Rudimentary considerations for effective quasi-Newton updates in nonlinear finite element analysis

Abstract The quasi-Newton update method is employed as an option to accelerate the convergence and improve the overall effectiveness of the modified Newton's iteration. When the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method was implemented and tested in the general-purpose finite element analysis program MSC/NASTRAN, our experience showed that the implementation method and adjustment of parameters had a significant impact on the program's performance. This paper reviews the rudiments of the BFGS update method and proposes an efficient implementation scheme based on extensive testing and parametric studies.