Mercurial > repos > public > sbplib_julia
changeset 865:545a6c1a0a0e feature/laplace_opset
Merge default again
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Fri, 02 Jul 2021 14:23:33 +0200 |
| parents | 4d40d31c35f2 (diff) 80d88bb1c5bd (current diff) |
| children | 1784b1c0af3e 9929c99754fb |
| files | |
| diffstat | 5 files changed, 286 insertions(+), 12 deletions(-) [+] |
line wrap: on
line diff
diff -r 80d88bb1c5bd -r 545a6c1a0a0e Notes.md --- a/Notes.md Fri Jul 02 13:46:39 2021 +0200 +++ b/Notes.md Fri Jul 02 14:23:33 2021 +0200 @@ -130,6 +130,7 @@ - [ ] How do we handle mixes of periodic and non-periodic grids? Seems it should be supported on the grid level and on the 1d operator level. Between there it should be transparent. - [ ] Can we have a trait to tell if a TensorMapping is transposable? - [ ] Is it ok to have "Constructors" for abstract types which create subtypes? For example a Grids() functions that gives different kind of grids based on input? + - [ ] Figure out how to treat the borrowing parameters of operators. Include in into the struct? Expose via function dispatched on the operator type and grid? ## Regions and tensormappings - [ ] Use a trait to indicate if a TensorMapping uses indices with regions.
diff -r 80d88bb1c5bd -r 545a6c1a0a0e src/Grids/AbstractGrid.jl --- a/src/Grids/AbstractGrid.jl Fri Jul 02 13:46:39 2021 +0200 +++ b/src/Grids/AbstractGrid.jl Fri Jul 02 14:23:33 2021 +0200 @@ -7,7 +7,7 @@ """ abstract type AbstractGrid end - +export AbstractGrid function dimension end function points end export dimension, points
diff -r 80d88bb1c5bd -r 545a6c1a0a0e src/SbpOperators/SbpOperators.jl --- a/src/SbpOperators/SbpOperators.jl Fri Jul 02 13:46:39 2021 +0200 +++ b/src/SbpOperators/SbpOperators.jl Fri Jul 02 14:23:33 2021 +0200 @@ -3,6 +3,7 @@ using Sbplib.RegionIndices using Sbplib.LazyTensors using Sbplib.Grids +using Sbplib.StaticDicts include("stencil.jl") include("d2.jl")
diff -r 80d88bb1c5bd -r 545a6c1a0a0e src/SbpOperators/volumeops/laplace/laplace.jl --- a/src/SbpOperators/volumeops/laplace/laplace.jl Fri Jul 02 13:46:39 2021 +0200 +++ b/src/SbpOperators/volumeops/laplace/laplace.jl Fri Jul 02 14:23:33 2021 +0200 @@ -1,19 +1,146 @@ """ - laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) + Laplace{T, Dim, TMdiffop} <: TensorMapping{T,Dim,Dim} + Laplace(grid::AbstractGrid, fn; order) + +Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a +`TensorMapping`. Additionally, `Laplace` stores the inner product and boundary +operators relevant for constructing a SBP finite difference scheme as `TensorMapping`s. + +Laplace(grid, fn; order) creates the Laplace operator defined on `grid`, +where the operators are read from TOML. The differential operator is created +using `laplace(grid::AbstractGrid,...)`. + +Note that all properties of Laplace, excluding the Differential operator `D`, are +abstract types. For performance reasons, they should therefore be +accessed via the provided getter functions (e.g `inner_product(::Laplace)`). + +""" +struct Laplace{T, Dim, TMdiffop<:TensorMapping{T,Dim,Dim}} <: TensorMapping{T,Dim,Dim} + D::TMdiffop # Differential operator + H::TensorMapping # Inner product operator + H_inv::TensorMapping # Inverse inner product operator + e::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary restriction operators. + d::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Normal derivative operators + H_boundary::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary quadrature operators # TODO: Boundary inner product? +end +export Laplace + +function Laplace(grid::AbstractGrid, fn; order) + # TODO: Removed once we can construct the volume and + # boundary operators by op(grid, fn; order,...). + # Read stencils + op = read_D2_operator(fn; order) + D_inner_stecil = op.innerStencil + D_closure_stencils = op.closureStencils + H_closure_stencils = op.quadratureClosure + e_closure_stencil = op.eClosure + d_closure_stencil = op.dClosure + + # Volume operators + Δ = laplace(grid, D_inner_stecil, D_closure_stencils) + H = inner_product(grid, H_closure_stencils) + H⁻¹ = inverse_inner_product(grid, H_closure_stencils) + + # Boundary operator - id pairs + ids = boundary_identifiers(grid) + n_ids = length(ids) + e_pairs = ntuple(i -> ids[i] => boundary_restriction(grid,e_closure_stencil,ids[i]),n_ids) + d_pairs = ntuple(i -> ids[i] => normal_derivative(grid,d_closure_stencil,ids[i]),n_ids) + Hᵧ_pairs = ntuple(i -> ids[i] => inner_product(boundary_grid(grid,ids[i]),H_closure_stencils),n_ids) + + return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs)) +end + +# TODO: Consider pretty printing of the following form +# Base.show(io::IO, L::Laplace{T, Dim}) where {T,Dim,TM} = print(io, "Laplace{$T, $Dim, $TM}(", L.D, L.H, L.H_inv, L.e, L.d, L.H_boundary, ")") + +LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D) +LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D) +LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...) + + +""" + inner_product(L::Lapalace) + +Returns the inner product operator associated with `L` + +""" +inner_product(L::Laplace) = L.H +export inner_product + + +""" + inverse_inner_product(L::Lapalace) + +Returns the inverse of the inner product operator associated with `L` + +""" +inverse_inner_product(L::Laplace) = L.H_inv +export inverse_inner_product + + +""" + boundary_restriction(L::Lapalace,id::BoundaryIdentifier) + boundary_restriction(L::Lapalace,ids::NTuple{N,BoundaryIdentifier}) + boundary_restriction(L::Lapalace,ids...) + +Returns boundary restriction operator(s) associated with `L` for the boundary(s) +identified by id(s). + +""" +boundary_restriction(L::Laplace,id::BoundaryIdentifier) = L.e[id] +boundary_restriction(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.e[ids[i]],N) +boundary_restriction(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.e[ids[i]],N) +export boundary_restriction + + +""" + normal_derivative(L::Lapalace,id::BoundaryIdentifier) + normal_derivative(L::Lapalace,ids::NTuple{N,BoundaryIdentifier}) + normal_derivative(L::Lapalace,ids...) + +Returns normal derivative operator(s) associated with `L` for the boundary(s) +identified by id(s). + +""" +normal_derivative(L::Laplace,id::BoundaryIdentifier) = L.d[id] +normal_derivative(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N) +normal_derivative(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N) +export normal_derivative + + +# TODO: boundary_inner_product? +""" + boundary_quadrature(L::Lapalace,id::BoundaryIdentifier) + boundary_quadrature(L::Lapalace,ids::NTuple{N,BoundaryIdentifier}) + boundary_quadrature(L::Lapalace,ids...) + +Returns boundary quadrature operator(s) associated with `L` for the boundary(s) +identified by id(s). + +""" +boundary_quadrature(L::Laplace,id::BoundaryIdentifier) = L.H_boundary[id] +boundary_quadrature(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N) +boundary_quadrature(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N) +export boundary_quadrature + + +""" + laplace(grid, inner_stencil, closure_stencils) Creates the Laplace operator operator `Δ` as a `TensorMapping` -`Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using -the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils` -for the points in the closure regions. +`Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,N on the N-dimensional +`grid`, using the stencil `inner_stencil` in the interior and a set of stencils +`closure_stencils` for the points in the closure regions. On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s where the sum is carried out lazily. """ -function laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim +function laplace(grid::AbstractGrid, inner_stencil, closure_stencils) Δ = second_derivative(grid, inner_stencil, closure_stencils, 1) - for d = 2:Dim + for d = 2:dimension(grid) Δ += second_derivative(grid, inner_stencil, closure_stencils, d) end return Δ
