Mercurial > repos > public > sbplib_julia

annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 668:2d56a53a1646 feature/laplace_opset

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Simplify construction of boundary-operator pairs in Laplace constructor
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 31 Jan 2021 22:19:53 +0100
parents f3a0d1f7d842
children 011863b3f24c
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
624
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
1 """
667
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
2 Laplace{T,Dim,...}()
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
3 Laplace(grid::EquidistantGrid, fn; order)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
4
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
5 Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
6 `TensorMapping`. Additionally, `Laplace` stores the quadrature, and boundary
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
7 operators relevant for constructing a SBP finite difference scheme as `TensorMapping`s.
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
8 """
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
9 struct Laplace{T, Dim, Rb, TMdiffop<:TensorMapping{T,Dim,Dim}, # Differential operator tensor mapping
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
10 TMqop<:TensorMapping{T,Dim,Dim}, # Quadrature operator tensor mapping
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
11 TMbop<:TensorMapping{T,Rb,Dim}, # Boundary operator tensor mapping
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
12 TMbqop<:TensorMapping{T,Rb,Rb}, # Boundary quadrature tensor mapping
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
13 BID<:BoundaryIdentifier} <: TensorMapping{T,Dim,Dim}
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
14 D::TMdiffop # Difference operator
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
15 H::TMqop # Quadrature (norm) operator
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
16 H_inv::TMqop # Inverse quadrature (norm) operator
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
17 e::Dict{BID,TMbop} # Boundary restriction operators
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
18 d::Dict{BID,TMbop} # Normal derivative operators
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
19 H_boundary::Dict{BID,TMbqop} # Boundary quadrature operators
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
20 end
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
21 export Laplace
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
22
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
23 function Laplace(grid::EquidistantGrid, fn; order)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
24 # TODO: Removed once we can construct the volume and
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
25 # boundary operators by op(grid, fn; order,...).
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
26 # Read stencils
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
27 op = read_D2_operator(fn; order)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
28 D_inner_stecil = op.innerStencil
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
29 D_closure_stencils = op.closureStencils
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
30 H_closure_stencils = op.quadratureClosure
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
31 e_closure_stencil = op.eClosure
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
32 d_closure_stencil = op.dClosure
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
33
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
34 # Volume operators
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
35 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
36 H = DiagonalQuadrature(grid, H_closure_stencils)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
37 H⁻¹ = InverseDiagonalQuadrature(grid, H_closure_stencils)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
38
668
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
39 # Pair operators with boundary ids
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
40 bids = boundary_identifiers(grid)
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
41 # Boundary operators
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
42 e_pairs = ntuple(i -> Pair(bids[i],BoundaryRestriction(grid,e_closure_stencil,bids[i])),length(bids))
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
43 d_pairs = ntuple(i -> Pair(bids[i],NormalDerivative(grid,d_closure_stencil,bids[i])),length(bids))
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
44 # Boundary quadratures are constructed on the lower-dimensional grid defined
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
45 # by the coordinite directions orthogonal to that of the boundary.
667
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
46 dims = collect(1:dimension(grid))
668
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
47 orth_grids = ntuple(i -> restrict(grid,dims[dims .!= dim(bids[i])]),length(bids))
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
48 Hᵧ_pairs = ntuple(i -> Pair(bids[i],DiagonalQuadrature(orth_grids[i],H_closure_stencils)),length(bids))
2d56a53a1646 Simplify construction of boundary-operator pairs in Laplace constructor
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 667
diff changeset
49
667
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
50 return Laplace(Δ, H, H⁻¹, Dict(e_pairs), Dict(d_pairs), Dict(Hᵧ_pairs))
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
51 end
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
52
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
53 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
54 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
55 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
56
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
57 quadrature(L::Laplace) = L.H
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
58 export quadrature
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
59 inverse_quadrature(L::Laplace) = L.H_inv
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
60 export inverse_quadrature
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
61 boundary_restriction(L::Laplace,bid::BoundaryIdentifier) = L.e[bid]
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
62 export boundary_restriction
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
63 normal_derivative(L::Laplace,bid::BoundaryIdentifier) = L.d[bid]
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
64 export normal_derivative
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
65 boundary_quadrature(L::Laplace,bid::BoundaryIdentifier) = L.H_boundary[bid]
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
66 export boundary_quadrature
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
67
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
68 """
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
69 laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
624
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
70
648
d6edde60909b Fix typo in documentation and remove obsolete out-commented code.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 624
diff changeset
71 Creates the Laplace operator operator `Δ` as a `TensorMapping`
624
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
72
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
73 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
74 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
75 for the points in the closure regions.
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
76
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
77 On a one-dimensional `grid`, `Δ` is a `SecondDerivative`. On a multi-dimensional `grid`, `Δ` is the sum of
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
78 multi-dimensional `SecondDerivative`s where the sum is carried out lazily.
a85db383484f Update documentation and remove some out-commented lines
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 618
diff changeset
79 """
667
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
80 function laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
616
d9324671b412 Use julian naming conventions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 611
diff changeset
81 Δ = SecondDerivative(grid, inner_stencil, closure_stencils, 1)
611
e71f2f81b5f8 NOT WORKING: Draft implementation of VolumeOperator and make SecondDerivative specialize it. Reformulate Laplace for the new SecondDerivative.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 542
diff changeset
82 for d = 2:Dim
616
d9324671b412 Use julian naming conventions
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 611
diff changeset
83 Δ += SecondDerivative(grid, inner_stencil, closure_stencils, d)
356
0844069ab5ff Reinclude SbpOperators and fix most of the code and tests there.
Jonatan Werpers <jonatan@werpers.com>
parents: 333
diff changeset
84 end
611
e71f2f81b5f8 NOT WORKING: Draft implementation of VolumeOperator and make SecondDerivative specialize it. Reformulate Laplace for the new SecondDerivative.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 542
diff changeset
85 return Δ
356
0844069ab5ff Reinclude SbpOperators and fix most of the code and tests there.
Jonatan Werpers <jonatan@werpers.com>
parents: 333
diff changeset
86 end
667
f3a0d1f7d842 Make Laplace a type storing relevant operators used when writing a scheme, e.g. quadratures, normal derivatives etc.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 648
diff changeset
87 export laplace