Parallel Multigrid with ADI-like Smoothers in Two Dimensions

Craig C. Douglas
University of Kentucky
Department of Mathematics
715 Patterson Office Tower
Lexington, KY 40506-0027, USA

Sachit Malhotra
Yale Center for Parallel Supercomputing
Department of Computer Science
Yale University
New Haven, CT 06520-8285 USA

Martin H. Schultz
Department of Computer Science
Yale University
New Haven, CT 06520-8285 USA

Abstract

Alternating direction iterative (ADI) methods do not usually work well on parallel computers due to having to do parallel rather than serial tridiagonal solves in all but one dimension. An ADI-like iteration is developed and analyzed which does not require parallel tridiagonal solves in any direction, has at least as good of a convergence rate as ADI, and has almost no communication when imbedded as a smoother inside of a multigrid solver. Numerical experiments on a network of workstations and a parallel computer are included.


Contributed February 28, 1997.