Mercurial > repos > public > sbplib_julia
changeset 211:1ad91e11b1f4 package_refactor
Move DiffOps and Grids into packages
author | Jonatan Werpers <jonatan@werpers.com> |
---|---|
date | Wed, 26 Jun 2019 10:44:20 +0200 |
parents | 2aa33d0eef90 |
children | aa17d4d9d09e |
files | AbstractGrid.jl DiffOps/Project.toml DiffOps/src/DiffOps.jl EquidistantGrid.jl Grids/Project.toml Grids/src/AbstractGrid.jl Grids/src/EquidistantGrid.jl Grids/src/Grids.jl Manifest.toml Project.toml diffOp.jl sbp.jl |
diffstat | 12 files changed, 322 insertions(+), 293 deletions(-) [+] |
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--- a/AbstractGrid.jl Tue Jun 25 17:26:39 2019 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,15 +0,0 @@ -abstract type AbstractGrid end - -function dimension(grid::AbstractGrid) - error("Not implemented for abstact type AbstractGrid") -end - -function points(grid::AbstractGrid) - error("Not implemented for abstact type AbstractGrid") -end - -# Evaluate function f on the grid g -function evalOn(g::AbstractGrid, f::Function) - F(x) = f(x...) - return F.(points(g)) -end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/DiffOps/Project.toml Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,4 @@ +name = "DiffOps" +uuid = "39474f48-97ec-11e9-01fc-6ddcbe5918df" +authors = ["Jonatan Werpers <jonatan.werpers@it.uu.se>"] +version = "0.1.0"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/DiffOps/src/DiffOps.jl Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,220 @@ +abstract type DiffOp end + +# 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? +function apply(D::DiffOp, v::AbstractVector, i::Int) + error("not implemented") +end + +function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real + error("not implemented") +end + +function matrixRepresentation(D::DiffOp) + error("not implemented") +end + +abstract type DiffOpCartesian{Dim} <: DiffOp end + +# DiffOp must have a grid of dimension Dim!!! +function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim} + for I ∈ eachindex(D.grid) + u[I] = apply(D, v, I) + end + + return nothing +end + +function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T + apply_region!(D, u, v, Lower, Lower) + apply_region!(D, u, v, Lower, Interior) + apply_region!(D, u, v, Lower, Upper) + apply_region!(D, u, v, Interior, Lower) + apply_region!(D, u, v, Interior, Interior) + apply_region!(D, u, v, Interior, Upper) + apply_region!(D, u, v, Upper, Lower) + apply_region!(D, u, v, Upper, Interior) + apply_region!(D, u, v, Upper, Upper) + return nothing +end + +# Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable +function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T + for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2)) + @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2])) + @inbounds u[I] = apply(D, v, indextuple) + end + return nothing +end + +function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T + apply_region_tiled!(D, u, v, Lower, Lower) + apply_region_tiled!(D, u, v, Lower, Interior) + apply_region_tiled!(D, u, v, Lower, Upper) + apply_region_tiled!(D, u, v, Interior, Lower) + apply_region_tiled!(D, u, v, Interior, Interior) + apply_region_tiled!(D, u, v, Interior, Upper) + apply_region_tiled!(D, u, v, Upper, Lower) + apply_region_tiled!(D, u, v, Upper, Interior) + apply_region_tiled!(D, u, v, Upper, Upper) + return nothing +end + +using TiledIteration +function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T + ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2)) + # TODO: Pass Tilesize to function + for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2)) + for j ∈ tileaxs[2], i ∈ tileaxs[1] + I = ri[i,j] + u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2]))) + end + end + return nothing +end + +function apply(D::DiffOp, v::AbstractVector)::AbstractVector + u = zeros(eltype(v), size(v)) + apply!