diff -r 80d88bb1c5bd -r 545a6c1a0a0e test/SbpOperators/volumeops/laplace/laplace_test.jl --- a/test/SbpOperators/volumeops/laplace/laplace_test.jl Fri Jul 02 13:46:39 2021 +0200 +++ b/test/SbpOperators/volumeops/laplace/laplace_test.jl Fri Jul 02 14:23:33 2021 +0200 @@ -3,12 +3,85 @@ using Sbplib.SbpOperators using Sbplib.Grids using Sbplib.LazyTensors +using Sbplib.RegionIndices +using Sbplib.StaticDicts @testset "Laplace" begin g_1D = EquidistantGrid(101, 0.0, 1.) g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.)) + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) @testset "Constructors" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + + @testset "1D" begin + # Create all tensor mappings included in Laplace + Δ = laplace(g_1D, op.innerStencil, op.closureStencils) + H = inner_product(g_1D, op.quadratureClosure) + Hi = inverse_inner_product(g_1D, op.quadratureClosure) + + (id_l, id_r) = boundary_identifiers(g_1D) + + e_l = boundary_restriction(g_1D,op.eClosure,id_l) + e_r = boundary_restriction(g_1D,op.eClosure,id_r) + e_dict = StaticDict(id_l => e_l, id_r => e_r) + + d_l = normal_derivative(g_1D,op.dClosure,id_l) + d_r = normal_derivative(g_1D,op.dClosure,id_r) + d_dict = StaticDict(id_l => d_l, id_r => d_r) + + H_l = inner_product(boundary_grid(g_1D,id_l),op.quadratureClosure) + H_r = inner_product(boundary_grid(g_1D,id_r),op.quadratureClosure) + Hb_dict = StaticDict(id_l => H_l, id_r => H_r) + + L = Laplace(g_1D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test L == Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) + @test L isa TensorMapping{T,1,1} where T + @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) + end + @testset "3D" begin + # Create all tensor mappings included in Laplace + Δ = laplace(g_3D, op.innerStencil, op.closureStencils) + H = inner_product(g_3D, op.quadratureClosure) + Hi = inverse_inner_product(g_3D, op.quadratureClosure) + + (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) + e_l = boundary_restriction(g_3D,op.eClosure,id_l) + e_r = boundary_restriction(g_3D,op.eClosure,id_r) + e_s = boundary_restriction(g_3D,op.eClosure,id_s) + e_n = boundary_restriction(g_3D,op.eClosure,id_n) + e_b = boundary_restriction(g_3D,op.eClosure,id_b) + e_t = boundary_restriction(g_3D,op.eClosure,id_t) + e_dict = StaticDict(id_l => e_l, id_r => e_r, + id_s => e_s, id_n => e_n, + id_b => e_b, id_t => e_t) + + d_l = normal_derivative(g_3D,op.dClosure,id_l) + d_r = normal_derivative(g_3D,op.dClosure,id_r) + d_s = normal_derivative(g_3D,op.dClosure,id_s) + d_n = normal_derivative(g_3D,op.dClosure,id_n) + d_b = normal_derivative(g_3D,op.dClosure,id_b) + d_t = normal_derivative(g_3D,op.dClosure,id_t) + d_dict = StaticDict(id_l => d_l, id_r => d_r, + id_s => d_s, id_n => d_n, + id_b => d_b, id_t => d_t) + + H_l = inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure) + H_r = inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure) + H_s = inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure) + H_n = inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure) + H_b = inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure) + H_t = inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure) + Hb_dict = StaticDict(id_l => H_l, id_r => H_r, + id_s => H_s, id_n => H_n, + id_b => H_b, id_t => H_t) + + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test L == Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) + @test L isa TensorMapping{T,3,3} where T + @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) + end + end + + @testset "laplace" begin @testset "1D" begin L = laplace(g_1D, op.innerStencil, op.closureStencils) @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils) @@ -21,9 +94,83 @@ Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2) Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,3) @test L == Dxx + Dyy + Dzz + @test L isa TensorMapping{T,3,3} where T end end + @testset "inner_product" begin + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test inner_product(L) == inner_product(g_3D,op.quadratureClosure) + end + + @testset "inverse_inner_product" begin + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test inverse_inner_product(L) == inverse_inner_product(g_3D,op.quadratureClosure) + end + + @testset "boundary_restriction" begin + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) + @test boundary_restriction(L,id_l) == boundary_restriction(g_3D,op.eClosure,id_l) + @test boundary_restriction(L,id_r) == boundary_restriction(g_3D,op.eClosure,id_r) + @test boundary_restriction(L,id_s) == boundary_restriction(g_3D,op.eClosure,id_s) + @test boundary_restriction(L,id_n) == boundary_restriction(g_3D,op.eClosure,id_n) + @test boundary_restriction(L,id_b) == boundary_restriction(g_3D,op.eClosure,id_b) + @test boundary_restriction(L,id_t) == boundary_restriction(g_3D,op.eClosure,id_t) + + ids = boundary_identifiers(g_3D) + es = boundary_restriction(L,ids) + @test es == (boundary_restriction(L,id_l), + boundary_restriction(L,id_r), + boundary_restriction(L,id_s), + boundary_restriction(L,id_n), + boundary_restriction(L,id_b), + boundary_restriction(L,id_t)); + @test es == boundary_restriction(L,ids...) + end + + @testset "normal_derivative" begin + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) + @test normal_derivative(L,id_l) == normal_derivative(g_3D,op.dClosure,id_l) + @test normal_derivative(L,id_r) == normal_derivative(g_3D,op.dClosure,id_r) + @test normal_derivative(L,id_s) == normal_derivative(g_3D,op.dClosure,id_s) + @test normal_derivative(L,id_n) == normal_derivative(g_3D,op.dClosure,id_n) + @test normal_derivative(L,id_b) == normal_derivative(g_3D,op.dClosure,id_b) + @test normal_derivative(L,id_t) == normal_derivative(g_3D,op.dClosure,id_t) + + ids = boundary_identifiers(g_3D) + ds = normal_derivative(L,ids) + @test ds == (normal_derivative(L,id_l), + normal_derivative(L,id_r), + normal_derivative(L,id_s), + normal_derivative(L,id_n), + normal_derivative(L,id_b), + normal_derivative(L,id_t)); + @test ds == normal_derivative(L,ids...) + end + + @testset "boundary_quadrature" begin + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) + @test boundary_quadrature(L,id_l) == inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure) + @test boundary_quadrature(L,id_r) == inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure) + @test boundary_quadrature(L,id_s) == inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure) + @test boundary_quadrature(L,id_n) == inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure) + @test boundary_quadrature(L,id_b) == inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure) + @test boundary_quadrature(L,id_t) == inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure) + + ids = boundary_identifiers(g_3D) + H_gammas = boundary_quadrature(L,ids) + @test H_gammas == (boundary_quadrature(L,id_l), + boundary_quadrature(L,id_r), + boundary_quadrature(L,id_s), + boundary_quadrature(L,id_n), + boundary_quadrature(L,id_b), + boundary_quadrature(L,id_t)); + @test H_gammas == boundary_quadrature(L,ids...) + end + # Exact differentiation is measured point-wise. In other cases # the error is measured in the l2-norm. @testset "Accuracy" begin @@ -40,8 +187,7 @@ # 2nd order interior stencil, 1st order boundary stencil, # implies that L*v should be exact for binomials up to order 2. @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - L = laplace(g_3D,op.innerStencil,op.closureStencils) + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=2) @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9 @@ -51,8 +197,7 @@ # 4th order interior stencil, 2nd order boundary stencil, # implies that L*v should be exact for binomials up to order 3. @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - L = laplace(g_3D,op.innerStencil,op.closureStencils) + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) # NOTE: high tolerances for checking the "exact" differentiation # due to accumulation of round-off errors/cancellation errors? @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9