A new wavelet transform preconditioner for iterative solution of elastohydrodynamic lubrication problems

Abstract

We develop a novel preconditioning strategy, based on a non-standard, Discrete Wavelet Transform (DWT), for the dense, non-symmetric, linear systems that must be solved when Newton's method is used in the solution of Elastohydrodynamic Lubrication (EHL) problems. Simple band preconditioners and sparse preconditioners based on standard DWT have been found to be of limited value for EHL problems, since they may be singular, give poor convergence or be expensive to apply. We present algorithms for preconditioner design based on detecting non-smooth diagonal bands within an otherwise smooth matrix and applying a non-standard DWT to compress the part of the matrix away from the band. We illustrate, by numerical examples, the improvements that can be made when our methods are used.

Keywords:

• Preconditioning
• GMRES
• wavelet transform
• dense matrices
• elastohydrodynamic lubrication

C.R. Categories:

• G.1.3
• G.1.5
• G.1.8

^∗Supported by the Engineering and Physical Sciences Research Council, UK.

^∗Supported by the Engineering and Physical Sciences Research Council, UK.

Notes

^∗Supported by the Engineering and Physical Sciences Research Council, UK.