A New Technique for 3-D Domain Decomposition on Multicomputers which Reduces Message-Passing

Algorithms for many geometric and physical algorithms rely on a decomposition of 3-D space. The cubical decomposition that is typically used can lead to costly communication overheads when implemented on multicomputers since each cubical cell is adjacent to, and may interact with, as many as 26 neighbouring cells. We explore an alternate decomposition based on truncated octahedra that, along with other advantages, reduces message passing. The cost of implementing the communication structure resulting from this decomposition on low degree regular communication networks is studied. We show that this structure can be embedded with dilation 2 onto a 3-D mesh. A dilation 3 embedding onto a 4-regular graph is also presented.