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annotate DiffOps/src/laplace.jl @ 282:ce6a2f3f732a boundary_conditions

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Make Laplace a TensorOperator and add tests. NOTE: Two of the tests for Laplace2D are currently failing.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 09 Jan 2020 10:54:24 +0100
parents 1eefaefdd0c7
children 12a12a5cd973
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282
ce6a2f3f732a Make Laplace a TensorOperator and add tests. NOTE: Two of the tests for Laplace2D are currently failing.
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1 struct Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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2 grid::EquidistantGrid{Dim,T}
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3 a::T # TODO: Better name?
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4 op::D2{T,N,M,K}
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5 end
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6 export Laplace
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8 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) where Dim = size(L.grid)
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9
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10 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
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11 error("not implemented")
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12 end
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13
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14 # u = L*v
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15 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
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16 uᵢ = L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[1], v, I[1])
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17 return uᵢ
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18 end
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21 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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22 # 2nd x-derivative
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23 @inbounds vx = view(v, :, Int(I[2]))
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24 @inbounds uᵢ = L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[1], vx , I[1])
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25 # 2nd y-derivative
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26 @inbounds vy = view(v, Int(I[1]), :)
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27 @inbounds uᵢ += L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[2], vy, I[2])
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28 return uᵢ
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29 end
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31 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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32 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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33 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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34 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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35 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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37 """
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38 Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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40 Implements the quadrature operator `H` of Dim dimension as a TensorMapping
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41 """
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42 struct Quadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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43 op::D2{T,N,M,K}
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44 grid::EquidistantGrid{Dim,T}
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45 end
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46 export Quadrature
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47
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48 LazyTensors.domain_size(H::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = size(H.grid)
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49
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50 @inline function LazyTensors.apply(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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51 N = size(H.grid)
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52 # Quadrature in x direction
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53 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
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54 # Quadrature in y-direction
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55 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
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56 return q
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57 end
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58
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59 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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61
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62 """
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63 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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64
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65 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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66 """
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67 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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68 op::D2{T,N,M,K}
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69 grid::EquidistantGrid{Dim,T}
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70 end
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71 export InverseQuadrature
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72
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73 LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = size(H_inv.grid)
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74
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75 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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76 N = size(H_inv.grid)
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77 # Inverse quadrature in x direction
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78 @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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79 # Inverse quadrature in y-direction
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80 @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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81 return q_inv
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82 end
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83
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84 LazyTensors.apply_transpose(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H_inv,v,I)
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85
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86 """
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87 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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88
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89 Implements the boundary operator `e` as a TensorMapping
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90 """
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91 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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92 op::D2{T,N,M,K}
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93 grid::EquidistantGrid{2}
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94 bId::CartesianBoundary
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95 end
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96 export BoundaryValue
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97
235
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98 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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99 # Can we give special treatment to TensorMappings that go to a higher dim?
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100 LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T = size(e.grid)
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101 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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102
258
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103 # TODO: Make this independent of dimension
281
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104 function LazyTensors.apply(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
248
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105 i = I[dim(e.bId)]
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106 j = I[3-dim(e.bId)]
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107 N_i = size(e.grid)[dim(e.bId)]
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108 return apply_boundary_value(e.op, v[j], i, N_i, region(e.bId))
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109 end
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110
281
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111 function LazyTensors.apply_transpose(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
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112 u = selectdim(v,3-dim(e.bId),Int(I[1]))
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113 return apply_boundary_value_transpose(e.op, u, region(e.bId))
228
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114 end
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115
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116 """
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117 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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118
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119 Implements the boundary operator `d` as a TensorMapping
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120 """
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121 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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122 op::D2{T,N,M,K}
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123 grid::EquidistantGrid{2}
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124 bId::CartesianBoundary
228
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125 end
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126 export NormalDerivative
228
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127
247
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128 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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129 # Can we give special treatment to TensorMappings that go to a higher dim?
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130 LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer}) = size(e.grid)
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131 LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
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132
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133 # TODO: Not type stable D:<
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134 # TODO: Make this independent of dimension
281
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135 function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
248
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136 i = I[dim(d.bId)]
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137 j = I[3-dim(d.bId)]
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138 N_i = size(d.grid)[dim(d.bId)]
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139 h_inv = inverse_spacing(d.grid)[dim(d.bId)]
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140 return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
228
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141 end
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142
281
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143 function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
280
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144 u = selectdim(v,3-dim(d.bId),Int(I[1]))
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145 return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
228
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146 end
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147
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148 """
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149 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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150
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151 Implements the boundary operator `q` as a TensorOperator
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152 """
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153 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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154 op::D2{T,N,M,K}
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155 grid::EquidistantGrid{2}
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156 bId::CartesianBoundary
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157 end
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158 export BoundaryQuadrature
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159
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160 # TODO: Make this independent of dimension
262
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161 # TODO: Dispatch directly on Index{R}?
281
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162 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
268
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163 h = spacing(q.grid)[3-dim(q.bId)]
259
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164 N = size(v)
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165 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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166 end
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167
281
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168 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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169
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170
228
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171
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172
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173 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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174
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175 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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176 e = boundary_value(L, Bid())
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177 d = normal_derivative(L, Bid())
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178 Hᵧ = boundary_quadrature(L, Bid())
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179 H⁻¹ = inverse_quadrature(L)
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180 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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181 end
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182
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183 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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184 tau::Float64
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185 end
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186
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187 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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188 e = boundary_value(L, Bid())
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189 d = normal_derivative(L, Bid())
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190 Hᵧ = boundary_quadrature(L, Bid())
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191 H⁻¹ = inverse_quadrature(L)
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192 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
228
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193 # Need to handle scalar multiplication and addition of TensorMapping
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194 end
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195
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196 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
248
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197 # return apply(s.L, v, i) +
228
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198 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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199 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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200 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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201 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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202 # end