On mapping data and computation for parallel sparse Cholesky factorization

Abstract

When performing the Cholesky factorization of a sparse matrix on a distributed-memory multiprocessor, the methods used for mapping the elements of the matrix and the operations constituting the factorization to the processors can have a significant impact on the communication overhead incurred. This paper explores how two techniques, one used when mapping dense Cholesky factorization and the other used when mapping sparse Cholesky factorization, can be integrated to achieve a communication-efficient parallel sparse Cholesky factorization. Two localizing techniques to further reduce the communication overhead are also described. The mapping strategies proposed here, as well as other previously proposed strategies fit into the unifying framework developed in this paper. Communication statistics for sample sparse matrices are included. >