An inexact Newton method for solving complementarity problems in hydrodynamic lubrication

We present an iterative procedure based on a damped inexact Newton iteration for solving linear complementarity problems. We introduce the method in the framework of a popular problem arising in mechanical engineering: the analysis of cavitation in lubricated contacts. In this context, we show how the perturbation and the damping parameter are chosen in our method and we prove the global convergence of the entire procedure. A Fortran implementation of the method is finally analyzed. First, we validate the procedure and analyze all its components, performing also a comparison with a recently proposed technique based on the Fischer–Burmeister–Newton iteration. Then, we solve a 2D problem and provide some insights on an efficient implementation of the method exploiting routines of the Lapack and of the PETSc packages for the solution of inner linear systems.