Multi-pass Mapping Schemes for Parallel Sparse Matrix Computations

Abstract

AbstractConsider 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.KeywordsSparse MatrixCholesky FactorizationProportional MappingNest DissectionFactorization StepThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.