--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/d2_2nd.txt	Thu Jan 10 14:57:18 2019 +0100
@@ -0,0 +1,13 @@
+# D2 order 2
+
+boundary_stencils
+1 -2 1
+
+inner_stencil
+1 -2 1
+
+e
+1
+
+d1
+-3/2 2 -1/2

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/d2_4th.txt	Thu Jan 10 14:57:18 2019 +0100
@@ -0,0 +1,16 @@
+# D2 order 4
+
+boundary_stencils
+     2    -5       4      -1     0     0
+     1    -2       1       0     0     0
+ -4/43 59/43 -110/43   59/43 -4/43     0
+ -1/49     0   59/49 -118/49 64/49 -4/49
+
+inner_stencil
+-1/12     4/3  -5/2   4/3 -1/12
+
+e
+1
+
+d1
+-11/6 3 -3/2 1/3
\ No newline at end of file

--- a/diffOp.jl	Thu Jan 10 14:55:57 2019 +0100
+++ b/diffOp.jl	Thu Jan 10 14:57:18 2019 +0100
@@ -29,7 +29,7 @@
 end
 
 # u = L*v
-function apply(L::Laplace1D, u::AbstractVector, v::AbstractVector)
+function apply!(L::Laplace1D, u::AbstractVector, v::AbstractVector)
     N = closureSize(L.op)
     M = length(v)
 

--- a/grid.jl	Thu Jan 10 14:55:57 2019 +0100
+++ b/grid.jl	Thu Jan 10 14:57:18 2019 +0100
@@ -133,4 +133,10 @@
     end
 end
 
+# Evaluate function f on the grid g
+function evalOn(g::Grid, f::Function)
+    F(x) = f(x...)
+    return F.(points(g))
 end
+
+end

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/h_2nd.txt	Thu Jan 10 14:57:18 2019 +0100
@@ -0,0 +1,7 @@
+# H order 2
+
+closure
+1/2
+
+inner_stencil
+1

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/h_4th.txt	Thu Jan 10 14:57:18 2019 +0100
@@ -0,0 +1,7 @@
+# H order 4
+
+closure
+17/48 59/48 43/48 49/48
+
+inner_stencil
+1
\ No newline at end of file

--- a/sbpD2.jl	Thu Jan 10 14:55:57 2019 +0100
+++ b/sbpD2.jl	Thu Jan 10 14:57:18 2019 +0100
@@ -1,4 +1,3 @@
-
 struct D2{T}
     quadratureClosure::Vector{T}
     innerStencil::Stencil
@@ -9,4 +8,66 @@
 
 function closureSize(D::D2)::Int
     return length(quadratureClosure)
-end
\ No newline at end of file
+end
+
+function readOperator(D2fn, Hfn)
+    d = readSectionedFile(D2fn)
+    h = readSectionedFile(Hfn)
+
+    # Create inner stencil
+    innerStencilWeights = stringToVector(Float64, d["inner_stencil"][1])
+    width = length(innerStencilWeights)
+    r = (-div(width,2), div(width,2))
+
+    innerStencil = Stencil(r, innerStencilWeights)
+
+    # Create boundary stencils
+    boundarySize = length(d["boundary_stencils"])
+    closureStencils = Vector{Stencil}()
+
+    for i ∈ 1:boundarySize
+        stencilWeights = stringToVector(Float64, d["boundary_stencils"][i])
+        width = length(stencilWeights)
+        r = (1-i,width-i)
+        push!(closureStencils,Stencil(r, stencilWeights))
+    end
+
+    d2 = D2(
+        stringToVector(Float64, h["closure"][1]),
+        innerStencil,
+        closureStencils,
+        stringToVector(Float64, d["e"][1]),
+        stringToVector(Float64, d["d1"][1]),
+    )
+
+    return d2
+end
+
+
+function readSectionedFile(filename)::Dict{String, Vector{String}}
+    f = open(filename)
+    sections = Dict{String, Vector{String}}()
+    currentKey = ""
+
+    for ln ∈ eachline(f)
+        if ln == "" || ln[1] == '#' # Skip comments and empty lines
+            continue
+        end
+
+        if isletter(ln[1]) # Found start of new section
+            if ~haskey(sections, ln)
+                sections[ln] =  Vector{String}()
+            end
+            currentKey = ln
+            continue
+        end
+
+        push!(sections[currentKey], ln)
+    end
+
+    return sections
+end
+
+function stringToVector(T::DataType, s::String)
+    return T.(eval.(Meta.parse.(split(s))))
+end

--- a/stencil.jl	Thu Jan 10 14:55:57 2019 +0100
+++ b/stencil.jl	Thu Jan 10 14:57:18 2019 +0100
@@ -24,9 +24,9 @@
     end
 end
 
-function apply(s::Stencil, v::AbstractVector, i::Int)
-    w = zero(v[0])
-    for j ∈ i+(s.range[1]:s.range[2])
+function apply(s::Stencil, v::AbstractVector, i::Int; stride::Int = 1)
+    w = zero(eltype(v))
+    for j ∈ i .+ stride.*(s.range[1]:s.range[2])
         w += v[j]
     end
     return w