The efficient parallel iterative solution of large sparse linear systems
The development of efficient, general-purpose software for the iterative solution of sparse linear systems on a parallel MIMD computer requires an interesting combination of expertise. Parallel graph heuristics, convergence analysis, and basic linear algebra implementation issues must all be considered. In this paper, we discuss how we have incorporated recent results in these areas into a general-purpose iterative solver. First, we consider two recently developed parallel graph coloring heuristics. We show how the method proposed by Luby, based on determining maximal independent sets, can be modified to run in an asynchronous manner and give aa expected running time bound for this modified heuristic. In addition, a number of graph reduction heuristics are described that are used in our implementation to improve the individual processor performance. The effect of these various graph reductions on the solution of sparse triangular systems is categorized. Finally, we discuss the performance of this solver from the perspective of two large-scale applications: a piezoelectric crystal finite-element modeling problem, and a nonlinear optimization problem to determine the minimum energy configuration of a three-dimensional, layered superconductor model.
- Research Organization:
- Argonne National Lab., IL (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 7284734
- Report Number(s):
- ANL/CP-76726; CONF-9110404-1; ON: DE92018769
- Resource Relation:
- Conference: IMA workshop on sparse matrix computations: graph theory issues and algorithms, Minneapolis, MN (United States), 14-18 Oct 1991
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
MATRICES
ITERATIVE METHODS
ALGORITHMS
ARRAY PROCESSORS
NONLINEAR PROBLEMS
PARALLEL PROCESSING
SUPERCONDUCTIVITY
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
MATHEMATICAL LOGIC
PHYSICAL PROPERTIES
PROGRAMMING
990200* - Mathematics & Computers