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annotate DiffOps/src/laplace.jl @ 247:ed29ee13e92e boundary_conditions

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Restructure laplace.jl
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 27 Jun 2019 09:43:44 +0200
parents a827568fc251
children 05e7bbe0af97
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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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 # e::BoundaryValue
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6 # d::NormalDerivative
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7 end
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8
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9 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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10 error("not implemented")
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11 end
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12
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13 # u = L*v
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14 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
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15 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
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16 return uᵢ
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17 end
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18
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19 @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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20 # 2nd x-derivative
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21 @inbounds vx = view(v, :, Int(I[2]))
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22 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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23 # 2nd y-derivative
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24 @inbounds vy = view(v, Int(I[1]), :)
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25 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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26 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
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27 return uᵢ
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28 end
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29
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30 # Slow but maybe convenient?
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31 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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32 I = Index{Unknown}.(Tuple(i))
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33 apply(L, v, I)
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34 end
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35
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36
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37
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38 """
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39 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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40
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41 Implements the boundary operator `e` as a TensorMapping
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42 """
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43 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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44 op::D2{T,N,M,K}
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45 grid::EquidistantGrid
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46 bId::CartesianBoundary
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47 end
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48 export BoundaryValue
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49
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50 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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51 # Can we give special treatment to TensorMappings that go to a higher dim?
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52 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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53 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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54
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55 function LazyTensors.apply(e::BoundaryValue, v::AbstractArray, I::NTuple{2,Int})
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56 i = I[dim(e.bId)]
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57 j = I[3-dim(e.bId)]
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58 N_i = size(e.grid)[dim(e.bId)]
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59
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60 if region(e.bId) == Lower
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61 # NOTE: closures are indexed by offset. Fix this D:<
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62 return e.op.eClosure[i-1]*v[j]
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63 elseif region(e.bId) == Upper
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64 return e.op.eClosure[N_i-i]*v[j]
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65 end
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66 end
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67
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68 function LazyTensors.apply_transpose(e::BoundaryValue, v::AbstractArray, I::NTuple{1,Int})
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69 u = selectdim(v,3-dim(e.bId),I[1])
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70 return apply_e(e.op, u, region(e.bId))
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71 end
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72
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73
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74
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75 """
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76 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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77
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78 Implements the boundary operator `d` as a TensorMapping
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79 """
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80 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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81 op::D2{T,N,M,K}
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82 grid::EquidistantGrid
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83 bId::CartesianBoundary
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84 end
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85 export NormalDerivative
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86
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87 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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88 # Can we give special treatment to TensorMappings that go to a higher dim?
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89 LazyTensors.range_size(e::NormalDerivative{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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90 LazyTensors.domain_size(e::NormalDerivative{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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91
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92 # Not correct abstraction level
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93 # TODO: Not type stable D:<
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94 function LazyTensors.apply(d::NormalDerivative, v::AbstractArray, I::NTuple{2,Int})
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95 i = I[dim(d.bId)]
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96 j = I[3-dim(d.bId)]
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97 N_i = size(d.grid)[dim(d.bId)]
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98
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99 if region(d.bId) == Lower
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100 # Note, closures are indexed by offset. Fix this D:<
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101 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
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102 elseif region(d.bId) == Upper
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103 return -d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-i]*v[j]
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104 end
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105 end
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106
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107 function LazyTensors.apply_transpose(d::NormalDerivative, v::AbstractArray, I::NTuple{1,Int})
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108 u = selectdim(v,3-dim(d.bId),I[1])
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109 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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110 end
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111
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112
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113
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114 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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115
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116 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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117 e = BoundaryValue(L.op, L.grid, Bid())
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118 d = NormalDerivative(L.op, L.grid, Bid())
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119 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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120 # TODO: Implement BoundaryQuadrature method
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121
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122 return -L.Hi*e*Hᵧ*(d'*v - g)
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123 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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124 end
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125
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126 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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127 tau::Float64
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128 end
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129
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130 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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131 e = BoundaryValue(L.op, L.grid, Bid())
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132 d = NormalDerivative(L.op, L.grid, Bid())
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133 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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134 # TODO: Implement BoundaryQuadrature method
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135
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136 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
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137 # Need to handle scalar multiplication and addition of TensorMapping
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138 end
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139
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140 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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141 # return apply(s.L, v, i) +
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142 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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143 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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144 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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145 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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146 # end