A modified discrete scheme in the Ausas cavitation algorithm

In order to reduce the dependence of accuracy on the number of grids in the Ausas cavitation algorithm, a modified Ausas algorithm was presented. By modifying the mass-conservative Reynolds equation with the concept of linear complementarity problems (LCPs), the coupling of film thickness h and density ratio θ disappeared. The modified equation achieved a new discrete scheme that ensured a complete second-order-accurate central difference scheme for the full film region, avoiding a hybrid-order-accurate discrete scheme. A journal bearing case was studied to show the degree of accuracy improvement and the calculation time compared to a standard LCP solver. The results showed that the modified Ausas algorithm made the asymptotic and convergent behavior with the increase of nodes disappear and allowed for the use of coarse meshes to obtain sufficient accuracy. The calculation time of the modified Ausas algorithm is shorter than the LCP solver (Lemke's pivoting algorithm) for middle and large scale problems.

Path-following interior-point algorithm for monotone linear complementarity problems

This paper presents a path-following full-Newton step interior-point algorithm for solving monotone linear complementarity problems. Under new choices of the defaults of the updating barrier parameter [Formula: see text] and the threshold [Formula: see text] which defines the size of the neighborhood of the central-path, we show that the short-step algorithm has the best-known polynomial complexity, namely, [Formula: see text]. Finally, some numerical results are reported to show the efficiency of our algorithm.

Predictor-Corrector Interior-Point Algorithm for the General Linear Complementarity Problem

We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. We analyze the method proposed by Illés, Nagy and Terlaky [1] that extends the algorithm published by Potra and Liu [2] to general linear complementarity problems. A new method for determining the step size of the corrector direction is presented. Using the code implemented in the C++ programming language, we can solve large-scale problems based on sufficient matrices.

Implementation of the Full-Newton Step Algorithm for Weighted Linear Complementarity Problems

We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from the implementation point of view. We studied two variants, which differ only in the method of updating the parameter which characterizes the central path. The implementation was done in the C++ programming language and the obtained numerical results prove the efficiency of the proposed method.