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annotate DiffOps/src/laplace.jl @ 273:babc4288e6a6 boundary_conditions

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Dispatch apply(Quadrature) etc on region indices and create utility wrapper function dispatching on standard ints
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 06 Jan 2020 10:48:38 +0100
parents ccef055233a2
children fe9e8737ddfa
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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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ccef055233a2 Move general methods for D2 to ConstantStencilOperator and increase verbosity of method names for clarity
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13 uᵢ = L.a * SbpOperators.apply_2nd_derivative(L.op, inverse_spacing(L.grid)[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_2nd_derivative(L.op, inverse_spacing(L.grid)[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_2nd_derivative(L.op, inverse_spacing(L.grid)[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 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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35 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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9405c19b76bc Move boundary_value and similar methods of laplce
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36 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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37 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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5571d2c5bf0f Implement BaoundaryQuadrature for Laplace
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38 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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39
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40 """
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41 Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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42
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43 Implements the quadrature operator `H` of Dim dimension as a TensorMapping
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44 """
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45 struct Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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46 op::D2{T,N,M,K}
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47 grid::EquidistantGrid{Dim,T}
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48 end
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49 export Quadrature
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50
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51 LazyTensors.range_size(H::Quadrature{2}, domain_size::NTuple{2,Integer}) where T = size(H.grid)
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52 LazyTensors.domain_size(H::Quadrature{2}, range_size::NTuple{2,Integer}) where T = size(H.grid)
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53
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54 # TODO: Dispatch on Tuple{Index{R1},Index{R2}}?
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55 @inline function LazyTensors.apply(H::Quadrature{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
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56 N = size(H.grid)
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57 # Quadrature in x direction
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58 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
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59 # Quadrature in y-direction
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60 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
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61 return q
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62 end
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63
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64 function LazyTensors.apply(H::Quadrature{2}, v::AbstractArray{T,2} where T, i::NTuple{2,Integer})
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65 I = Index{Unknown}.(i)
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66 LazyTensors.apply(H, v, I)
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67 end
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68
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69 LazyTensors.apply_transpose(H::Quadrature{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}} where {R1, R2}) = LazyTensors.apply(H,v,I)
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70
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71 function LazyTensors.apply_transpose(H::Quadrature{2}, v::AbstractArray{T,2} where T, i::NTuple{2,Integer})
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72 I = Index{Unknown}.(i)
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73 LazyTensors.apply_transpose(H, v, I)
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74 end
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75
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76 """
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77 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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78
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79 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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80 """
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81 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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82 op::D2{T,N,M,K}
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83 grid::EquidistantGrid{Dim,T}
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84 end
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85 export InverseQuadrature
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86
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87 LazyTensors.range_size(H_inv::InverseQuadrature{2}, domain_size::NTuple{2,Integer}) where T = size(H_inv.grid)
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88 LazyTensors.domain_size(H_inv::InverseQuadrature{2}, range_size::NTuple{2,Integer}) where T = size(H_inv.grid)
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89
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90 # TODO: Dispatch on Tuple{Index{R1},Index{R2}}?
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91 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2}, v::AbstractArray{T,2} where T, I::NTuple{2,Integer})
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92 I = CartesianIndex(I);
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93 N = size(H_inv.grid)
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94 # Inverse quadrature in x direction
268
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95 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[1], v[I] , I[1], N[1])
262
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96 # Inverse quadrature in y-direction
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97 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[2], q_inv, I[2], N[2])
262
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98 return q_inv
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99 end
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100
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101 LazyTensors.apply_transpose(H_inv::InverseQuadrature{2}, v::AbstractArray{T,2} where T, I::NTuple{2,Integer}) = LazyTensors.apply(H_inv,v,I)
235
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102
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103 """
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104 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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105
258
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106 Implements the boundary operator `e` as a TensorMapping
235
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107 """
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108 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
248
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109 op::D2{T,N,M,K}
255
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110 grid::EquidistantGrid{2}
248
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111 bId::CartesianBoundary
228
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112 end
235
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113 export BoundaryValue
228
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114
235
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115 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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116 # Can we give special treatment to TensorMappings that go to a higher dim?
