Parallel sparse matrix computations: Wavefront minimization of sparse matrices. Final report for the period ending June 14, 1998
Gary Kumfert and Alex Pothen have improved the quality and run time of two ordering algorithms for minimizing the wavefront and envelope size of sparse matrices and graphs. These algorithms compute orderings for irregular data structures (e.g., unstructured meshes) that reduce the number of cache misses on modern workstation architectures. They have completed the implementation of a parallel solver for sparse, symmetric indefinite systems for distributed memory computers such as the IBM SP-2. The indefiniteness requires one to incorporate block pivoting (2 by 2 blocks) in the algorithm, thus demanding dynamic, parallel data structures. This is the first reported parallel solver for the indefinite problem. Direct methods for solving systems of linear equations employ sophisticated combinatorial and algebraic algorithms that contribute to software complexity, and hence it is natural to consider object-oriented design (OOD) in this context. The authors have continued to create software for solving sparse systems of linear equations by direct methods employing OOD. Fast computation of robust preconditioners is a priority for solving large systems of equations on unstructured grids and in other applications. They have developed new algorithms and software that can compute incomplete factorization preconditioners for high level fill in time proportional to the number of floating point operations and memory accesses.
- Research Organization:
- Old Dominion Univ., Dept. of Computer Science, Norfolk, VA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- FG05-94ER25216
- OSTI ID:
- 329566
- Report Number(s):
- DOE/ER/25216-T1; ON: DE99002142; TRN: AHC29912%%84
- Resource Relation:
- Other Information: PBD: Feb 1999
- Country of Publication:
- United States
- Language:
- English
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