Multi-pass mapping schemes for parallel sparse matrix computations

Authors:
Konrad Malkowski;Padma Raghavan
Affiliations:
Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA;Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

Citing 11
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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.