On vectorizing incomplete factorization and ssor preconditioners
The authors consider the problem of vectorizing the recursive calculations found in modified incomplete factorizations and SSOR preconditioners for the conjugate gradient method. They examine matrix problems derived from partial differential equations which are discretized on regular 2-D and 3-D grids, where the grid nodes are ordered in the natural ordering. By performing data dependency analyses of the computations, the authors show that there is concurrency in both the factorization and the forward and backsolves. The computations may be performed with an average vector length of O(n) on an n/sup 2/ or n/sup 3/ grid in two and three dimensions. Numerical studies on four model problems show that the conjugate gradient method using these vectorized implementations of the modified incomplete factorizations and SSOR preconditioners achieves overall speeds approaching 100 megaflops on a Cray X-MP/24 vector computer. Furthermore, these methods require considerably less overall execution time than diagonal scaling and no-fill red-black incomplete factorization preconditioners, both of which allow full vectorization but are not as convergent.
- Research Organization:
- Engineering Technology Applications, Boeing Computer Services, Seattle, WA 98124-0346
- OSTI ID:
- 5398435
- Journal Information:
- SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 9:1; ISSN SIJCD
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990210* -- Supercomputers-- (1987-1989)
990220 -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
COMPUTER CALCULATIONS
COMPUTERS
CRAY COMPUTERS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATRICES
NUMERICAL SOLUTION
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING
VECTOR PROCESSING