Mercurial > repos > public > sbplib_julia
changeset 702:3cd582257072 feature/laplace_opset
Merge in default
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
---|---|
date | Mon, 15 Feb 2021 11:30:34 +0100 |
parents | 54ce3f9771e5 (diff) 38f9894279cd (current diff) |
children | 988e9cfcd58d |
files | Notes.md src/SbpOperators/volumeops/laplace/laplace.jl src/SbpOperators/volumeops/quadratures/inverse_quadrature.jl src/SbpOperators/volumeops/quadratures/quadrature.jl test/testSbpOperators.jl |
diffstat | 3 files changed, 172 insertions(+), 0 deletions(-) [+] |
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--- a/Notes.md Mon Feb 15 11:13:12 2021 +0100 +++ b/Notes.md Mon Feb 15 11:30:34 2021 +0100 @@ -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.
--- a/src/SbpOperators/volumeops/laplace/laplace.jl Mon Feb 15 11:13:12 2021 +0100 +++ b/src/SbpOperators/volumeops/laplace/laplace.jl Mon Feb 15 11:30:34 2021 +0100 @@ -1,3 +1,69 @@ +""" + Laplace{T,Dim,...}() + Laplace(grid::EquidistantGrid, fn; order) + +Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a +`TensorMapping`. Additionally, `Laplace` stores the quadrature, and boundary +operators relevant for constructing a SBP finite difference scheme as `TensorMapping`s. + +Laplace(grid::EquidistantGrid, fn; order) creates the Laplace operator on an +equidistant grid, where the operators are read from a TOML. The laplace operator +is created using laplace(grid,...). +""" +struct Laplace{T, Dim, Rb, TMdiffop<:TensorMapping{T,Dim,Dim}, # Differential operator tensor mapping + TMqop<:TensorMapping{T,Dim,Dim}, # Quadrature operator tensor mapping + TMbop<:TensorMapping{T,Rb,Dim}, # Boundary operator tensor mapping + TMbqop<:TensorMapping{T,Rb,Rb}, # Boundary quadrature tensor mapping + BID<:BoundaryIdentifier} <: TensorMapping{T,Dim,Dim} + D::TMdiffop # Difference operator + H::TMqop # Quadrature (norm) operator + H_inv::TMqop # Inverse quadrature (norm) operator + e::Dict{BID,TMbop} # Boundary restriction operators + d::Dict{BID,TMbop} # Normal derivative operators + H_boundary::Dict{BID,TMbqop} # Boundary quadrature operators +end +export Laplace + +function Laplace(grid::EquidistantGrid, 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 + bids = boundary_identifiers(grid) + e_pairs = ntuple(i -> Pair(bids[i],boundary_restriction(grid,e_closure_stencil,bids[i])),length(bids)) + d_pairs = ntuple(i -> Pair(bids[i],normal_derivative(grid,d_closure_stencil,bids[i])),length(bids)) + Hᵧ_pairs = ntuple(i -> Pair(bids[i],inner_product(boundary_grid(grid,bids[i]),H_closure_stencils)),length(bids)) + + return Laplace(Δ, H, H⁻¹, Dict(e_pairs), Dict(d_pairs), Dict(Hᵧ_pairs)) +end + +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...) + +quadrature(L::Laplace) = L.H +export quadrature +inverse_quadrature(L::Laplace) = L.H_inv +export inverse_quadrature +boundary_restriction(L::Laplace,bid::BoundaryIdentifier) = L.e[bid] +export boundary_restriction +normal_derivative(L::Laplace,bid::BoundaryIdentifier) = L.d[bid] +export normal_derivative +boundary_quadrature(L::Laplace,bid::BoundaryIdentifier) = L.H_boundary[bid] +export boundary_quadrature + """ laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
--- a/test/testSbpOperators.jl Mon Feb 15 11:13:12 2021 +0100 +++ b/test/testSbpOperators.jl Mon Feb 15 11:30:34 2021 +0100 @@ -339,6 +339,95 @@ @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 = Dict(Pair(id_l,e_l),Pair(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 = Dict(Pair(id_l,d_l),Pair(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 = Dict(Pair(id_l,H_l),Pair(id_r,H_r)) + + # TODO: Not sure why this doesnt work? Comparing the fields of + # Laplace seems to work. Reformulate below once solved. + @test_broken Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) == Laplace(g_1D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + L = Laplace(g_1D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test L.D == Δ + @test L.H == H + @test L.H_inv == Hi + @test L.e == e_dict + @test L.d == d_dict + @test L.H_boundary == 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 = Dict(Pair(id_l,e_l),Pair(id_r,e_r), + Pair(id_s,e_s),Pair(id_n,e_n), + Pair(id_b,e_b),Pair(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 = Dict(Pair(id_l,d_l),Pair(id_r,d_r), + Pair(id_s,d_s),Pair(id_n,d_n), + Pair(id_b,d_b),Pair(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 = Dict(Pair(id_l,H_l),Pair(id_r,H_r), + Pair(id_s,H_s),Pair(id_n,H_n), + Pair(id_b,H_b),Pair(id_t,H_t)) + + # TODO: Not sure why this doesnt work? Comparing the fields of + # Laplace seems to work. Reformulate below once solved. + @test_broken Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) == Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4) + @test L.D == Δ + @test L.H == H + @test L.H_inv == Hi + @test L.e == e_dict + @test L.d == d_dict + @test L.H_boundary == 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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "1D" begin L = laplace(g_1D, op.innerStencil, op.closureStencils) @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils) @test L isa TensorMapping{T,1,1} where T @@ -350,9 +439,25 @@ 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 "quadrature" begin + end + + @testset "inverse_quadrature" begin + end + + @testset "boundary_restriction" begin + end + + @testset "normal_restriction" begin + end + + @testset "boundary_quadrature" begin + end + # Exact differentiation is measured point-wise. In other cases # the error is measured in the l2-norm. @testset "Accuracy" begin