Parallel solution of unstructured, sparse systems of linear equations

Conference · Fri Dec 31 04:00:00 EST 1993

OSTI ID:55317

Jones, M T; Plassmann, P E ^[1]

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1. Argonne National Lab., IL (United States)

The computational kernel of many large-scale applications is the solution of sparse linear systems. In this paper we endorse a particular perspective: (1) in many applications, one is interested in solving as large a problem as can fit into the available memory of the machine, and (2) the underlying geometric structure of these applications in often three-dimensional or greater. These observations, and a simple back-of-the-envelope calculation, lead one to conclude that a parallel direct factorization method is in general not feasible for such problems, in terms of the space and time required. We have developed an approach to the iterative solution of sparse linear systems that ensures scalable performance. Central to our approach is a reordering of the matrix based on a coloring of the symmetric graph corresponding to the nonzero structure of the matrix, or a related graph. To determine this ordering, we use a recently developed parallel heuristic modified here by two graph reductions that improve the performance on advanced RISC processors.

• OSTI ID: 55317
• Report Number(s): DOE/ER/25151--1-Vol.1; CONF-930331--Vol.1
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPUTER ARCHITECTURE
FACTORIZATION
MATRICES
MEMORY MANAGEMENT
NUMERICAL SOLUTION
PARALLEL PROCESSING