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annotate SbpOperators/src/laplace/laplace.jl @ 300:b00eea62c78e

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Create 1D tensor mapping for diagonal norm quadratures, and make the multi-dimensional quadrature use those. Move Qudrature from laplace.jl into Quadrature.jl
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 23 Jun 2020 17:32:54 +0200
parents f63232aeb1c6
children 6fa2ba769ae3
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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.
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1 """
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2 Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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3
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4 Implements the Laplace operator `L` in Dim dimensions as a tensor operator
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5 The multi-dimensional tensor operator consists of a tuple of 1D SecondDerivative
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6 tensor operators.
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7 """
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8 struct Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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9 D2::NTuple(Dim,SecondDerivative{T,N,M,K})
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10 #TODO: Write a good constructor
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11 end
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12 export Laplace
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14 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) = range_size
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16 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
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17 error("not implemented")
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18 end
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19
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20 function LazyTensors.apply_transpose(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim} = LazyTensors.apply(L, v, I)
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21
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22 # u = L*v
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23 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
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24 @inbounds u = apply(L.D2[1],v,I)
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25 return u
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26 end
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27
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29 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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30 # 2nd x-derivative
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31 @inbounds vx = view(v, :, Int(I[2]))
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32 @inbounds uᵢ = apply(L.D2[1], vx , I[1])
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33
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34 # 2nd y-derivative
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35 @inbounds vy = view(v, Int(I[1]), :)
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36 @inbounds uᵢ += apply(L.D2[2], vy , I[2])
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37
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38 return uᵢ
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39 end
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40
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41 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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42 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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43 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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44 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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45 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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46 export quadrature
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49 """
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50 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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51
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52 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
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53 """
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54 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
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55 op::D2{T,N,M,K}
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56 grid::EquidistantGrid{Dim,T}
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57 end
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58 export InverseQuadrature
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59
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60 LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
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61
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62 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
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63 N = size(H_inv.grid)
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64 # Inverse quadrature in x direction
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65 @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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66 # Inverse quadrature in y-direction
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67 @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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68 return q_inv
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69 end
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70
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71 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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72
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73 """
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74 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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75
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76 Implements the boundary operator `e` as a TensorMapping
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77 """
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78 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
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79 op::D2{T,N,M,K}
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80 grid::EquidistantGrid{2}
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81 bId::CartesianBoundary
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82 end
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83 export BoundaryValue
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84
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85 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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86 # Can we give special treatment to TensorMappings that go to a higher dim?
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87 function LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T
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88 if dim(e.bId) == 1
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89 return (UnknownDim, domain_size[1])
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90 elseif dim(e.bId) == 2
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91 return (domain_size[1], UnknownDim)
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92 end
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93 end
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94 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
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95 # TODO: Make a nicer solution for 3-dim(e.bId)
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96
258
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97 # TODO: Make this independent of dimension
281
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98 function LazyTensors.apply(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
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99 i = I[dim(e.bId)]
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100 j = I[3-dim(e.bId)]
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101 N_i = size(e.grid)[dim(e.bId)]
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102 return apply_boundary_value(e.op, v[j], i, N_i, region(e.bId))
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103 end
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104
281
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105 function LazyTensors.apply_transpose(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
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106 u = selectdim(v,3-dim(e.bId),Int(I[1]))
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107 return apply_boundary_value_transpose(e.op, u, region(e.bId))
228
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108 end
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109
247
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110 """
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111 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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112
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113 Implements the boundary operator `d` as a TensorMapping
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114 """
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115 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
248
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116 op::D2{T,N,M,K}
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117 grid::EquidistantGrid{2}
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118 bId::CartesianBoundary
228
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119 end
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120 export NormalDerivative
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121
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122 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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123 # Can we give special treatment to TensorMappings that go to a higher dim?
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124 function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
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125 if dim(e.bId) == 1
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126 return (UnknownDim, domain_size[1])
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127 elseif dim(e.bId) == 2
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128 return (domain_size[1], UnknownDim)
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129 end
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130 end
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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
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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))
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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
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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))
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146 end
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147
259
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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
281
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161 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
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162 h = spacing(q.grid)[3-dim(q.bId)]
259
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163 N = size(v)
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164 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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165 end
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166
281
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167 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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168
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169
228
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170
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171
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172 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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173
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174 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
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175 e = boundary_value(L, Bid())
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176 d = normal_derivative(L, Bid())
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177 Hᵧ = boundary_quadrature(L, Bid())
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178 H⁻¹ = inverse_quadrature(L)
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179 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
228
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180 end
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181
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182 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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183 tau::Float64
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184 end
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185
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186 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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187 e = boundary_value(L, Bid())
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188 d = normal_derivative(L, Bid())
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189 Hᵧ = boundary_quadrature(L, Bid())
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190 H⁻¹ = inverse_quadrature(L)
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191 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
228
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192 # Need to handle scalar multiplication and addition of TensorMapping
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193 end
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194
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195 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
248
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196 # return apply(s.L, v, i) +
228
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197 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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198 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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199 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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200 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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201 # end