Performance investigation of quasi-Newton-based parallel nonlinear FEM for large-deformation elastic-plastic analysis over 100 thousand degrees of freedom

Quasi-Newton-based nonlinear finite element methods were extensively studied in the 1970s and 1980s. However, they have almost disappeared due to their poorer convergence performance than the Newton-Raphson method. An advantage of quasi-Newton methods over the Newton-Raphson method is shorter computational time even with a larger number of iterations. The speedup must grow as the number of degrees of freedom (DOFs) increases. Since computers and computational methods have been advancing steadily in the last 40 years, significant speedup can be expected at present. Therefore, we present a framework of a quasi-Newton-based parallel nonlinear finite element method consisting of a quasi-Newton method, implementation for parallel computing and a nonlinear material model. The advances of the present framework are a large number of DOFs and the use of a modern nonlinear material model. The number of DOFs exceeded 100 thousand in all analyses and reached one million in some analyses. This was enabled by the implementation of a quasi-Newton method for parallel computing and the use of a parallel sparse direct solver library. Note that, for more than several or ten million DOFs, an iterative linear solution method is generally preferred, resulting in the loss of the advantage of quasi-Newton methods. Furthermore, a modern finite-strain elastoplasticity material model with a realistic multilinear stress-strain curve was used in the present study, whereas an infinitesimal elastoplasticity model with a bilinear stress-strain curve was popular in the 1980s. Performance investigation of the present framework is given in the present paper. The quasi-Newton-based present framework achieved speedup of more than 30 times in modern large-deformation elastic-plastic analyses involving approximately one million DOFs, compared to the Newton-Raphson method.