Efficient Parallel Numerical Solver for the Elastohydrodynamic Reynolds–Hertz Problem

Abstract

[Abstract] This work presents a parallel version of a complex numerical algorithm for solving an elastohydrodynamic piezoviscous lubrication problem studied in tribology. The numerical algorithm combines regula falsi, fixed point techniques, finite elements and duality methods. The execution of the sequential program on a workstation requires significant CPU time and memory resources. Thus, in order to reduce the computational cost, we have applied parallelization techniques to the most costly parts of the original source code. Some blocks of the sequential code were also redesigned for the execution on a multicomputer. In this paper, our parallel version is described in detail, execution times that show its efficiency in terms of speedups are presented, and new numerical results that establish the convergence of the algorithm for higher imposed load values when using finer meshes are depicted. As a whole, this paper tries to illustrate the difficulties involved in parallelizing and optimizing complex numerical algorithms based on finite elements.