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117 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
244
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118 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
235
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119
258
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120 # TODO: Make this independent of dimension
239
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121 function LazyTensors.apply(e::BoundaryValue, v::AbstractArray, I::NTuple{2,Int})
248
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122 i = I[dim(e.bId)]
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123 j = I[3-dim(e.bId)]
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124 N_i = size(e.grid)[dim(e.bId)]
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125 return apply_boundary_value(e.op, v[j], N_i, i, region(e.bId))
228
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126 end
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127
239
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128 function LazyTensors.apply_transpose(e::BoundaryValue, v::AbstractArray, I::NTuple{1,Int})
248
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129 u = selectdim(v,3-dim(e.bId),I[1])
269
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130 return apply_boundary_value_transpose(e.op, u, region(e.bId))
228
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131 end
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132
247
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133 """
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134 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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135
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136 Implements the boundary operator `d` as a TensorMapping
247
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137 """
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138 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
248
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139 op::D2{T,N,M,K}
255
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140 grid::EquidistantGrid{2}
248
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141 bId::CartesianBoundary
228
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142 end
247
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143 export NormalDerivative
228
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144
247
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145 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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146 # Can we give special treatment to TensorMappings that go to a higher dim?
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147 LazyTensors.range_size(e::NormalDerivative{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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148 LazyTensors.domain_size(e::NormalDerivative{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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149
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150 # TODO: Not type stable D:<
258
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151 # TODO: Make this independent of dimension
247
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152 function LazyTensors.apply(d::NormalDerivative, v::AbstractArray, I::NTuple{2,Int})
248
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153 i = I[dim(d.bId)]
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154 j = I[3-dim(d.bId)]
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155 N_i = size(d.grid)[dim(d.bId)]
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156 h_inv = inverse_spacing(d.grid)[dim(d.bId)]
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157 return apply_normal_derivative(d.op, h_inv, v[j], N_i, i, region(d.bId))
228
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158 end
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159
247
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160 function LazyTensors.apply_transpose(d::NormalDerivative, v::AbstractArray, I::NTuple{1,Int})
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161 u = selectdim(v,3-dim(d.bId),I[1])
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162 return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
228
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163 end
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164
259
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165 """
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166 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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167
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168 Implements the boundary operator `q` as a TensorOperator
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169 """
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170 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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171 op::D2{T,N,M,K}
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172 grid::EquidistantGrid{2}
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173 bId::CartesianBoundary
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174 end
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175 export BoundaryQuadrature
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176
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177 # TODO: Make this independent of dimension
262
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178 # TODO: Dispatch directly on Index{R}?
259
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179 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Int}) where T
268
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180 h = spacing(q.grid)[3-dim(q.bId)]
259
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181 N = size(v)
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182 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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183 end
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184
262
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185 LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Int}) where T = LazyTensors.apply(q,v,I)
259
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186
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187
228
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188
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189
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190 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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191
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192 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
266
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193 e = boundary_value(L, Bid())
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194 d = normal_derivative(L, Bid())
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195 Hᵧ = boundary_quadrature(L, Bid())
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196 H⁻¹ = inverse_quadrature(L)
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197 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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198 end
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199
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200 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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201 tau::Float64
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202 end
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203
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204 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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205 e = boundary_value(L, Bid())
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206 d = normal_derivative(L, Bid())
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207 Hᵧ = boundary_quadrature(L, Bid())
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208 H⁻¹ = inverse_quadrature(L)
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209 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
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210 # Need to handle scalar multiplication and addition of TensorMapping
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211 end
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212
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213 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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214 # return apply(s.L, v, i) +
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215 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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216 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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217 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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218 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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219 # end