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annotate SbpOperators/src/laplace/laplace.jl @ 312:c1fcc35e19cb

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Make Laplace consist of tuples of SecondDerivatives. Begin cleanup of functionallity which should be moved to separate files. WIP
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 09 Sep 2020 21:18:28 +0200
parents 6fa2ba769ae3
children 9cc5d1498b2d
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c1fcc35e19cb Make Laplace consist of tuples of SecondDerivatives. Begin cleanup of functionallity which should be moved to separate files. WIP
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1 export Laplace
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2 """
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3 Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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4
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5 Implements the Laplace operator `L` in Dim dimensions as a tensor operator
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6 The multi-dimensional tensor operator consists of a tuple of 1D SecondDerivative
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7 tensor operators.
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8 """
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9 #export quadrature, inverse_quadrature, boundary_quadrature, boundary_value, normal_derivative
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10 struct Laplace{Dim,T,N,M,K} <: TensorOperator{T,Dim}
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11 D2::NTuple{Dim,SecondDerivative{T,N,M,K}}
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12 #TODO: Write a good constructor
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13 end
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14
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15 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) where {Dim} = range_size
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16
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17 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim}
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18 error("not implemented")
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19 end
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20
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21 # u = L*v
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22 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::Index) where T
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23 @inbounds u = LazyTensors.apply(L.D2[1],v,I)
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24 return u
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25 end
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26
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27 # TODO: Fix dispatch on tuples!
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28 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::Index, J::Index) where T
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29 # 2nd x-derivative
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30 @inbounds vx = view(v, :, Int(J))
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31 @inbounds uᵢ = LazyTensors.apply(L.D2[1], vx , I)
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32
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33 # 2nd y-derivative
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34 @inbounds vy = view(v, Int(I), :)
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35 @inbounds uᵢ += LazyTensors.apply(L.D2[2], vy , J)
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36
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37 return uᵢ
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38 end
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39
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40 @inline function LazyTensors.apply_transpose(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim}
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41 return LazyTensors.apply(L, v, I)
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42 end
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43
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44 # quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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45 # inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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46 # boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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47 # normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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48 # boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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49 # export NormalDerivative
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50 # """
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51 # NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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52 #
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53 # Implements the boundary operator `d` as a TensorMapping
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54 # """
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55 # struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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56 # op::D2{T,N,M,K}
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57 # grid::EquidistantGrid{2}
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58 # bId::CartesianBoundary
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59 # end
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60 #
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61 # # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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62 # # Can we give special treatment to TensorMappings that go to a higher dim?
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63 # function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
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64 # if dim(e.bId) == 1
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65 # return (UnknownDim, domain_size[1])
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66 # elseif dim(e.bId) == 2
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67 # return (domain_size[1], UnknownDim)
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68 # end
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69 # end
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70 # LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
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71 #
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72 # # TODO: Not type stable D:<
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73 # # TODO: Make this independent of dimension
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74 # function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
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75 # i = I[dim(d.bId)]
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76 # j = I[3-dim(d.bId)]
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77 # N_i = size(d.grid)[dim(d.bId)]
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78 # h_inv = inverse_spacing(d.grid)[dim(d.bId)]
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79 # return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
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80 # end
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81 #
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82 # function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
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83 # u = selectdim(v,3-dim(d.bId),Int(I[1]))
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84 # return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
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85 # end
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86 #
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87 # """
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88 # BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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89 #
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90 # Implements the boundary operator `q` as a TensorOperator
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91 # """
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92 # export BoundaryQuadrature
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93 # struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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94 # op::D2{T,N,M,K}
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95 # grid::EquidistantGrid{2}
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96 # bId::CartesianBoundary
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97 # end
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98 #
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99 #
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100 # # TODO: Make this independent of dimension
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101 # function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
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102 # h = spacing(q.grid)[3-dim(q.bId)]
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103 # N = size(v)
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104 # return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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105 # end
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106 #
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107 # LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T = LazyTensors.apply(q,v,I)
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108 #
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109 #
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110 #
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111 #
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112 # struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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113 #
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114 # function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
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115 # e = boundary_value(L, Bid())
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116 # d = normal_derivative(L, Bid())
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117 # Hᵧ = boundary_quadrature(L, Bid())
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118 # H⁻¹ = inverse_quadrature(L)
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119 # return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
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120 # end
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121 #
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122 # struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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123 # tau::Float64
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124 # end
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125 #
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126 # function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
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127 # e = boundary_value(L, Bid())
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128 # d = normal_derivative(L, Bid())
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129 # Hᵧ = boundary_quadrature(L, Bid())
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130 # H⁻¹ = inverse_quadrature(L)
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131 # return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
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132 # # Need to handle scalar multiplication and addition of TensorMapping
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133 # end
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134
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135 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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136 # return apply(s.L, v, i) +
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137 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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138 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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139 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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140 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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141 # end