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comparison DiffOps/src/DiffOps.jl @ 225:3ab0c61f1367 boundary_conditions

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Merge in package_refactor
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2019 14:02:28 +0200
parents b3506cfbb9d8
children eb8525066f9b 5acef2d5db2e
comparison
equal deleted inserted replaced
210:2aa33d0eef90 225:3ab0c61f1367
1 module DiffOps
2
3 using RegionIndices
4 using SbpOperators
5 using Grids
6
7 export Laplace
8
9 abstract type DiffOp end
10
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?
12 function apply(D::DiffOp, v::AbstractVector, i::Int)
13 error("not implemented")
14 end
15
16 function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real
17 error("not implemented")
18 end
19
20 function matrixRepresentation(D::DiffOp)
21 error("not implemented")
22 end
23
24 abstract type DiffOpCartesian{Dim} <: DiffOp end
25
26 # DiffOp must have a grid of dimension Dim!!!
27 function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim}
28 for I ∈ eachindex(D.grid)
29 u[I] = apply(D, v, I)
30 end
31
32 return nothing
33 end
34 export apply!
35
36 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
37 apply_region!(D, u, v, Lower, Lower)
38 apply_region!(D, u, v, Lower, Interior)
39 apply_region!(D, u, v, Lower, Upper)
40 apply_region!(D, u, v, Interior, Lower)
41 apply_region!(D, u, v, Interior, Interior)
42 apply_region!(D, u, v, Interior, Upper)
43 apply_region!(D, u, v, Upper, Lower)
44 apply_region!(D, u, v, Upper, Interior)
45 apply_region!(D, u, v, Upper, Upper)
46 return nothing
47 end
48
49 # Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable
50 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
51 for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2))
52 @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2]))
53 @inbounds u[I] = apply(D, v, indextuple)
54 end
55 return nothing
56 end
57 export apply_region!
58
59 function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
60 apply_region_tiled!(D, u, v, Lower, Lower)
61 apply_region_tiled!(D, u, v, Lower, Interior)
62 apply_region_tiled!(D, u, v, Lower, Upper)
63 apply_region_tiled!(D, u, v, Interior, Lower)
64 apply_region_tiled!(D, u, v, Interior, Interior)
65 apply_region_tiled!(D, u, v, Interior, Upper)
66 apply_region_tiled!(D, u, v, Upper, Lower)
67 apply_region_tiled!(D, u, v, Upper, Interior)
68 apply_region_tiled!(D, u, v, Upper, Upper)
69 return nothing
70 end
71
72 using TiledIteration
73 function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
74 ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2))
75 # TODO: Pass Tilesize to function
76 for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2))
77 for j ∈ tileaxs[2], i ∈ tileaxs[1]
78 I = ri[i,j]
79 u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2])))
80 end
81 end
82 return nothing
83 end
84 export apply_region_tiled!
85
86 function apply(D::DiffOp, v::AbstractVector)::AbstractVector
87 u = zeros(eltype(v), size(v))
88 apply!(D,v,u)
89 return u
90 end
91
92 export apply
93
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 """
197 A BoundaryCondition should implement the method
198 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
199 """
200 abstract type BoundaryCondition end
201
202 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
203
204 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
205 e = BoundaryValue(L.op, L.grid, Bid())
206 d = NormalDerivative(L.op, L.grid, Bid())
207 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
208 # TODO: Implement BoundaryQuadrature method
209
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
236 end # module