ideas sketch for fusion

src/mesh/column_mesh.jl

@@ -236,6 +236,12 @@ struct CenterFiniteDifferenceMesh{T,C} <: AbstractMesh
 end
 =# 
 
+# TODO:
+# - add interval domain
+# - move order out of Mesh?
+# - 
+# 
+
 """
     ColumnMesh
 
@@ -255,6 +261,7 @@ struct ColumnMesh{S, F, C, ICF, ∇CF, ∇FC, ∇FF, O} <: AbstractMesh
     order::O
 end
 
+
 function ColumnMesh{S}(
     face::F,
     cent::C,
@@ -539,6 +546,15 @@ function ∇_cent_to_face_operator(
     return SparseMatrix{n_rows, n_cols}(sparse_mat)
 end
 
+
+struct Gradient{From,To} <: Operator{From,To}
+end
+
+function full_stencil(Gradient{Cent,Face}, mesh)
+
+end 
+
+
 """
     ∇_face_to_cent_operator(::OrderOfAccuracy{2}, Δh_face::AbstractVector)
 
@@ -603,6 +619,60 @@ function ∇_face_to_face_operator(
     return SparseMatrix{n_rows,n_rows}(sparse_mat)
 end
 
+#=
+
+TODO: start sketching out ideas for fusing operations
+
+# A is on a center mesh with halo 1
+# v is on a face mesh with halo 0
+Face(A) # interpolate to face mesh with halo 0
+v*Face(A) # elementwise multiplication (face mesh halo 0)
+Gradient(v*Face(A)) # center mesh with halo 0
+map(Gradient(v*Face(A)), column) # gradient on to CenterColumnMesh
+
+
+#         center  face
+# ----             -2
+#          -1
+# ----             -1
+# Halo      0
+# ====              0
+#           1
+# ----
+#           2
+# ....
+#           n
+# ====              n    
+# Halo     n+1
+# ----             n+1
+
+
+#         center  face
+# ----              1
+#           1
+# ----              h
+# Halo      h
+# ====             h+1
+#          h+1
+# ----
+#           4
+# ....
+#          n+h
+# ====            n+h+1   
+# Halo    n+h+1
+# ----            n+h+2
+
+for i = 1:n
+    face_a1 = (A[i-1] + A[i]) / 2
+    face_a2 = (A[i] + A[i+1]) / 2
+    va1 = v*face_a1
+    va2 = v*face_a2
+    (va2 - va1) / Δh
+end
+
+
+diff(field)[i] = (field[i] - field[i-1]) / deltaH
+=#
 
 #####
 ##### 2nd Dderivative operators