Combining Nonlinear FETI-DP Methods and Quasi-Newton Methods using an SQP Approach

TL;DR

This paper presents a novel approach combining nonlinear FETI-DP methods with Quasi-Newton techniques via SQP to efficiently solve nonlinear finite element problems, demonstrating improved convergence through Hessian updates in structural mechanics simulations.

Contribution

It introduces a new integration of nonlinear FETI-DP and Quasi-Newton methods using SQP, with strategies for Hessian approximation and restart to enhance convergence.

Findings

Numerical experiments show accelerated convergence.

Effective parallel solution for nonlinear structural problems.

Hessian recomputation improves solution efficiency.

Abstract

The combination of nonlinear FETI-DP (Dual Primal Finite Element Tearing and Interconnecting) and Quasi-Newton methods using a sequential quadratic programming (SQP) approach is considered. Nonlinear FETI-DP methods are parallel iterative solution methods for nonlinear finite element problems, based on divide and conquer, using Lagrange multipliers. In the method, we use Quasi-Newton approximations of Hessian for the quadratic programs, where the initial approximation uses the exact Hessian. To accelerate the convergence, we recompute the initial Hessian and restart the Quasi-Newton approximation. We provide numerical experiments using homogeneous model problems from nonlinear structural mechanics.