Iterative Methods

Human Capital and Mobility (HCM)

Iterative Methods
In recent years, interest has grown considerably in developing effective iterative methods for computing solutions to large linear systems arising from 3-D problems in basic science and engineering. For many of these problems, it is in fact the solution of these systems which is computationally the most difficult aspect of the simulation. Further, vector and parallel supercomputers now provide unprecedented computational power and offer the possibility of performing new and extremely large-scale simulations. Therefore, the development of faster and more robust iterative solvers and preconditioners which can be efficiently mapped to a variety of computer architectures is of fundamental importance in that it will be of great assistance to scientists and engineers throughout many disciplines.

Goals
In conjunction with the Human Capital and Mobility program, we are carrying out the study, development and analysis of a variety of iterative methods and preconditioners applied to challenging problems of significant importance in both industrial and academic worlds. As part of the HCM project, we have established a network of recognized leaders in the area of scientific computing. The network consists of experts in direct solvers, iterative solvers, preconditioning methods, finite element techniques, and computational fluid dynamics. The primary goal of the project is the development of new iterative methods and preconditioners for highly nonsymmetric and/or highly indefinite problems.

Results
Important results have been achieved concerning the error analysis of Krylov subspace methods (including a detailed study of stopping criteria), the development of new efficient hybrid iterative solvers for indefinite and nonsymmetric problems, the analysis and implementation of parallel block iterative schemes for heterogeneous computing environments, and the application of such innovative techniques to several difficult problems, especially in CFD. These activities have been documented in numerous published papers and research reports. The project started in January 1994 and is scheduled to end in September 1996.

Consortium
Partners in this project are CEA (France), CERFACS, Dassault Aviation (France), IAN-CNR Pavia (Italy), Utrecht University (the Netherlands) and CRS4 (Italy).

An HCM Meeting on Iterative Methods was held at CERFACS, November 7-8, 1994.

Local contact: Michele Benzi (benzi@cerfacs.fr)