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arXiv · 2410.24138

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

Alexander Heinlein·Kyrill Ho·Axel Klawonn·Martin Lanser
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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.

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Alexander Heinlein, Kyrill Ho, Axel Klawonn, Martin Lanser. 2024-10-31. Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch. https://arxiv.org/abs/2410.24138

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