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annotate DiffOps/src/DiffOps.jl @ 227:eb8525066f9b boundary_conditions

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Express the DiffOp interface in a better way
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2019 14:40:51 +0200
parents b3506cfbb9d8
children cd60382f392b
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1 module DiffOps
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2
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3 using RegionIndices
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4 using SbpOperators
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5 using Grids
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6
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7 export Laplace
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8
227
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9 """
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10 DiffOp
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11
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12 Supertype of differential operator discretisations.
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13 The action of the DiffOp is defined in the method
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14 apply(D::DiffOp, v::AbstractVector, I...)
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15 """
2
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16 abstract type DiffOp end
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17
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18 function apply end
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19
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20 function matrixRepresentation(D::DiffOp)
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21 error("not implemented")
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22 end
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23
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24 abstract type DiffOpCartesian{Dim} <: DiffOp end
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25
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26 # DiffOp must have a grid of dimension Dim!!!
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27 function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim}
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28 for I ∈ eachindex(D.grid)
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29 u[I] = apply(D, v, I)
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30 end
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31
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32 return nothing
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33 end
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34 export apply!
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35
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36 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
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37 apply_region!(D, u, v, Lower, Lower)
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38 apply_region!(D, u, v, Lower, Interior)
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39 apply_region!(D, u, v, Lower, Upper)
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40 apply_region!(D, u, v, Interior, Lower)
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41 apply_region!(D, u, v, Interior, Interior)
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42 apply_region!(D, u, v, Interior, Upper)
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43 apply_region!(D, u, v, Upper, Lower)
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44 apply_region!(D, u, v, Upper, Interior)
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45 apply_region!(D, u, v, Upper, Upper)
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46 return nothing
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47 end
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48
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49 # Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable
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50 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
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51 for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2))
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52 @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2]))
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53 @inbounds u[I] = apply(D, v, indextuple)
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54 end
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55 return nothing
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56 end
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57 export apply_region!
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58
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59 function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
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60 apply_region_tiled!(D, u, v, Lower, Lower)
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61 apply_region_tiled!(D, u, v, Lower, Interior)
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62 apply_region_tiled!(D, u, v, Lower, Upper)
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63 apply_region_tiled!(D, u, v, Interior, Lower)
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64 apply_region_tiled!(D, u, v, Interior, Interior)
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65 apply_region_tiled!(D, u, v, Interior, Upper)
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66 apply_region_tiled!(D, u, v, Upper, Lower)
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67 apply_region_tiled!(D, u, v, Upper, Interior)
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68 apply_region_tiled!(D, u, v, Upper, Upper)
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69 return nothing
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70 end
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71
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72 using TiledIteration
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73 function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
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74 ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2))
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75 # TODO: Pass Tilesize to function
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76 for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2))
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77 for j ∈ tileaxs[2], i ∈ tileaxs[1]
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78 I = ri[i,j]
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79 u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2])))
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80 end
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81 end
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82 return nothing
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83 end
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84 export apply_region_tiled!
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85
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86 function apply(D::DiffOp, v::AbstractVector)::AbstractVector
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87 u = zeros(eltype(v), size(v))
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88 apply!(D,v,u)
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89 return u
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90 end
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91
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92 export apply
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93
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94 struct NormalDerivative{N,M,K}
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95 op::D2{Float64,N,M,K}
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96 grid::EquidistantGrid
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97 bId::CartesianBoundary
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98 end
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99
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100 function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer)
172
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101 u = selectdim(v,3-dim(d.bId),I)
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102 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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103 end
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104
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105 # Not correct abstraction level
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106 # TODO: Not type stable D:<
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107 function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer})
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108 i = I[dim(d.bId)]
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109 j = I[3-dim(d.bId)]
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110 N_i = d.grid.size[dim(d.bId)]
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111
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112 r = getregion(i, closureSize(d.op), N_i)
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113
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114 if r != region(d.bId)
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115 return 0
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116 end
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117
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118 if r == Lower
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119 # Note, closures are indexed by offset. Fix this D:<
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120 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
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121 elseif r == Upper
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122 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j]
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123 end
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124 end
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125
173
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126 struct BoundaryValue{N,M,K}
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127 op::D2{Float64,N,M,K}
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128 grid::EquidistantGrid
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129 bId::CartesianBoundary
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130 end
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131
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132 function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer})
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133 i = I[dim(e.bId)]
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134 j = I[3-dim(e.bId)]
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135 N_i = e.grid.size[dim(e.bId)]
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136
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137 r = getregion(i, closureSize(e.op), N_i)
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138
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139 if r != region(e.bId)
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140 return 0
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141 end
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142
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143 if r == Lower
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144 # Note, closures are indexed by offset. Fix this D:<
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145 return e.op.eClosure[i-1]*v[j]
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146 elseif r == Upper
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147 return e.op.eClosure[N_i-j]*v[j]
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148 end
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149 end
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150
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151 function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer)
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152 u = selectdim(v,3-dim(e.bId),I)
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153 return apply_e(e.op, u, region(e.bId))
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154 end
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155
95
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156 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
168
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157 grid::EquidistantGrid{Dim,T}
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158 a::T
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159 op::D2{Float64,N,M,K}
223
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160 # e::BoundaryValue
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161 # d::NormalDerivative
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162 end
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163
95
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164 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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165 error("not implemented")
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166 end
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167
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168 # u = L*v
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169 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
223
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170 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
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171 return uᵢ
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172 end
49
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173
129
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174 @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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175 # 2nd x-derivative
118
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176 @inbounds vx = view(v, :, Int(I[2]))
223
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177 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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178 # 2nd y-derivative
118
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179 @inbounds vy = view(v, Int(I[1]), :)
223
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180 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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181 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
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182 return uᵢ
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183 end
99
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184
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185 # Slow but maybe convenient?
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186 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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187 I = Index{Unknown}.(Tuple(i))
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188 apply(L, v, I)
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189 end
135
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190
154
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191 struct BoundaryOperator
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192
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193 end
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194
168
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195
135
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196 """
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197 A BoundaryCondition should implement the method
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198 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
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199 """
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200 abstract type BoundaryCondition end
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201
174
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202 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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203
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204 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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205 e = BoundaryValue(L.op, L.grid, Bid())
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206 d = NormalDerivative(L.op, L.grid, Bid())
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207 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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208 # TODO: Implement BoundaryQuadrature method
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209
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210 return -L.Hi*e*Hᵧ*(d'*v - g)
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211 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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212 end
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213
145
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214 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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215 tau::Float64
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216 end
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217
174
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218 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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219 e = BoundaryValue(L.op, L.grid, Bid())
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220 d = NormalDerivative(L.op, L.grid, Bid())
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221 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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222 # TODO: Implement BoundaryQuadrature method
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223
174
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224 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
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225 # Need to handle scalar multiplication and addition of TensorMapping
135
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226 end
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227
168
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228 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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229 # return apply(s.L, v, i) +
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230 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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231 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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232 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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233 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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234 # end
215
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235
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236 end # module