--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/laplace/laplace.jl	Fri Sep 25 13:06:02 2020 +0200
@@ -0,0 +1,138 @@
+export Laplace
+"""
+    Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
+
+Implements the Laplace operator `L` in Dim dimensions as a tensor operator
+The multi-dimensional tensor operator consists of a tuple of 1D SecondDerivative
+tensor operators.
+"""
+#export quadrature, inverse_quadrature, boundary_quadrature, boundary_value, normal_derivative
+struct Laplace{Dim,T,N,M,K} <: TensorOperator{T,Dim}
+    D2::NTuple{Dim,SecondDerivative{T,N,M,K}}
+    #TODO: Write a good constructor
+end
+
+LazyTensors.domain_size(L::Laplace{Dim}, range_size::NTuple{Dim,Integer}) where {Dim} = range_size
+
+function LazyTensors.apply(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim}
+    error("not implemented")
+end
+
+# u = L*v
+function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::Index) where T
+    @inbounds u = LazyTensors.apply(L.D2[1],v,I)
+    return u
+end
+
+function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::Index, J::Index) where T
+    # 2nd x-derivative
+    @inbounds vx = view(v, :, Int(J))
+    @inbounds uᵢ = LazyTensors.apply(L.D2[1], vx , I)
+
+    # 2nd y-derivative
+    @inbounds vy = view(v, Int(I), :)
+    @inbounds uᵢ += LazyTensors.apply(L.D2[2], vy , J)
+
+    return uᵢ
+end
+
+LazyTensors.apply_transpose(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim} = LazyTensors.apply(L, v, I...)
+
+# quadrature(L::Laplace) = Quadrature(L.op, L.grid)
+# inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
+# boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
+# normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
+# boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
+# export NormalDerivative
+# """
+#     NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
+#
+# Implements the boundary operator `d` as a TensorMapping
+# """
+# struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
+#     op::D2{T,N,M,K}
+#     grid::EquidistantGrid{2}
+#     bId::CartesianBoundary
+# end
+#
+# # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
+# # Can we give special treatment to TensorMappings that go to a higher dim?
+# function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
+#     if dim(e.bId) == 1
+#         return (UnknownDim, domain_size[1])
+#     elseif dim(e.bId) == 2
+#         return (domain_size[1], UnknownDim)
+#     end
+# end
+# LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
+#
+# # TODO: Not type stable D:<
+# # TODO: Make this independent of dimension
+# function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
+#     i = I[dim(d.bId)]
+#     j = I[3-dim(d.bId)]
+#     N_i = size(d.grid)[dim(d.bId)]
+#     h_inv = inverse_spacing(d.grid)[dim(d.bId)]
+#     return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
+# end
+#
+# function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
+#     u = selectdim(v,3-dim(d.bId),Int(I[1]))
+#     return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
+# end
+#
+# """
+#     BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
+#
+# Implements the boundary operator `q` as a TensorOperator
+# """
+# export BoundaryQuadrature
+# struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
+#     op::D2{T,N,M,K}
+#     grid::EquidistantGrid{2}
+#     bId::CartesianBoundary
+# end
+#
+#
+# # TODO: Make this independent of dimension
+# function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
+#     h = spacing(q.grid)[3-dim(q.bId)]
+#     N = size(v)
+#     return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
+# end
+#
+# LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T = LazyTensors.apply(q,v,I)
+#
+#
+#
+#
+# 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 = boundary_value(L, Bid())
+#     d = normal_derivative(L, Bid())
+#     Hᵧ = boundary_quadrature(L, Bid())
+#     H⁻¹ = inverse_quadrature(L)
+#     return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
+# 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 = boundary_value(L, Bid())
+#     d = normal_derivative(L, Bid())
+#     Hᵧ = boundary_quadrature(L, Bid())
+#     H⁻¹ = inverse_quadrature(L)
+#     return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
+#     # 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