Multigrid methods for EHD problems

                       Elyas Nurgat and Martin Berzins
                                 ------------
                  School of Computer Studies and CFD Centre 
                  The University of Leeds, Leeds LS2 9JT, UK

           email: nurgat@scs.leeds.ac.uk    martin@scs.leeds.ac.uk

                                   ABSTRACT

The numerical solution of Elasto-Hydrodynamic (EHD) problems involves the
calculation of lubricant pressure and film thickness through the coupled
Reynolds (differential) and the Elastic Deformation (integral) equations.
This highly nonlinear system of equations has a dense sparsity pattern and
thus poses a formidable computational challenge for direct Newton solvers.
Multigrid methods, Venner and Lubrecht [1], provide one efficient method for
EHD problems.  A recent alternative is the powerful Effective Influence Newton
Method of Wang [2] which is based on the combination of more traditional
iterative methods with a greatly reduced Jacobian matrix.  This presentation
compares the strengths and weaknesses of these two methods and so constructs a
robust algorithm which has the best properties of both methods.  This new
algorithm uses the FDMG software [3] as a starting point and includes the
extensions used to couple the iterations of the differential and integral
parts.  Numerical results on demanding test problems show the success of the
new approach and suggest future developments needed to produce robust
multigrid solvers for this demanding class of problems.

References
----------
[1] C. H. Venner, A. A. Lubrecht.  Numerical simulation of a transverse ridge
in a circular EHL contact under rolling/sliding, Journal of Tribology, October
1994, Volume 116.

[2] D. Wang.  Elastohydrodynamic lubrication of point contacts for layers of
`soft' solids and for `monolithic' `hard' materials in the transient bouncing
ball problems, Ph.D.  thesis, University of Leeds, August 1994.

[3] G. J. Shaw.  FDMG multigrid software, Version 3.0.