @view a[Iview...]
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74 end
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75
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76 function apply_lower(op::SecondDerivativeVariable, v, I...)
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77 ṽ = derivative_view(op, v, I)
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78 c̃ = derivative_view(op, op.coefficient, I)
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79
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80 i = I[derivative_direction(op)]
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81 return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i)
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82 end
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83
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84 function apply_interior(op::SecondDerivativeVariable, v, I...)
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85 ṽ = derivative_view(op, v, I)
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86 c̃ = derivative_view(op, op.coefficient, I)
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87
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88 i = I[derivative_direction(op)]
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89 return apply_stencil(op.inner_stencil, c̃, ṽ, i)
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90 end
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91
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92 function apply_upper(op::SecondDerivativeVariable, v, I...)
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93 ṽ = derivative_view(op, v, I)
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94 c̃ = derivative_view(op, op.coefficient, I)
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95
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96 i = I[derivative_direction(op)]
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97 stencil = op.closure_stencils[op.size[derivative_direction(op)]-i+1]
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98 return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i)
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99 end
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100
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101 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index})
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102 if I[derivative_direction(op)] isa Index{Lower}
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103 return apply_lower(op, v, Int.(I)...)
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104 elseif I[derivative_direction(op)] isa Index{Upper}
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105 return apply_upper(op, v, Int.(I)...)
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106 else
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107 return apply_interior(op, v, Int.(I)...)
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108 end
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109 end
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110
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111 function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...)
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112 dir = derivative_direction(op)
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113
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114 i = I[dir]
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115 r = getregion(i, closure_size(op), op.size[dir])
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116
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117 I = map(i->Index(i, Interior), I)
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118 I = Base.setindex(I, Index(i, r), dir)
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119 return LazyTensors.apply(op, v, I...)
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120 end