Krylov Methods Preconditioned with Incompletely Factored Matrices on the CM-2

Abstract

The authors measured the performance of the components of the key iterative kernel of a preconditioned Krylov space iterative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. We timed sweeps over meshes, sparse triangular solves, and inner products on a large three dimensional model problem over a cube shape domain discretized with a seven point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. We also document rather dramatic deterioration in performance when these ideal conditions no longer apply. A synthetic workload generator was developed to produce and solve a parameterized family of increasingly irregular problems. Keywords: PARIS programming language; Assembly languages.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1989
Accession Number
ADA217403

Entities

People

  • Harry Berryman
  • Joel Saltz
  • Ravi Mirchandaney
  • William Gropp

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Assembly Languages
  • Cartesian Coordinates
  • Computer Science
  • Degradation
  • Differential Equations
  • Embedding
  • Equations
  • Geometry
  • Grids
  • High Level Languages
  • Iterations
  • Language
  • Measurement
  • Partial Differential Equations
  • Three Dimensional
  • Two Dimensional
  • Workload

Readers

  • Computational Fluid Dynamics (CFD)
  • Parallel and Distributed Computing.

Technology Areas

  • Space