(D,v,u) + return u +end + +struct NormalDerivative{N,M,K} + op::D2{Float64,N,M,K} + grid::EquidistantGrid + bId::CartesianBoundary +end + +function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer) + u = selectdim(v,3-dim(d.bId),I) + return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId)) +end + +# Not correct abstraction level +# TODO: Not type stable D:< +function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer}) + i = I[dim(d.bId)] + j = I[3-dim(d.bId)] + N_i = d.grid.size[dim(d.bId)] + + r = getregion(i, closureSize(d.op), N_i) + + if r != region(d.bId) + return 0 + end + + if r == Lower + # Note, closures are indexed by offset. Fix this D:< + return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j] + elseif r == Upper + return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j] + end +end + +struct BoundaryValue{N,M,K} + op::D2{Float64,N,M,K} + grid::EquidistantGrid + bId::CartesianBoundary +end + +function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer}) + i = I[dim(e.bId)] + j = I[3-dim(e.bId)] + N_i = e.grid.size[dim(e.bId)] + + r = getregion(i, closureSize(e.op), N_i) + + if r != region(e.bId) + return 0 + end + + if r == Lower + # Note, closures are indexed by offset. Fix this D:< + return e.op.eClosure[i-1]*v[j] + elseif r == Upper + return e.op.eClosure[N_i-j]*v[j] + end +end + +function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer) + u = selectdim(v,3-dim(e.bId),I) + return apply_e(e.op, u, region(e.bId)) +end + +struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim} + grid::EquidistantGrid{Dim,T} + a::T + op::D2{Float64,N,M,K} + e::BoundaryValue + d::NormalDerivative +end + +function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim + error("not implemented") +end + +# u = L*v +function apply(L::Laplace{1}, v::AbstractVector, i::Int) + uᵢ = L.a * apply(L.op, L.grid.spacing[1], v, i) + return uᵢ +end + +@inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2} + # 2nd x-derivative + @inbounds vx = view(v, :, Int(I[2])) + @inbounds uᵢ = L.a*apply(L.op, L.grid.inverse_spacing[1], vx , I[1]) + # 2nd y-derivative + @inbounds vy = view(v, Int(I[1]), :) + @inbounds uᵢ += L.a*apply(L.op, L.grid.inverse_spacing[2], vy, I[2]) + return uᵢ +end + +# Slow but maybe convenient? +function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2}) + I = Index{Unknown}.(Tuple(i)) + apply(L, v, I) +end + +struct BoundaryOperator + +end + + +""" +A BoundaryCondition should implement the method + sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...) +""" +abstract type BoundaryCondition end + +struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end + +function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid} + e = BoundaryValue(L.op, L.grid, Bid()) + d = NormalDerivative(L.op, L.grid, Bid()) + Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid()) + # TODO: Implement BoundaryQuadrature method + + return -L.Hi*e*Hᵧ*(d'*v - g) + # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on +end + +struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition + tau::Float64 +end + +function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid} + e = BoundaryValue(L.op, L.grid, Bid()) + d = NormalDerivative(L.op, L.grid, Bid()) + Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid()) + # TODO: Implement BoundaryQuadrature method + + return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g) + # Need to handle scalar multiplication and addition of TensorMapping +end + +# function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D +# return apply(s.L, v, i) + +# sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) + +# sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) + +# sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) + +# sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i) +# end
