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annotate DiffOps/src/laplace.jl @ 266:9ad447176ba1 boundary_conditions

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Minor work on implementation of SATs for laplace
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 05 Dec 2019 09:27:31 +0100
parents f1e90a92ad74
children f67ce2eb6019
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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 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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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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38 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
228
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39
262
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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::NTuple{2,Integer})
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56 I = CartesianIndex(I);
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57 N = size(H.grid)
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58 # Quadrature in x direction
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59 @inbounds q = apply_quadrature(H.op, H.grid.spacing[1], v[I] , I[1], N[1])
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60 # Quadrature in y-direction
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61 @inbounds q = apply_quadrature(H.op, H.grid.spacing[2], q, I[2], N[2])
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62 return q
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63 end
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64
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65 LazyTensors.apply_transpose(H::Quadrature{2}, v::AbstractArray{T,2} where T, I::NTuple{2,Integer}) = LazyTensors.apply(H,v,I)
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66
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67 """
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68 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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69
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70 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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71 """
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72 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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73 op::D2{T,N,M,K}
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74 grid::EquidistantGrid{Dim,T}
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75 end
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76 export InverseQuadrature
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77
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78 LazyTensors.range_size(H_inv::InverseQuadrature{2}, domain_size::NTuple{2,Integer}) where T = size(H_inv.grid)
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79 LazyTensors.domain_size(H_inv::InverseQuadrature{2}, range_size::NTuple{2,Integer}) where T = size(H_inv.grid)
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80
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81 # TODO: Dispatch on Tuple{Index{R1},Index{R2}}?
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82 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2}, v::AbstractArray{T,2} where T, I::NTuple{2,Integer})
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83 I = CartesianIndex(I);
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84 N = size(H_inv.grid)
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85 # Inverse quadrature in x direction
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86 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, H_inv.grid.inverse_spacing[1], v[I] , I[1], N[1])
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87 # Inverse quadrature in y-direction
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88 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, H_inv.grid.inverse_spacing[2], q_inv, I[2], N[2])
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89 return q_inv
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90 end
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91
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92 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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93
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94 """
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95 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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96
258
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97 Implements the boundary operator `e` as a TensorMapping
235
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98 """
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99 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
248
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100 op::D2{T,N,M,K}
255
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101 grid::EquidistantGrid{2}
248
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102 bId::CartesianBoundary
228
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103 end
235
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104 export BoundaryValue
228
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105
235
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106 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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107 # Can we give special treatment to TensorMappings that go to a higher dim?
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108 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
244
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109 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
235
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110
258
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111 # TODO: Make this independent of dimension
239
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112 function LazyTensors.apply(e::BoundaryValue, v::AbstractArray, I::NTuple{2,Int})
248
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113 i = I[dim(e.bId)]
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114 j = I[3-dim(e.bId)]
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115 N_i = size(e.grid)[dim(e.bId)]
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116 return apply_e(e.op, v[j], N_i, i, region(e.bId))
228
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117 end
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118
239
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119 function LazyTensors.apply_transpose(e::BoundaryValue, v::AbstractArray, I::NTuple{1,Int})
248
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120 u = selectdim(v,3-dim(e.bId),I[1])
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121 return apply_e_T(e.op, u, region(e.bId))
228
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122 end
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123
247
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124 """
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125 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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126
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127 Implements the boundary operator `d` as a TensorMapping
247
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128 """
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129 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
248
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130 op::D2{T,N,M,K}
255
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131 grid::EquidistantGrid{2}
248
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132 bId::CartesianBoundary
228
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133 end
247
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134 export NormalDerivative
228
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135
247
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136 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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137 # Can we give special treatment to TensorMappings that go to a higher dim?
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138 LazyTensors.range_size(e::NormalDerivative{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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139 LazyTensors.domain_size(e::NormalDerivative{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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140
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141 # TODO: Not type stable D:<
258
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142 # TODO: Make this independent of dimension
247
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143 function LazyTensors.apply(d::NormalDerivative, v::AbstractArray, I::NTuple{2,Int})
248
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144 i = I[dim(d.bId)]
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145 j = I[3-dim(d.bId)]
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146 N_i = size(d.grid)[dim(d.bId)]
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147 h_inv = d.grid.inverse_spacing[dim(d.bId)]
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148 return apply_d(d.op, h_inv, v[j], N_i, i, region(d.bId))
228
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149 end
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150
247
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151 function LazyTensors.apply_transpose(d::NormalDerivative, v::AbstractArray, I::NTuple{1,Int})
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152 u = selectdim(v,3-dim(d.bId),I[1])
248
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153 return apply_d_T(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
228
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154 end
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155
259
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156 """
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157 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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158
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159 Implements the boundary operator `q` as a TensorOperator
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160 """
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161 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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162 op::D2{T,N,M,K}
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163 grid::EquidistantGrid{2}
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164 bId::CartesianBoundary
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165 end
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166 export BoundaryQuadrature
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167
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168 # TODO: Make this independent of dimension
262
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169 # TODO: Dispatch directly on Index{R}?
259
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170 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Int}) where T
262
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171 h = q.grid.spacing[3-dim(q.bId)]
259
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172 N = size(v)
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173 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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174 end
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175
262
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176 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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177
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178
228
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179
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180
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181 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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182
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183 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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184 e = boundary_value(L, Bid())
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185 d = normal_derivative(L, Bid())
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186 Hᵧ = boundary_quadrature(L, Bid())
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187 H⁻¹ = inverse_quadrature(L)
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188 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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189 end
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190
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191 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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192 tau::Float64
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193 end
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194
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195 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
266
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196 e = boundary_value(L, Bid())
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197 d = normal_derivative(L, Bid())
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198 Hᵧ = boundary_quadrature(L, Bid())
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199 H⁻¹ = inverse_quadrature(L)
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200 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
228
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201 # Need to handle scalar multiplication and addition of TensorMapping
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202 end
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203
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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204 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
248
05e7bbe0af97 Merge refactoring of laplace
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 247 245
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205 # return apply(s.L, v, i) +
228
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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206 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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207 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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208 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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209 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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210 # end