Efficient parallel numerical solver for the elastohydrodynamic Reynolds-Hertz problem

This work presents a parallel version of a complex numerical algorithm for solving an el-astohydrodynamic piezoviscous lubrication problem studied in tribology. The numerical algorithm combines regula falsi, ®xed point techniques, ®nite elements and duality methods. The execution of the sequential program on a workstation requires signi®cant CPU time and memory resources. Thus, in order to reduce the computational cost, we have applied parall-elization 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 eciency in terms of speedups are presented, and new numerical results that establish the convergence of the algorithm for higher imposed load values when using ®ner meshes are depicted. As a whole, this paper tries to illustrate the diculties involved in parallelizing and optimizing complex numerical algorithms based on ®nite elements.