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RESEARCH PAPERS

Accelerating Vector Iteration Methods

[+] Author and Article Information
M. Papadrakakis

Institute of Structural Analysis and Aseismic Research, National Technical University, Athens (147) Greece

J. Appl. Mech 53(2), 291-297 (Jun 01, 1986) (7 pages) doi:10.1115/1.3171754 History: Received December 21, 1984; Revised October 28, 1985; Online July 21, 2009

Abstract

This paper describes a technique for accelerating the convergence properties of iterative methods for the solution of large sparse symmetric linear systems that arise from the application of finite element method. The technique is called partial preconditioning process (PPR) and can be combined with pure vector iteration methods, such as the conjugate gradient, the dynamic relaxation, and the Chebyshev semi-iterative methods. The proposed triangular splitting preconditioner combines Evans’ SSOR preconditioner with a drop-off tolerance criterion. The (PPR) is attractive in a FE framework because it is simple and can be implemented at the element level as opposed to incomplete Cholesky preconditioners, which require a sparse assembly. The method, despite its simplicity, is shown to be more efficient on a set of test problems for certain values of the drop-off tolerance parameter than the partial elimination method.

Copyright © 1986 by ASME
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