--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SbpOperators/src/Quadrature.jl	Tue Jun 23 17:32:54 2020 +0200
@@ -0,0 +1,76 @@
+# At the moment the grid property is used all over. It could possibly be removed if we implement all the 1D operators as TensorMappings
+"""
+    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the quadrature operator `Q` of Dim dimension as a TensorMapping
+The multi-dimensional tensor operator consists of a tuple of 1D DiagonalQuadrature
+tensor operators.
+"""
+struct Quadrature{Dim,T<:Real,N,M} <: TensorOperator{T,Dim}
+    H::NTuple{Dim,DiagonalQuadrature{T,N,M}}
+end
+export Quadrature
+
+LazyTensors.domain_size(Q::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
+
+function LazyTensors.apply(Q::Quadrature{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim}
+    error("not implemented")
+end
+
+LazyTensors.apply_transpose(Q::Quadrature{Dim,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where {Dim,T} = LazyTensors.apply(Q,v,I)
+
+@inline function LazyTensors.apply(Q::Quadrature{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
+    @inbounds q = apply(Q.H[1], v , I[1])
+    return q
+end
+
+@inline function LazyTensors.apply(Q::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 = apply(Q.H[1], vx , I[1])
+    # Quadrature in y-direction
+    @inbounds vy = view(v, Int(I[1]), :)
+    @inbounds qy = apply(Q.H[2], vy, I[2])
+    return qx*qy
+end
+
+"""
+    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the quadrature operator `H` of Dim dimension as a TensorMapping
+"""
+struct DiagonalQuadrature{T<:Real,N,M} <: TensorOperator{T,1}
+    h::T # The grid spacing could be included in the stencil already. Preferable?
+    closure::NTuple{M,T}
+    #TODO: Write a nice constructor
+end
+
+@inline function LazyTensors.apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
+    return @inbounds apply(H, v, I[1])
+end
+
+LazyTensors.apply_transpose(H::Quadrature{Dim,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H,v,I)
+
+@inline LazyTensors.apply(H::DiagonalQuadrature, v::AbstractVector{T}, i::Index{Lower}) where T
+    return @inbounds H.h*H.closure[Int(i)]*v[Int(i)]
+end
+@inline LazyTensors.apply(H::DiagonalQuadrature,v::AbstractVector{T}, i::Index{Upper}) where T
+    N = length(v);
+    return @inbounds H.h*H.closure[N-Int(i)+1]v[Int(i)]
+end
+
+@inline LazyTensors.apply(H::DiagonalQuadrature, v::AbstractVector{T}, i::Index{Interior}) where T
+    return @inbounds H.h*v[Int(i)]
+end
+
+function LazyTensors.apply(H::DiagonalQuadrature,  v::AbstractVector{T}, index::Index{Unknown}) where T
+    N = length(v);
+    r = getregion(Int(index), closuresize(H), N)
+    i = Index(Int(index), r)
+    return LazyTensors.apply(H, v, i)
+end
+export LazyTensors.apply
+
+function closuresize(H::DiagonalQuadrature{T<:Real,N,M}) where {T,N,M}
+    return M
+end

--- a/SbpOperators/src/laplace/laplace.jl	Tue Jun 23 17:31:50 2020 +0200
+++ b/SbpOperators/src/laplace/laplace.jl	Tue Jun 23 17:32:54 2020 +0200
@@ -2,8 +2,8 @@
     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 simply consists of a tuple of the 1D
-Laplace tensor operator as defined by ConstantLaplaceOperator.
+The multi-dimensional tensor operator consists of a tuple of 1D SecondDerivative
+tensor operators.
 """
 struct Laplace{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
     D2::NTuple(Dim,SecondDerivative{T,N,M,K})
@@ -17,20 +17,23 @@
     error("not implemented")
 end
 
+function LazyTensors.apply_transpose(L::Laplace{Dim,T}, v::AbstractArray{T,Dim}, I::NTuple{Dim,Index}) where {T,Dim} = LazyTensors.apply(L, v, I)
+
 # u = L*v
 function LazyTensors.apply(L::Laplace{1,T}, v::AbstractVector{T}, I::NTuple{1,Index}) where T
-    return apply(L.D2[1],v,I)
+    @inbounds u = apply(L.D2[1],v,I)
+    return u
 end
 
 
 @inline function LazyTensors.apply(L::Laplace{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
     # 2nd x-derivative
     @inbounds vx = view(v, :, Int(I[2]))
-    @inbounds uᵢ = apply(L.D2[1], vx , (I[1],)) #Tuple conversion here is ugly. How to do it? Should we use indexing here?
+    @inbounds uᵢ = apply(L.D2[1], vx , I[1])
 
     # 2nd y-derivative
     @inbounds vy = view(v, Int(I[1]), :)
-    @inbounds uᵢ += apply(L.D2[2], vy , (I[2],)) #Tuple conversion here is ugly. How to do it?
+    @inbounds uᵢ += apply(L.D2[2], vy , I[2])
 
     return uᵢ
 end
@@ -42,31 +45,6 @@
 boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
 export quadrature
 
-# At the moment the grid property is used all over. It could possibly be removed if we implement all the 1D operators as TensorMappings
-"""
-    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
-
-Implements the quadrature operator `H` of Dim dimension as a TensorMapping
-"""
-struct Quadrature{Dim,T<:Real,N,M,K} <: TensorOperator{T,Dim}
-    op::D2{T,N,M,K}
-    grid::EquidistantGrid{Dim,T}
-end
-export Quadrature
-
-LazyTensors.domain_size(H::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
-
-@inline function LazyTensors.apply(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T
-    N = size(H.grid)
-    # Quadrature in x direction
-    @inbounds q = apply_quadrature(H.op, spacing(H.grid)[1], v[I] , I[1], N[1])
-    # Quadrature in y-direction
-    @inbounds q = apply_quadrature(H.op, spacing(H.grid)[2], q, I[2], N[2])
-    return q
-end
-
-LazyTensors.apply_transpose(H::Quadrature{2,T}, v::AbstractArray{T,2}, I::NTuple{2,Index}) where T = LazyTensors.apply(H,v,I)
-
 
 """
     InverseQuadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}