Normalized Convergence Rates for the PSMG Method

Abstract

In a previous paper we have introduced an efficient multiscale PDE solver for massively parallel architectures, which called Parallel Superconvergent Multigrid, or PSMG. In this paper we derive sharp estimates for the normalized work involved in PSMG solution - the number of parallel arithmetic and communication operations required per digit of error reduction. PSMG is shown to provide fourth-order accurate solutions of Poisson type equations at convergence rates of .00165 per single relaxation iteration, and with parallel operation counts per grid level of 5.75 communications and 8.62 computations for each digit of error reduction. We show that PSMG requires less than half as many arithmetic and one fifth as many communication operations, per digit of error reduction, as a parallel standard multigrid algorithm (RBTRB) presented recently by N. Decker.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1990
Accession Number
ADA231311

Entities

People

  • Oliver A. Mcbryan
  • Paul O. Frederickson

Organizations

  • Research Institute for Advanced Computer Science

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Arithmetic
  • Boundaries
  • Computations
  • Computer Science
  • Computers
  • Convergence
  • Equations
  • Frequency
  • Grids
  • Interpolation
  • Iterations
  • Notation
  • Poisson Equation
  • Residuals
  • Standards

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  • Computational Fluid Dynamics (CFD)
  • Computer Programming and Software Development.
  • Linear Algebra