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annotate DiffOps/src/laplace.jl @ 286:7247e85dc1e8 tensor_mappings

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Start separating ConstantStencilOp into multiple 1D tensor mappings, e.g. ConstantLaplaceOp. Sketch an implementation of the multi-D laplace tensor operator as a tuple of 1D laplace tensor operators.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 22 Jun 2020 19:47:20 +0200
parents e21dcda55163
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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7247e85dc1e8 Start separating ConstantStencilOp into multiple 1D tensor mappings, e.g. ConstantLaplaceOp. Sketch an implementation of the multi-D laplace tensor operator as a tuple of 1D laplace tensor operators.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 285
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1 #TODO: move to sbpoperators.jl
7247e85dc1e8 Start separating ConstantStencilOp into multiple 1D tensor mappings, e.g. ConstantLaplaceOp. Sketch an implementation of the multi-D laplace tensor operator as a tuple of 1D laplace tensor operators.
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2 """
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3 Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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4
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5 Implements the Laplace operator `L` in Dim dimensions as a tensor operator
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6 The multi-dimensional tensor operator simply consists of a tuple of the 1D
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7 Laplace tensor operator as defined by ConstantLaplaceOperator.
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8 """
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9 struct Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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10 tensorOps::NTuple(Dim,ConstantLaplaceOperator{T,N,M,K})
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11 #TODO: Write a good constructor
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12 end
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13 export Laplace
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15 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) = range_size
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16
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17 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
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18 error("not implemented")
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19 end
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20
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21 # u = L*v
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22 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
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23 return apply(L.tensorOps[1],v,I)
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24 end
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25
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26
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27 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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28 # 2nd x-derivative
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29 @inbounds vx = view(v, :, Int(I[2]))
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30 @inbounds uᵢ = apply(L.tensorOps[1], vx , (I[1],)) #Tuple conversion here is ugly. How to do it? Should we use indexing here?
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31
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32 # 2nd y-derivative
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33 @inbounds vy = view(v, Int(I[1]), :)
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34 @inbounds uᵢ += apply(L.tensorOps[2], vy , (I[2],)) #Tuple conversion here is ugly. How to do it?
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35
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36 return uᵢ
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37 end
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38
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39 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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40 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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41 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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42 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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43 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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44 export quadrature
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45
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46 # At the moment the grid property is used all over. It could possibly be removed if we implement all the 1D operators as TensorMappings
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47 """
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48 Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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49
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50 Implements the quadrature operator `H` of Dim dimension as a TensorMapping
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51 """
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52 struct Quadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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53 op::D2{T,N,M,K}
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54 grid::EquidistantGrid{Dim,T}
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55 end
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56 export Quadrature
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57
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58 LazyTensors.domain_size(H::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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59
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60 @inline function LazyTensors.apply(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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61 N = size(H.grid)
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62 # Quadrature in x direction
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63 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
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64 # Quadrature in y-direction
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65 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
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66 return q
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67 end
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68
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69 LazyTensors.apply_transpose(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H,v,I)
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babc4288e6a6 Dispatch apply(Quadrature) etc on region indices and create utility wrapper function dispatching on standard ints
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70
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71
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72 """
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73 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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74
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75 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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76 """
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77 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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78 op::D2{T,N,M,K}
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79 grid::EquidistantGrid{Dim,T}
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80 end
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81 export InverseQuadrature
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82
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83 LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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84
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85 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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86 N = size(H_inv.grid)
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87 # Inverse quadrature in x direction
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88 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[1], v[I] , I[1], N[1])
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89 # Inverse quadrature in y-direction
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90 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[2], q_inv, I[2], N[2])
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91 return q_inv
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92 end
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93
281
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94 LazyTensors.apply_transpose(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H_inv,v,I)
235
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95
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96 """
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97 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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98
258
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99 Implements the boundary operator `e` as a TensorMapping
235
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100 """
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101 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
248
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102 op::D2{T,N,M,K}
255
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103 grid::EquidistantGrid{2}
248
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104 bId::CartesianBoundary
228
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105 end
235
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106 export BoundaryValue
228
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107
235
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108 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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109 # Can we give special treatment to TensorMappings that go to a higher dim?
284
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110 function LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T
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111 if dim(e.bId) == 1
285
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112 return (UnknownDim, domain_size[1])
284
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113 elseif dim(e.bId) == 2
285
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114 return (domain_size[1], UnknownDim)
284
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115 end
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116 end
244
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117 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
284
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118 # TODO: Make a nicer solution for 3-dim(e.bId)
235
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119
258
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120 # TODO: Make this independent of dimension
281
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121 function LazyTensors.apply(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
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], i, N_i, region(e.bId))
228
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126 end
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127
281
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128 function LazyTensors.apply_transpose(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
280
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129 u = selectdim(v,3-dim(e.bId),Int(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
258
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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?
284
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147 function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
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148 if dim(e.bId) == 1
285
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149 return (UnknownDim, domain_size[1])
284
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150 elseif dim(e.bId) == 2
285
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151 return (domain_size[1], UnknownDim)
284
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152 end
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153 end
281
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154 LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
247
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155
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156 # TODO: Not type stable D:<
258
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157 # TODO: Make this independent of dimension
281
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158 function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
248
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159 i = I[dim(d.bId)]
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160 j = I[3-dim(d.bId)]
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161 N_i = size(d.grid)[dim(d.bId)]
268
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162 h_inv = inverse_spacing(d.grid)[dim(d.bId)]
280
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163 return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
228
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164 end
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165
281
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166 function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
280
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167 u = selectdim(v,3-dim(d.bId),Int(I[1]))
269
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168 return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
228
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169 end
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170
259
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171 """
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172 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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173
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174 Implements the boundary operator `q` as a TensorOperator
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175 """
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176 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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177 op::D2{T,N,M,K}
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178 grid::EquidistantGrid{2}
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179 bId::CartesianBoundary
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180 end
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181 export BoundaryQuadrature
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182
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183 # TODO: Make this independent of dimension
281
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184 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
268
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185 h = spacing(q.grid)[3-dim(q.bId)]
259
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186 N = size(v)
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187 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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188 end
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189
281
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190 LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T = LazyTensors.apply(q,v,I)
259
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191
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192
228
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193
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194
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195 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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196
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197 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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198 e = boundary_value(L, Bid())
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199 d = normal_derivative(L, Bid())
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200 Hᵧ = boundary_quadrature(L, Bid())
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201 H⁻¹ = inverse_quadrature(L)
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202 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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203 end
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204
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205 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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206 tau::Float64
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207 end
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208
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209 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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210 e = boundary_value(L, Bid())
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211 d = normal_derivative(L, Bid())
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212 Hᵧ = boundary_quadrature(L, Bid())
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213 H⁻¹ = inverse_quadrature(L)
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214 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
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215 # Need to handle scalar multiplication and addition of TensorMapping
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216 end
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217
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218 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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219 # return apply(s.L, v, i) +
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220 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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221 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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222 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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223 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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224 # end