Projected AQIF Parallel Algorithm for Solving EHL Line and Point Contact Problems: Parallel Computing

Abstract

A novel parallel approach is developed for solving EHL line and point contact problems. The main motivation of algorithm comes from solving a discrete variational inequality problems on parallel computer by introducing a novel solver named as projected alternate quadrant interlocking factorization (PAQIF). The PAQIF has the property that when complementarity system

$$\displaystyle \begin{aligned} L_{0} x \ge b,\\ x \ge 0,\\ x(L_{0}x - b) = 0 \end{aligned} $$

is banded with semibandwidth β _v, the space generated by e _i., e _n−i; 1 ≤ i ≤ β _v is invariant under the transformation W ⁻¹. Hence PAQIF is combined with partitioned scheme that renders a divide and conquer algorithm for solution of the banded linear complementarity system. The idea is extended to EHL problems by developing suitable preconditioner in the form of banded matrix.