Globalization of Nonlinear FETI-DP Domain Decomposition Methods Using an SQP Approach

Abstract

The globalization of Nonlinear FETI-DP (Dual Primal Finite Element Tearing and Interconnecting) methods is considered using a Sequential Quadratic Programming (SQP) approach. Nonlinear FETI-DP methods are parallel iterative solution methods for nonlinear finite element problems, based on divide and conquer, using Lagrange multipliers. In these methods, nonlinear elimination is an important ingredient to increase the convergence radius of Newton’s method. We prove standard globalization results for SQP-based globalization of Nonlinear FETI-DP, first for the case that the elimination set is empty. We then show how to combine nonlinear elimination and SQP-based globalization. The globalization preserves the block structure of the FETI-DP operator, which is the basis of the computational parallelism.Supporting numerical experiments using homogenous and heterogeneous model problems from nonlinear structural mechanics are provided. In the numerical experiments, we consider four standard choices of different elimination sets and different problem setups including stiff or almost incompressible inclusions in every subdomain. The numerical experiments illustrate that a good elimination set is important. However, the use of the SQP-based globalization approach presented here can improve the convergence of Nonlinear FETI-DP methods further, especially, if combined with a good choice of the elimination set.