On a multilevel preconditioning module for unstructured mesh Krylov solvers: Two-level Schwarz

Abstract

Multilevel methods offer the best promise to attain both fast convergence and parallel efficiency in the numerical solution of parabolic and elliptic partial differential equations. Unfortunately, they have not been widely used in part because of implementation difficulties for unstructured mesh solvers. To facilitate use, a multilevel preconditioner software module, ML, has been constructed. Several methods are provided requiring relatively modest programming effort on the part of the application developer. This report discusses the implementation of one method in the module: a two-level Krylov-Schwarz preconditioner. To illustrate the use of these methods in computational fluid dynamics (CFD) engineering applications, we present results for 2D and 3D CFD benchmark problems. Copyright © 2002 John Wiley & Sons, Ltd.