Minor points:

• The authors refer to “compile-time mapping”. It is unclear in what sense the data mapping could be “compile time”. Are languages envisaged which could represent complex grids as compile-time constant expressions?

• Section 2, notation: Why D^{h}? (What is the superscript for?)

• The notation

{D_{i}^{h}}_{i=1}^{P}

is unfamiliar. Why not use a standard notation like {D_{i}^{h} | 1 ≤ i ≤ P }, or simply {D_{i}^{h}}?

• Section 5.1, para 3: “the total message latency is proportional to the submesh connectivity”. Please explain.

I found the conclusion—that the most naive scheme works as well as the more complicated ones—appealing. I think it may be controversial.