--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/DiffOps/DiffOps.jl	Fri Sep 25 13:06:02 2020 +0200
@@ -0,0 +1,100 @@
+module DiffOps
+
+using RegionIndices
+using SbpOperators
+using Grids
+using LazyTensors
+
+"""
+    DiffOp
+
+Supertype of differential operator discretisations.
+The action of the DiffOp is defined in the method
+    apply(D::DiffOp, v::AbstractVector, I...)
+"""
+abstract type DiffOp end
+
+function apply 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
+export apply!
+
+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
+export apply_region!
+
+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
+export apply_region_tiled!
+
+function apply(D::DiffOp, v::AbstractVector)::AbstractVector
+    u = zeros(eltype(v), size(v))
+    apply!(D,v,u)
+    return u
+end
+
+export apply
+
+"""
+A BoundaryCondition should implement the method
+    sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
+"""
+abstract type BoundaryCondition end
+
+
+end # module