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.

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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

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Assembly Languages
  • Cartesian Coordinates
  • Computations
  • Computer Science
  • Differential Equations
  • Embedding
  • Equations
  • Grids
  • Iterations
  • Language
  • Linear Systems
  • Measurement
  • Military Research
  • Partial Differential Equations
  • Sparse Matrix
  • Three Dimensional
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematics or Statistics
  • Parallel and Distributed Computing.

Technology Areas

  • Space