Efficient implementation of a 3-dimensional ADI method on the iPSC/860

A comparison is made between several domain decomposition strategies for the solution of three-dimensional partial differential equations on a MIMD distributed memory parallel computer. The grids used are structured, and the numerical algorithm is alternating direction implicit (ADI). Important implementation issues regarding load balancing, storage requirements, network latency, and overlap of computations and communications are discussed. Results of the solution of the three-dimensional heat equation on the Intel iPSC/860 are presented for the three most viable methods. It is found that the Bruno-Cappello decomposition delivers optimal computational speed through an almost complete elimination of processor idle time, while providing good memory efficiency.