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annotate DiffOps/src/laplace.jl @ 285:e21dcda55163 boundary_conditions

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Add type representing an unknown dimension in the domain of tensormappings
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 19 Jun 2020 12:20:31 +0200
parents 0b8e041a1873
children 7247e85dc1e8
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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} # TODO: Should this be here? Should probably be possible to applay a Laplace object to any size grid function
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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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7
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8 # 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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9
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10 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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11
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12 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
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13 error("not implemented")
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14 end
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16 # u = L*v
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17 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
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18 uᵢ = L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[1], v, I[1])
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19 return uᵢ
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20 end
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21
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23 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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24 # 2nd x-derivative
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25 @inbounds vx = view(v, :, Int(I[2]))
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26 @inbounds uᵢ = L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[1], vx , I[1])
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27 # 2nd y-derivative
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28 @inbounds vy = view(v, Int(I[1]), :)
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29 @inbounds uᵢ += L.a*apply_2nd_derivative(L.op, inverse_spacing(L.grid)[2], vy, I[2])
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30 return uᵢ
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31 end
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32
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33 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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34 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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35 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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36 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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37 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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38 export quadrature
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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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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} <: TensorOperator{T,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.domain_size(H::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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52
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53 @inline function LazyTensors.apply(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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54 N = size(H.grid)
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55 # Quadrature in x direction
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56 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
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57 # Quadrature in y-direction
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58 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
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59 return q
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60 end
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61
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62 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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63
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64
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65 """
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66 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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67
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68 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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69 """
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70 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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71 op::D2{T,N,M,K}
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72 grid::EquidistantGrid{Dim,T}
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73 end
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74 export InverseQuadrature
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75
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76 LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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77
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78 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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79 N = size(H_inv.grid)
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80 # Inverse quadrature in x direction
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81 @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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82 # Inverse quadrature in y-direction
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83 @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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84 return q_inv
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85 end
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86
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87 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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88
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89 """
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90 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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91
258
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92 Implements the boundary operator `e` as a TensorMapping
235
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93 """
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94 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
248
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95 op::D2{T,N,M,K}
255
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96 grid::EquidistantGrid{2}
248
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97 bId::CartesianBoundary
228
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98 end
235
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99 export BoundaryValue
228
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100
235
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101 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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102 # Can we give special treatment to TensorMappings that go to a higher dim?
284
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103 function LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T
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104 if dim(e.bId) == 1
285
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105 return (UnknownDim, domain_size[1])
284
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106 elseif dim(e.bId) == 2
285
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107 return (domain_size[1], UnknownDim)
284
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108 end
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109 end
244
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110 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
284
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111 # TODO: Make a nicer solution for 3-dim(e.bId)
235
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112
258
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113 # TODO: Make this independent of dimension
281
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114 function LazyTensors.apply(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
248
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115 i = I[dim(e.bId)]
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116 j = I[3-dim(e.bId)]
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117 N_i = size(e.grid)[dim(e.bId)]
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118 return apply_boundary_value(e.op, v[j], i, N_i, region(e.bId))
228
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119 end
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120
281
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121 function LazyTensors.apply_transpose(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
280
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122 u = selectdim(v,3-dim(e.bId),Int(I[1]))
269
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123 return apply_boundary_value_transpose(e.op, u, region(e.bId))
228
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124 end
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125
247
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126 """
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127 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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128
258
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129 Implements the boundary operator `d` as a TensorMapping
247
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130 """
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131 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
248
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132 op::D2{T,N,M,K}
255
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133 grid::EquidistantGrid{2}
248
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134 bId::CartesianBoundary
228
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135 end
247
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136 export NormalDerivative
228
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137
247
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138 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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139 # Can we give special treatment to TensorMappings that go to a higher dim?
284
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140 function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
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141 if dim(e.bId) == 1
285
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142 return (UnknownDim, domain_size[1])
284
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143 elseif dim(e.bId) == 2
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144 return (domain_size[1], UnknownDim)
284
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145 end
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146 end
281
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147 LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
247
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148
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149 # TODO: Not type stable D:<
258
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150 # TODO: Make this independent of dimension
281
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151 function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
248
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152 i = I[dim(d.bId)]
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153 j = I[3-dim(d.bId)]
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154 N_i = size(d.grid)[dim(d.bId)]
268
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155 h_inv = inverse_spacing(d.grid)[dim(d.bId)]
280
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156 return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
228
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157 end
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158
281
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159 function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
280
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160 u = selectdim(v,3-dim(d.bId),Int(I[1]))
269
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161 return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
228
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162 end
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163
259
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164 """
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165 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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166
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167 Implements the boundary operator `q` as a TensorOperator
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168 """
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169 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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170 op::D2{T,N,M,K}
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171 grid::EquidistantGrid{2}
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172 bId::CartesianBoundary
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173 end
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174 export BoundaryQuadrature
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175
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176 # TODO: Make this independent of dimension
281
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177 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
268
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178 h = spacing(q.grid)[3-dim(q.bId)]
259
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179 N = size(v)
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180 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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181 end
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182
281
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183 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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184
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185
228
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186
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187
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188 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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189
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190 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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191 e = boundary_value(L, Bid())
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192 d = normal_derivative(L, Bid())
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193 Hᵧ = boundary_quadrature(L, Bid())
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194 H⁻¹ = inverse_quadrature(L)
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195 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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196 end
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197
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198 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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199 tau::Float64
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200 end
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201
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202 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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203 e = boundary_value(L, Bid())
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204 d = normal_derivative(L, Bid())
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205 Hᵧ = boundary_quadrature(L, Bid())
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206 H⁻¹ = inverse_quadrature(L)
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diff changeset
207 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
228
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208 # Need to handle scalar multiplication and addition of TensorMapping
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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209 end
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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210
5acef2d5db2e Move Laplace operator and related structs/functions to separate file.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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211 # 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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212 # 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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213 # 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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214 # 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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215 # 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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216 # 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>
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217 # end