Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch

TL;DR

This paper presents a new parallel implementation of a two-level nonlinear Schwarz method within the FROSch framework, demonstrating improved convergence for challenging nonlinear problems.

Contribution

It introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on FROSch, enhancing nonlinear convergence in complex problems.

Findings

Preliminary results show improved convergence for nonlinear diffusion problems.

Effective parallel implementation demonstrated on 2D nonlinear elasticity.

Framework integrated into Sandia's Trilinos library.

Abstract

Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia's Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large deformations.