--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SbpOperators/src/InverseQuadrature.jl	Tue Jun 23 18:56:59 2020 +0200
@@ -0,0 +1,75 @@
+"""
+    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the inverse quadrature operator `Qi` of Dim dimension as a TensorOperator
+The multi-dimensional tensor operator consists of a tuple of 1D InverseDiagonalNorm
+tensor operators.
+"""
+struct Quadrature{Dim,T<:Real,N,M} <: TensorOperator{T,Dim}
+    Hi::NTuple{Dim,InverseDiagonalNorm{T,N,M}}
+end
+export Quadrature
+
+LazyTensors.domain_size(Qi::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
+
+function LazyTensors.apply(Qi::Quadrature{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
+    error("not implemented")
+end
+
+LazyTensors.apply_transpose(Qi::Quadrature{Dim,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where {Dim,T} = LazyTensors.apply(Q,v,I)
+
+@inline function LazyTensors.apply(Qi::Quadrature{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
+    @inbounds q = apply(Qi.Hi[1], v , I[1])
+    return q
+end
+
+@inline function LazyTensors.apply(Qi::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
+    # Quadrature in x direction
+    @inbounds vx = view(v, :, Int(I[2]))
+    @inbounds qx_inv = apply(Qi.Hi[1], vx , I[1])
+    # Quadrature in y-direction
+    @inbounds vy = view(v, Int(I[1]), :)
+    @inbounds qy_inv = apply(Qi.Hi[2], vy, I[2])
+    return qx_inv*qy_inv
+end
+
+"""
+    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the quadrature operator `Hi` of Dim dimension as a TensorMapping
+"""
+struct InverseDiagonalNorm{T<:Real,N,M} <: TensorOperator{T,1}
+    h_inv::T # The reciprocl grid spacing could be included in the stencil already. Preferable?
+    closure::NTuple{M,T}
+    #TODO: Write a nice constructor
+end
+
+@inline function LazyTensors.apply(Hi::InverseDiagonalNorm{T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
+    return @inbounds apply(Hi, v, I[1])
+end
+
+LazyTensors.apply_transpose(Hi::Quadrature{Dim,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(Hi,v,I)
+
+@inline LazyTensors.apply(Hi::InverseDiagonalNorm, v::AbstractVector{T}, i::Index{Lower}) where T
+    return @inbounds Hi.h_inv*Hi.closure[Int(i)]*v[Int(i)]
+end
+@inline LazyTensors.apply(Hi::InverseDiagonalNorm,v::AbstractVector{T}, i::Index{Upper}) where T
+    N = length(v);
+    return @inbounds Hi.h_inv*Hi.closure[N-Int(i)+1]v[Int(i)]
+end
+
+@inline LazyTensors.apply(Hi::InverseDiagonalNorm, v::AbstractVector{T}, i::Index{Interior}) where T
+    return @inbounds Hi.h_inv*v[Int(i)]
+end
+
+function LazyTensors.apply(Hi::InverseDiagonalNorm,  v::AbstractVector{T}, index::Index{Unknown}) where T
+    N = length(v);
+    r = getregion(Int(index), closuresize(Hi), N)
+    i = Index(Int(index), r)
+    return LazyTensors.apply(Hi, v, i)
+end
+export LazyTensors.apply
+
+function closuresize(Hi::InverseDiagonalNorm{T<:Real,N,M}) where {T,N,M}
+    return M
+end

--- a/SbpOperators/src/laplace/laplace.jl	Tue Jun 23 18:53:20 2020 +0200
+++ b/SbpOperators/src/laplace/laplace.jl	Tue Jun 23 18:56:59 2020 +0200
@@ -45,31 +45,6 @@
 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
 export quadrature
 
-
-"""
-    InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
-
-Implements the inverse quadrature operator `inv(H)` of Dim dimension as a TensorMapping
-"""
-struct InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
-    op::D2{T,N,M,K}
-    grid::EquidistantGrid{Dim,T}
-end
-export InverseQuadrature
-
-LazyTensors.domain_size(H_inv::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
-
-@inline function LazyTensors.apply(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
-    N = size(H_inv.grid)
-    # Inverse quadrature in x direction
-    @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[1], v[I] , I[1], N[1])
-    # Inverse quadrature in y-direction
-    @inbounds q_inv = apply_inverse_quadrature(H_inv.op, inverse_spacing(H_inv.grid)[2], q_inv, I[2], N[2])
-    return q_inv
-end
-
-LazyTensors.apply_transpose(H_inv::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H_inv,v,I)
-
 """
     BoundaryValue{T,N,M,K} <: TensorMapping{T,2,1}