--- a/EquidistantGrid.jl Tue Jun 25 17:26:39 2019 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -# EquidistantGrid is a grid with equidistant grid spacing per coordinat -# direction. The domain is defined through the two points P1 = x̄₁, P2 = x̄₂ -# by the exterior product of the vectors obtained by projecting (x̄₂-x̄₁) onto -# the coordinate directions. E.g for a 2D grid with x̄₁=(-1,0) and x̄₂=(1,2) -# the domain is defined as (-1,1)x(0,2). - -struct EquidistantGrid{Dim,T<:Real} <: AbstractGrid - size::NTuple{Dim, Int} # First coordinate direction stored first - limit_lower::NTuple{Dim, T} - limit_upper::NTuple{Dim, T} - inverse_spacing::NTuple{Dim, T} # The reciprocal of the grid spacing - - # General constructor - function EquidistantGrid(size::NTuple{Dim, Int}, limit_lower::NTuple{Dim, T}, limit_upper::NTuple{Dim, T}) where Dim where T - @assert all(size.>0) - @assert all(limit_upper.-limit_lower .!= 0) - inverse_spacing = (size.-1)./abs.(limit_upper.-limit_lower) - return new{Dim,T}(size, limit_lower, limit_upper, inverse_spacing) - end -end - -function Base.eachindex(grid::EquidistantGrid) - CartesianIndices(grid.size) -end - -# Returns the number of dimensions of an EquidistantGrid. -# -# @Input: grid - an EquidistantGrid -# @Return: dimension - The dimension of the grid -function dimension(grid::EquidistantGrid) - return length(grid.size) -end - -# Returns the spacing of the grid -# -function spacing(grid::EquidistantGrid) - return 1.0./grid.inverse_spacing -end - -# Computes the points of an EquidistantGrid as an array of tuples with -# the same dimension as the grid. -# -# @Input: grid - an EquidistantGrid -# @Return: points - the points of the grid. -function points(grid::EquidistantGrid) - # TODO: Make this return an abstract array? - indices = Tuple.(CartesianIndices(grid.size)) - h = spacing(grid) - return broadcast(I -> grid.limit_lower .+ (I.-1).*h, indices) -end - -function pointsalongdim(grid::EquidistantGrid, dim::Integer) - @assert dim<=dimension(grid) - @assert dim>0 - points = collect(range(grid.limit_lower[dim],stop=grid.limit_upper[dim],length=grid.size[dim])) -end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Grids/Project.toml Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,4 @@ +name = "Grids" +uuid = "960fdf28-97ed-11e9-2a74-bd90bf2fab5a" +authors = ["Jonatan Werpers <jonatan.werpers@it.uu.se>"] +version = "0.1.0"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Grids/src/AbstractGrid.jl Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,15 @@ +abstract type AbstractGrid end + +function dimension(grid::AbstractGrid) + error("Not implemented for abstact type AbstractGrid") +end + +function points(grid::AbstractGrid) + error("Not implemented for abstact type AbstractGrid") +end + +# Evaluate function f on the grid g +function evalOn(g::AbstractGrid, f::Function) + F(x) = f(x...) + return F.(points(g)) +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Grids/src/EquidistantGrid.jl Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,56 @@ +# EquidistantGrid is a grid with equidistant grid spacing per coordinat +# direction. The domain is defined through the two points P1 = x̄₁, P2 = x̄₂ +# by the exterior product of the vectors obtained by projecting (x̄₂-x̄₁) onto +# the coordinate directions. E.g for a 2D grid with x̄₁=(-1,0) and x̄₂=(1,2) +# the domain is defined as (-1,1)x(0,2). + +struct EquidistantGrid{Dim,T<:Real} <: AbstractGrid + size::NTuple{Dim, Int} # First coordinate direction stored first + limit_lower::NTuple{Dim, T} + limit_upper::NTuple{Dim, T} + inverse_spacing::NTuple{Dim, T} # The reciprocal of the grid spacing + + # General constructor + function EquidistantGrid(size::NTuple{Dim, Int}, limit_lower::NTuple{Dim, T}, limit_upper::NTuple{Dim, T}) where Dim where T + @assert all(size.>0) + @assert all(limit_upper.-limit_lower .!= 0) + inverse_spacing = (size.-1)./abs.(limit_upper.-limit_lower) + return new{Dim,T}(size, limit_lower, limit_upper, inverse_spacing) + end +end + +function Base.eachindex(grid::EquidistantGrid) + CartesianIndices(grid.size) +end + +# Returns the number of dimensions of an EquidistantGrid. +# +# @Input: grid - an EquidistantGrid +# @Return: dimension - The dimension of the grid +function dimension(grid::EquidistantGrid) + return length(grid.size) +end + +# Returns the spacing of the grid +# +function spacing(grid::EquidistantGrid) + return 1.0./grid.inverse_spacing +end + +# Computes the points of an EquidistantGrid as an array of tuples with +# the same dimension as the grid. +# +# @Input: grid - an EquidistantGrid +# @Return: points - the points of the grid. +function points(grid::EquidistantGrid) + # TODO: Make this return an abstract array? + indices = Tuple.