Wavelet preconditioned Newton-Krylov method for elastohydrodynamic lubrication of line contact problems

In this paper, wavelet preconditioned Newton-Krylov method is used for the solution of elastohydrodynamic lubrication line contact problem. A finite difference method is used for the solution of EHL equations. The method comprise the non-linear Newton iteration on the outer loop and a linear iteration on the inside loop where wavelet based preconditioned GMRES (Generalized Minimum Residual Method of Krylov subspaces) is used. In the scheme, the Jacobian matrix-vector product is approximated accurately with much ease (without forming Jacobian explicitly and requiring no extra storage). It overcomes the limitations of conventional schemes for the investigation of the EHL problems, for computing pressure and film thickness distributions, covering wide range of physical parameters of practical interest. Also, the sensitivity of height and spread of pressure spike on load and other parameters are presented. To confirm and validate the solutions obtained, by the present method, are compared with those obtained by full approximation scheme of multigrid method.