Two-dimensional block partitionings for the parallel sparse Cholesky factorization

This paper presents a discussion on 2D block mappings for the sparse Cholesky factorization on parallel MIMD architectures with distributed memory. It introduces the fan-in algorithm in a general manner and proposes several mapping strategies. The grid mapping with row balancing, inspired by Rothberg's work (1994), is proved to be more robust than the original fan-out algorithm. Even more efficient is the proportional mapping, as shown by the experiments on a 32 processor IBM SP1 and on a Cray T3D. Subforest-to-subcube mappings are also considered and give good results on the T3D. This revised version was published online in August 2006 with corrections to the Cover Date.