(CartesianIndices(grid.size)) + h = spacing(grid) + return broadcast(I -> grid.limit_lower .+ (I.-1).*h, indices) +end + +function pointsalongdim(grid::EquidistantGrid, dim::Integer) + @assert dim<=dimension(grid) + @assert dim>0 + points = collect(range(grid.limit_lower[dim],stop=grid.limit_upper[dim],length=grid.size[dim])) +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Grids/src/Grids.jl Wed Jun 26 10:44:20 2019 +0200 @@ -0,0 +1,11 @@ +module Grids + +abstract type BoundaryIdentifier end +struct CartesianBoundary{Dim, R<:Region} <: BoundaryIdentifier end +dim(::CartesianBoundary{Dim, R}) where {Dim, R} = Dim +region(::CartesianBoundary{Dim, R}) where {Dim, R} = R + +include("AbstractGrid.jl") +include("EquidistantGrid.jl") + +end # module
--- a/Manifest.toml Tue Jun 25 17:26:39 2019 +0200 +++ b/Manifest.toml Wed Jun 26 10:44:20 2019 +0200 @@ -1,5 +1,15 @@ # This file is machine-generated - editing it directly is not advised +[[DiffOps]] +path = "DiffOps" +uuid = "39474f48-97ec-11e9-01fc-6ddcbe5918df" +version = "0.1.0" + +[[Grids]] +path = "Grids" +uuid = "960fdf28-97ed-11e9-2a74-bd90bf2fab5a" +version = "0.1.0" + [[LazyTensors]] path = "LazyTensors" uuid = "62fbed2c-918d-11e9-279b-eb3a325b37d3"
--- a/Project.toml Tue Jun 25 17:26:39 2019 +0200 +++ b/Project.toml Wed Jun 26 10:44:20 2019 +0200 @@ -1,2 +1,4 @@ [deps] +DiffOps = "39474f48-97ec-11e9-01fc-6ddcbe5918df" +Grids = "960fdf28-97ed-11e9-2a74-bd90bf2fab5a" LazyTensors = "62fbed2c-918d-11e9-279b-eb3a325b37d3"
--- a/diffOp.jl Tue Jun 25 17:26:39 2019 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,220 +0,0 @@ -abstract type DiffOp end - -# 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? -function apply(D::DiffOp, v::AbstractVector, i::Int) - error("not implemented") -end - -function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real - error("not implemented") -end - -function matrixRepresentation(D::DiffOp) - error("not implemented") -end - -abstract type DiffOpCartesian{Dim} <: DiffOp end - -# DiffOp must have a grid of dimension Dim!!! -function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim} - for I ∈ eachindex(D.grid) - u[I] = apply(D, v, I) - end - - return nothing -end - -function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T - apply_region!(D, u, v, Lower, Lower) - apply_region!(D, u, v, Lower, Interior) - apply_region!(D, u, v, Lower, Upper) - apply_region!(D, u, v, Interior, Lower) - apply_region!(D, u, v, Interior, Interior) - apply_region!(D, u, v, Interior, Upper) - apply_region!(D, u, v, Upper, Lower) - apply_region!(D, u, v, Upper, Interior) - apply_region!(D, u, v, Upper, Upper) - return nothing -end - -# Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable -function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T - for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2)) - @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2])) - @inbounds u[I] = apply(D, v, indextuple) - end - return nothing -end - -function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T - apply_region_tiled!(D, u, v, Lower, Lower) - apply_region_tiled!(D, u, v, Lower, Interior) - apply_region_tiled!(D, u, v, Lower, Upper) - apply_region_tiled!(D, u, v, Interior, Lower) - apply_region_tiled!(D, u, v, Interior, Interior) - apply_region_tiled!(D, u, v, Interior, Upper) - apply_region_tiled!(D, u, v, Upper, Lower) - apply_region_tiled!(D, u, v, Upper, Interior) - apply_region_tiled!(D, u, v, Upper, Upper) - return nothing -end - -using TiledIteration -function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T - ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2)) - # TODO: Pass Tilesize to function - for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2)) - for j ∈ tileaxs[2], i ∈ tileaxs[1] - I = ri[i,j] - u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2]))) - end - end - return nothing -end - -function apply(D::DiffOp, v::AbstractVector)::AbstractVector - u = zeros(eltype(v), size(v)) - apply!