Paper Info
Title
Preconditioning strategies for linear systems arising in tire design
Abstract
This paper discusses the application of iterative methods for solving linear systems arising in static tire equilibrium computation. The heterogeneous material properties, nonlinear constraints, and a three dimensional finite element formulation make the linear systems arising in tire design difficult to solve by iterative methods, An analysis of the matrix characteristics helps understand this behaviour, This paper focuses on two preconditioning techniques: a variation of an incomplete LU factorization with threshold and a multilevel recursive solver. We propose to adapt these techniques in a number of ways to work for a class of realistic applications. In particular, it was found that these preconditioners improve convergence only when a rather large shift value is added to the matrix diagonal. A combination of other techniques such as filtering of small entries, pivoting in preconditioning, and a special way of defining levels for the multilevel recursive solver are shown to make these preconditioning strategies efficient for problems in fire design, We compare these techniques and assess their applicability when the linear system difficulty varies for the same class of problems, Copyright (C) 2000 John Whey & Sons, Ltd.
Year
DOI
Venue
2000
10.1002/1099-1506(200010/12)7:7/8<743::AID-NLA222>3.0.CO;2-O
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
incomplete LU factorization,multilevel preconditioning,ill-conditioned linear systems,generalized minimum residual method
Convergence (routing),Mathematical optimization,Nonlinear system,Linear system,Iterative method,Matrix (mathematics),Finite element method,Incomplete LU factorization,Solver,Mathematics
Journal
Volume
Issue
ISSN
7
7-8
1070-5325
Citations 
PageRank 
References 
9
0.84
7
Authors
4
Name
Order
Citations
PageRank
Maria Sosonkina18416.96
John T. Melson290.84
Yousef Saad31940254.74
Layne T. Watson41253290.45