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annotate DiffOps/src/laplace.jl @ 258:3ea8c60ccef3 boundary_conditions

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Fix a few typos in documentation and add a few TODOs
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 28 Jun 2019 14:11:57 +0200
parents e960b877e07e
children 5571d2c5bf0f
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5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
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1 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
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2 grid::EquidistantGrid{Dim,T}
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3 a::T
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4 op::D2{Float64,N,M,K}
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5 end
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6
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7 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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8 error("not implemented")
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9 end
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10
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11 # u = L*v
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12 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
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13 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
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14 return uᵢ
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15 end
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16
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17 @inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
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18 # 2nd x-derivative
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19 @inbounds vx = view(v, :, Int(I[2]))
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20 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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21 # 2nd y-derivative
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22 @inbounds vy = view(v, Int(I[1]), :)
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23 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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24 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
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25 return uᵢ
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26 end
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27
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28 # Slow but maybe convenient?
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29 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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30 I = Index{Unknown}.(Tuple(i))
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31 apply(L, v, I)
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32 end
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33
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34 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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35 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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36 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = throw(MethodError) # TODO: Implement this
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38
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39 """
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40 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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41
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42 Implements the boundary operator `e` as a TensorMapping
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43 """
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44 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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45 op::D2{T,N,M,K}
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46 grid::EquidistantGrid{2}
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47 bId::CartesianBoundary
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48 end
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49 export BoundaryValue
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50
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51 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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52 # Can we give special treatment to TensorMappings that go to a higher dim?
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53 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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54 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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55
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56 # TODO: Make this independent of dimension
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57 function LazyTensors.apply(e::BoundaryValue, v::AbstractArray, I::NTuple{2,Int})
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58 i = I[dim(e.bId)]
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59 j = I[3-dim(e.bId)]
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60 N_i = size(e.grid)[dim(e.bId)]
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61 return apply_e(e.op, v[j], N_i, i, region(e.bId))
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62 end
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63
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64 function LazyTensors.apply_transpose(e::BoundaryValue, v::AbstractArray, I::NTuple{1,Int})
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65 u = selectdim(v,3-dim(e.bId),I[1])
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66 return apply_e_T(e.op, u, region(e.bId))
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67 end
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70
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71 """
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72 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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73
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74 Implements the boundary operator `d` as a TensorMapping
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75 """
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76 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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77 op::D2{T,N,M,K}
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78 grid::EquidistantGrid{2}
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79 bId::CartesianBoundary
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80 end
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81 export NormalDerivative
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82
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83 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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84 # Can we give special treatment to TensorMappings that go to a higher dim?
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85 LazyTensors.range_size(e::NormalDerivative{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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86 LazyTensors.domain_size(e::NormalDerivative{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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87
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88 # TODO: Not type stable D:<
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89 # TODO: Make this independent of dimension
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90 function LazyTensors.apply(d::NormalDerivative, v::AbstractArray, I::NTuple{2,Int})
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91 i = I[dim(d.bId)]
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92 j = I[3-dim(d.bId)]
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93 N_i = size(d.grid)[dim(d.bId)]
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94 h_inv = d.grid.inverse_spacing[dim(d.bId)]
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95 return apply_d(d.op, h_inv, v[j], N_i, i, region(d.bId))
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96 end
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97
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98 function LazyTensors.apply_transpose(d::NormalDerivative, v::AbstractArray, I::NTuple{1,Int})
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99 u = selectdim(v,3-dim(d.bId),I[1])
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100 return apply_d_T(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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101 end
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102
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105 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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106
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107 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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108 e = boundary_value(L.op, Bid())
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109 d = normal_derivative(L.op, Bid())
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110 Hᵧ = boundary_quadrature(L.op, Bid())
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111
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112 return -L.Hi*e*Hᵧ*(d'*v - g)
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113 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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114 end
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115
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116 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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117 tau::Float64
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118 end
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119
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120 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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121 e = boundary_value(L.op, Bid())
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122 d = normal_derivative(L.op, Bid())
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123 Hᵧ = boundary_quadrature(L.op, Bid())
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124
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125 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
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126 # Need to handle scalar multiplication and addition of TensorMapping
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127 end
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128
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129 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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130 # return apply(s.L, v, i) +
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131 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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132 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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133 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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134 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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135 # end