Efficient implementation of numerical methods for solving bearing cavitation problems using symmetric system solvers

Since the successful application of the Elrod method to the Jakobsson–Floberg–Olsson (JFO) theory, many new alternative methods have been presented. In particular, over the past decade, the efficiency of cavitation algorithms has significantly improved, as demonstrated by the Fischer-Burmeister based unconstrained optimization methods and the modulus-based methods based on the generalized absolute value equation. This paper briefly reviewed the principles of these algorithms and compared their computational efficiency. Pseudocodes were included to illustrate their implementation. Taking advantage of linear direct solvers, a novel equivalent symmetric matrix equation was presented to promote the efficiency of these algorithms. A case of a surface-textured thrust bearing with multiple dimples was studied. The results showed that the method can save more than 2–5 times the computing time.