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comparison DiffOps/src/DiffOps.jl @ 228:5acef2d5db2e boundary_conditions

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Move Laplace operator and related structs/functions to separate file.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 26 Jun 2019 14:38:01 +0200
parents b3506cfbb9d8
children cd60382f392b
comparison
equal deleted inserted replaced
225:3ab0c61f1367 228:5acef2d5db2e
1 module DiffOps 1 module DiffOps
2 2
3 using RegionIndices 3 using RegionIndices
4 using SbpOperators 4 using SbpOperators
5 using Grids 5 using Grids
6
7 export Laplace
8 6
9 abstract type DiffOp end 7 abstract type DiffOp end
10 8
11 # TBD: The "error("not implemented")" thing seems to be hiding good error information. How to fix that? Different way of saying that these should be implemented? 9 # TBD: The "error("not implemented")" thing seems to be hiding good error information. How to fix that? Different way of saying that these should be implemented?
12 function apply(D::DiffOp, v::AbstractVector, i::Int) 10 function apply(D::DiffOp, v::AbstractVector, i::Int)
89 return u 87 return u
90 end 88 end
91 89
92 export apply 90 export apply
93 91
94 struct NormalDerivative{N,M,K}
95 op::D2{Float64,N,M,K}
96 grid::EquidistantGrid
97 bId::CartesianBoundary
98 end
99
100 function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer)
101 u = selectdim(v,3-dim(d.bId),I)
102 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
103 end
104
105 # Not correct abstraction level
106 # TODO: Not type stable D:<
107 function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer})
108 i = I[dim(d.bId)]
109 j = I[3-dim(d.bId)]
110 N_i = d.grid.size[dim(d.bId)]
111
112 r = getregion(i, closureSize(d.op), N_i)
113
114 if r != region(d.bId)
115 return 0
116 end
117
118 if r == Lower
119 # Note, closures are indexed by offset. Fix this D:<
120 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
121 elseif r == Upper
122 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j]
123 end
124 end
125
126 struct BoundaryValue{N,M,K}
127 op::D2{Float64,N,M,K}
128 grid::EquidistantGrid
129 bId::CartesianBoundary
130 end
131
132 function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer})
133 i = I[dim(e.bId)]
134 j = I[3-dim(e.bId)]
135 N_i = e.grid.size[dim(e.bId)]
136
137 r = getregion(i, closureSize(e.op), N_i)
138
139 if r != region(e.bId)
140 return 0
141 end
142
143 if r == Lower
144 # Note, closures are indexed by offset. Fix this D:<
145 return e.op.eClosure[i-1]*v[j]
146 elseif r == Upper
147 return e.op.eClosure[N_i-j]*v[j]
148 end
149 end
150
151 function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer)
152 u = selectdim(v,3-dim(e.bId),I)
153 return apply_e(e.op, u, region(e.bId))
154 end
155
156 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
157 grid::EquidistantGrid{Dim,T}
158 a::T
159 op::D2{Float64,N,M,K}
160 # e::BoundaryValue
161 # d::NormalDerivative
162 end
163
164 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
165 error("not implemented")
166 end
167
168 # u = L*v
169 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
170 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
171 return uᵢ
172 end
173
174 @inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
175 # 2nd x-derivative
176 @inbounds vx = view(v, :, Int(I[2]))
177 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
178 # 2nd y-derivative
179 @inbounds vy = view(v, Int(I[1]), :)
180 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
181 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
182 return uᵢ
183 end
184
185 # Slow but maybe convenient?
186 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
187 I = Index{Unknown}.(Tuple(i))
188 apply(L, v, I)
189 end
190
191 struct BoundaryOperator
192
193 end
194
195
196 """ 92 """
197 A BoundaryCondition should implement the method 93 A BoundaryCondition should implement the method
198 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...) 94 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
199 """ 95 """
200 abstract type BoundaryCondition end 96 abstract type BoundaryCondition end
201 97
202 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
203 98
204 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid} 99 include("laplace.jl")
205 e = BoundaryValue(L.op, L.grid, Bid()) 100 export Laplace
206 d = NormalDerivative(L.op, L.grid, Bid())
207 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
208 # TODO: Implement BoundaryQuadrature method
209 101
210 return -L.Hi*e*Hᵧ*(d'*v - g)
211 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
212 end
213
214 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
215 tau::Float64
216 end
217
218 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
219 e = BoundaryValue(L.op, L.grid, Bid())
220 d = NormalDerivative(L.op, L.grid, Bid())
221 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
222 # TODO: Implement BoundaryQuadrature method
223
224 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
225 # Need to handle scalar multiplication and addition of TensorMapping
226 end
227
228 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
229 # return apply(s.L, v, i) +
230 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
231 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
232 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
233 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
234 # end
235 102
236 end # module 103 end # module