Krylov Methods Preconditioned with Incompletely Factored Matrices on the CM-2
Abstract
This work measured what might be regarded best case timings for the sparse matrix vector multiplies, sparse triangular solves, and inner products that constitute the iterative portion of Krylov space programs that use incompletely factored matrices for preconditioning. Timings are performed on a large three dimensional model problem over a cube shaped domain discretized with a seven point template. The highest computational rate we achieved for the sparse triangular solve was 13.1 MFlops on 4K processors. This would correspond to 210 MFlops on an appropriately scaled problem on a 64K processor machine. The highest computational speed we achieved for a matrix vector multiply was 64.2 MFlops. This would correspond to a speed of 1027.0 MFlops in a 64K processor machine. Thus, for appropriately structured problems, the CM-2 achieves impressive computational speeds. The computational speed obtained from the CM-2 is compared.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1989
- Accession Number
- ADA206389
Entities
People
- Harry Berryman
- Joel Salz
- William Gropp
Organizations
- Yale University