Parallel solution of unstructured, sparse systems of linear equations
- 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; TRN: 94:007584-0082
- Resource Relation:
- Conference: 6. Society for Industrial and Applied Mathematics (SIAM) conference on parallel processing for scientific computing, Norfolk, VA (United States), 21-24 Mar 1993; Other Information: PBD: 1993; Related Information: Is Part Of Parallel processing for scientific computing: Proceedings. Volume 1; Sincovec, R.F.; Leuze, M.R. [eds.] [Oak Ridge National Lab., TN (United States)]; Keyes, D.E. [ed.] [Yale Univ., New Haven, CT (United States)]; Petzold, L.R. [ed.] [Minnesota Univ., Minneapolis, MN (United States)]; Reed, D.A. [ed.] [Illinois Univ., Chicago, IL (United States)]; PB: 522 p.
- Country of Publication:
- United States
- Language:
- English
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