Accession Number:

ADA222339

Title:

Parallel Performance of Domain-Decomposed Preconditioned Krylov Methods for PDEs with Adaptive Refinement

Descriptive Note:

Research rept.

Corporate Author:

YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE

Personal Author(s):

Report Date:

1990-04-01

Pagination or Media Count:

17.0

Abstract:

Preconditioners based on domain decomposition appear natural for the Krylov solution of implicitly discretized partial differential equations on parallel computers. Two-scale preconditioners involving independent subdomain solves and a global crosspoint system, as well as independent solves over interfaces of lower physical dimension have been known since the early 1980s to be near optimal in the sense of providing a bounded or at most logarithmically growing iteration count as the mesh is refined. However, overall computational complexity depends on the components of the preconditioner as well as the iteration count. The cost of exact subdomain solves grows superlinearly in arithmetic complexity, and that of the crosspoint system superlinearly in communication complexity. These factors make the preconditioner granularity and the choice of its components problem- and machine-dependent compromises. We present numerical experiments on both shared and distributed memory computers for convection-diffusion problems at modest Peclet or Reynolds numbers, without recirculation. Due to the development of boundary layers, these problems benefit from local mesh refinement, which is straightforward to accommodate within the domain decomposition framework in a locally uniform sense, but which introduces load balancing as a further consideration in choosing the granularity of the preconditioner.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE