Mercurial > repos > public > sbplib_julia

comparison SbpOperators/src/laplace/laplace.jl @ 293:f63232aeb1c6

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Move laplace.jl from DiffOps to SbpOperators. Rename constandlaplace to secondderivative
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 22 Jun 2020 22:08:56 +0200
parents DiffOps/src/laplace.jl@7247e85dc1e8
children b00eea62c78e
comparison
equal deleted inserted replaced
292:3747e5636eef 293:f63232aeb1c6
1 """
2 Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
3
4 Implements the Laplace operator `L` in Dim dimensions as a tensor operator
5 The multi-dimensional tensor operator simply consists of a tuple of the 1D
6 Laplace tensor operator as defined by ConstantLaplaceOperator.
7 """
8 struct Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
9 D2::NTuple(Dim,SecondDerivative{T,N,M,K})
10 #TODO: Write a good constructor
11 end
12 export Laplace
13
14 LazyTensors.domain_size(H::Laplace{Dim}, range_size::NTuple{Dim,Integer}) = range_size
15
16 function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
17 error("not implemented")
18 end
19
20 # u = L*v
21 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
22 return apply(L.D2[1],v,I)
23 end
24
25
26 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
27 # 2nd x-derivative
28 @inbounds vx = view(v, :, Int(I[2]))
29 @inbounds uᵢ = apply(L.D2[1], vx , (I[1],)) #Tuple conversion here is ugly. How to do it? Should we use indexing here?
30
31 # 2nd y-derivative
32 @inbounds vy = view(v, Int(I[1]), :)
33 @inbounds uᵢ += apply(L.D2[2], vy , (I[2],)) #Tuple conversion here is ugly. How to do it?
34
35 return uᵢ
36 end
37
38 quadrature(L::Laplace) = Quadrature(L.op, L.grid)
39 inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
40 boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
41 normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
42 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
43 export quadrature
44
45 # At the moment the grid property is used all over. It could possibly be removed if we implement all the 1D operators as TensorMappings
46 """
47 Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
48
49 Implements the quadrature operator `H` of Dim dimension as a TensorMapping
50 """
51 struct Quadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
52 op::D2{T,N,M,K}
53 grid::EquidistantGrid{Dim,T}
54 end
55 export Quadrature
56
57 LazyTensors.domain_size(H::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
58
59 @inline function LazyTensors.apply(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
60 N = size(H.grid)
61 # Quadrature in x direction
62 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
63 # Quadrature in y-direction
64 @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
65 return q
66 end
67
68 LazyTensors.apply_transpose(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H,v,I)
69
70
71 """
72 InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
73
74 Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
75 """
76 struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
77 op::D2{T,N,M,K}
78 grid::EquidistantGrid{Dim,T}
79 end
80 export InverseQuadrature
81
82 LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
83
84 @inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
85 N = size(H_inv.grid)
86 # Inverse quadrature in x direction
87 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[1], v[I] , I[1], N[1])
88 # Inverse quadrature in y-direction
89 @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[2], q_inv, I[2], N[2])
90 return q_inv
91 end
92
93 LazyTensors.apply_transpose(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H_inv,v,I)
94
95 """
96 BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
97
98 Implements the boundary operator `e` as a TensorMapping
99 """
100 struct BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}
101 op::D2{T,N,M,K}
102 grid::EquidistantGrid{2}
103 bId::CartesianBoundary
104 end
105 export BoundaryValue
106
107 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
108 # Can we give special treatment to TensorMappings that go to a higher dim?
109 function LazyTensors.range_size(e::BoundaryValue{T}, domain_size::NTuple{1,Integer}) where T
110 if dim(e.bId) == 1
111 return (UnknownDim, domain_size[1])
112 elseif dim(e.bId) == 2
113 return (domain_size[1], UnknownDim)
114 end
115 end
116 LazyTensors.domain_size(e::BoundaryValue{T}, range_size::NTuple{2,Integer}) where T = (range_size[3-dim(e.bId)],)
117 # TODO: Make a nicer solution for 3-dim(e.bId)
118
119 # TODO: Make this independent of dimension
120 function LazyTensors.apply(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
121 i = I[dim(e.bId)]
122 j = I[3-dim(e.bId)]
123 N_i = size(e.grid)[dim(e.bId)]
124 return apply_boundary_value(e.op, v[j], i, N_i, region(e.bId))
125 end
126
127 function LazyTensors.apply_transpose(e::BoundaryValue{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
128 u = selectdim(v,3-dim(e.bId),Int(I[1]))
129 return apply_boundary_value_transpose(e.op, u, region(e.bId))
130 end
131
132 """
133 NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
134
135 Implements the boundary operator `d` as a TensorMapping
136 """
137 struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
138 op::D2{T,N,M,K}
139 grid::EquidistantGrid{2}
140 bId::CartesianBoundary
141 end
142 export NormalDerivative
143
144 # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
145 # Can we give special treatment to TensorMappings that go to a higher dim?
146 function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
147 if dim(e.bId) == 1
148 return (UnknownDim, domain_size[1])
149 elseif dim(e.bId) == 2
150 return (domain_size[1], UnknownDim)
151 end
152 end
153 LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
154
155 # TODO: Not type stable D:<
156 # TODO: Make this independent of dimension
157 function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
158 i = I[dim(d.bId)]
159 j = I[3-dim(d.bId)]
160 N_i = size(d.grid)[dim(d.bId)]
161 h_inv = inverse_spacing(d.grid)[dim(d.bId)]
162 return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
163 end
164
165 function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
166 u = selectdim(v,3-dim(d.bId),Int(I[1]))
167 return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
168 end
169
170 """
171 BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
172
173 Implements the boundary operator `q` as a TensorOperator
174 """
175 struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
176 op::D2{T,N,M,K}
177 grid::EquidistantGrid{2}
178 bId::CartesianBoundary
179 end
180 export BoundaryQuadrature
181
182 # TODO: Make this independent of dimension
183 function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
184 h = spacing(q.grid)[3-dim(q.bId)]
185 N = size(v)
186 return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
187 end
188
189 LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T = LazyTensors.apply(q,v,I)
190
191
192
193
194 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
195
196 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
197 e = boundary_value(L, Bid())
198 d = normal_derivative(L, Bid())
199 Hᵧ = boundary_quadrature(L, Bid())
200 H⁻¹ = inverse_quadrature(L)
201 return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
202 end
203
204 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
205 tau::Float64
206 end
207
208 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
209 e = boundary_value(L, Bid())
210 d = normal_derivative(L, Bid())
211 Hᵧ = boundary_quadrature(L, Bid())
212 H⁻¹ = inverse_quadrature(L)
213 return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
214 # Need to handle scalar multiplication and addition of TensorMapping
215 end
216
217 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
218 # return apply(s.L, v, i) +
219 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
220 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
221 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
222 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
223 # end