A parallel adaptive method for pseudo-arclength continuation

Abstract

We parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length selection and inexact prediction. Prior attempts to parallelize pseudo-arclength continuation are typically based on parallelization of the linear solver which leads to completely solver-dependent software. In contrast, our method is completely independent of the internal solver and therefore applicable to a large domain of problems. Our software is easy to use and does not require the user to have extensive prior experience with High Performance Computing; all the user needs to provide is the implementation of the corrector step. When corrector steps are costly or continuation curves are complicated, we observe up to sixty percent speed up with moderate numbers of processors. We present results for a synthetic problem and a problem in turbulence.