Multi-pass mapping schemes for parallel sparse matrix computations

Abstract

Consider the solution of a large sparse linear system Ax = b on multiprocessors. A parallel sparse matrix factorization is required in a direct solver. Alternatively, if Krylov subspace iterative methods are used, then incomplete forms of parallel sparse factorization are required for preconditioning. In such schemes, the underlying parallel computation is tree-structured, utilizing task-parallelism at lower levels of the tree and data-parallelism at higher levels. The proportional heuristic has typically been used to map the data and computation to processors. However, for sparse systems from finite-element methods on complex domains, the resulting assignments can exhibit significant load-imbalances. In this paper, we develop a multi-pass mapping scheme to reduce such load imbalances and we demonstrate its effectiveness for a test suite of large sparse matrices. Our scheme can also be used to generate improved mappings for tree-structured applications beyond those considered in this paper. © Springer-Verlag Berlin Heidelberg 2005.