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annotate DiffOps/src/laplace.jl @ 245:d9e262cb2e8d boundary_conditions

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Rename apply_e and _d to _e_T and _d_T. Implement _e _d and using them in laplace.jl
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 27 Jun 2019 12:49:58 +0200
parents a827568fc251
children 3d83b4d78b55 05e7bbe0af97
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1 """
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2 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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3
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4 Implements the boundary operator `d` as a TensorMapping
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5 """
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6 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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7 op::D2{T,N,M,K}
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8 grid::EquidistantGrid
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9 bId::CartesianBoundary
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10 end
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11 export NormalDerivative
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12
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13 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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14 # Can we give special treatment to TensorMappings that go to a higher dim?
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15 LazyTensors.range_size(e::NormalDerivative{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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16 LazyTensors.domain_size(e::NormalDerivative{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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17
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18 # Not correct abstraction level
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19 # TODO: Not type stable D:<
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20 function LazyTensors.apply(d::NormalDerivative, v::AbstractArray, I::NTuple{2,Int})
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21 i = I[dim(d.bId)]
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22 j = I[3-dim(d.bId)]
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23 N_i = size(d.grid)[dim(d.bId)]
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24
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25 h_inv = d.grid.inverse_spacing[dim(d.bId)]
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26 return apply_d(d.op, h_inv, v[j], N_i, i, region(d.bId))
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27 end
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28
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29 function LazyTensors.apply_transpose(d::NormalDerivative, v::AbstractArray, I::NTuple{1,Int})
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30 u = selectdim(v,3-dim(d.bId),I[1])
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31 return apply_d_T(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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32 end
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33
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34
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35 """
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36 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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37
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38 Implements the boundary operator `e` as a TensorMapping
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39 """
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40 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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41 op::D2{T,N,M,K}
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42 grid::EquidistantGrid
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43 bId::CartesianBoundary
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44 end
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45 export BoundaryValue
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46
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47 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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48 # Can we give special treatment to TensorMappings that go to a higher dim?
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49 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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50 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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51
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52 function LazyTensors.apply(e::BoundaryValue, v::AbstractArray, I::NTuple{2,Int})
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53 i = I[dim(e.bId)]
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54 j = I[3-dim(e.bId)]
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55 N_i = size(e.grid)[dim(e.bId)]
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56
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57 return apply_e(e.op, v[j], N_i, i, region(e.bId))
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58 end
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59
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60 function LazyTensors.apply_transpose(e::BoundaryValue, v::AbstractArray, I::NTuple{1,Int})
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61 u = selectdim(v,3-dim(e.bId),I[1])
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62 return apply_e_T(e.op, u, region(e.bId))
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63 end
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64
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65
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66
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67 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
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68 grid::EquidistantGrid{Dim,T}
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69 a::T
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70 op::D2{Float64,N,M,K}
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71 # e::BoundaryValue
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72 # d::NormalDerivative
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73 end
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74
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75 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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76 error("not implemented")
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77 end
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78
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79 # u = L*v
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80 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
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81 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
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82 return uᵢ
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83 end
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84
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85 @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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86 # 2nd x-derivative
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87 @inbounds vx = view(v, :, Int(I[2]))
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88 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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89 # 2nd y-derivative
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90 @inbounds vy = view(v, Int(I[1]), :)
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91 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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92 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
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93 return uᵢ
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94 end
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95
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96 # Slow but maybe convenient?
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97 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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98 I = Index{Unknown}.(Tuple(i))
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99 apply(L, v, I)
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100 end
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101
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102
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103 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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104
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105 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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106 e = BoundaryValue(L.op, L.grid, Bid())
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107 d = NormalDerivative(L.op, L.grid, Bid())
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108 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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109 # TODO: Implement BoundaryQuadrature method
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110
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111 return -L.Hi*e*Hᵧ*(d'*v - g)
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112 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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113 end
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114
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115 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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116 tau::Float64
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117 end
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118
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119 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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120 e = BoundaryValue(L.op, L.grid, Bid())
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121 d = NormalDerivative(L.op, L.grid, Bid())
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122 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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123 # TODO: Implement BoundaryQuadrature method
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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