(D,v,u) - return u -end - -struct NormalDerivative{N,M,K} - op::D2{Float64,N,M,K} - grid::EquidistantGrid - bId::CartesianBoundary -end - -function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer) - u = selectdim(v,3-dim(d.bId),I) - return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId)) -end - -# Not correct abstraction level -# TODO: Not type stable D:< -function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer}) - i = I[dim(d.bId)] - j = I[3-dim(d.bId)] - N_i = d.grid.size[dim(d.bId)] - - r = getregion(i, closureSize(d.op), N_i) - - if r != region(d.bId) - return 0 - end - - if r == Lower - # Note, closures are indexed by offset. Fix this D:< - return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j] - elseif r == Upper - return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j] - end -end - -struct BoundaryValue{N,M,K} - op::D2{Float64,N,M,K} - grid::EquidistantGrid - bId::CartesianBoundary -end - -function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer}) - i = I[dim(e.bId)] - j = I[3-dim(e.bId)] - N_i = e.grid.size[dim(e.bId)] - - r = getregion(i, closureSize(e.op), N_i) - - if r != region(e.bId) - return 0 - end - - if r == Lower - # Note, closures are indexed by offset. Fix this D:< - return e.op.eClosure[i-1]*v[j] - elseif r == Upper - return e.op.eClosure[N_i-j]*v[j] - end -end - -function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer) - u = selectdim(v,3-dim(e.bId),I) - return apply_e(e.op, u, region(e.bId)) -end - -struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim} - grid::EquidistantGrid{Dim,T} - a::T - op::D2{Float64,N,M,K} - e::BoundaryValue - d::NormalDerivative -end - -function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim - error("not implemented") -end - -# u = L*v -function apply(L::Laplace{1}, v::AbstractVector, i::Int) - uᵢ = L.a * apply(L.op, L.grid.spacing[1], v, i) - return uᵢ -end - -@inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2} - # 2nd x-derivative - @inbounds vx = view(v, :, Int(I[2])) - @inbounds uᵢ = L.a*apply(L.op, L.grid.inverse_spacing[1], vx , I[1]) - # 2nd y-derivative - @inbounds vy = view(v, Int(I[1]), :) - @inbounds uᵢ += L.a*apply(L.op, L.grid.inverse_spacing[2], vy, I[2]) - return uᵢ -end - -# Slow but maybe convenient? -function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2}) - I = Index{Unknown}.(Tuple(i)) - apply(L, v, I) -end - -struct BoundaryOperator - -end - - -""" -A BoundaryCondition should implement the method - sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...) -""" -abstract type BoundaryCondition end - -struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end - -function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid} - e = BoundaryValue(L.op, L.grid, Bid()) - d = NormalDerivative(L.op, L.grid, Bid()) - Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid()) - # TODO: Implement BoundaryQuadrature method - - return -L.Hi*e*Hᵧ*(d'*v - g) - # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on -end - -struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition - tau::Float64 -end - -function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid} - e = BoundaryValue(L.op, L.grid, Bid()) - d = NormalDerivative(L.op, L.grid, Bid()) - Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid()) - # TODO: Implement BoundaryQuadrature method - - return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g) - # Need to handle scalar multiplication and addition of TensorMapping -end - -# function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D -# return apply(s.L, v, i) + -# sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) + -# sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) + -# sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) + -# sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i) -# end