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

Fuente: arXiv
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Autori principali: Heinlein, Alexander, Ho, Kyrill, Klawonn, Axel, Lanser, Martin
Natura: Preprint
Pubblicazione: 2024
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author Heinlein, Alexander
Ho, Kyrill
Klawonn, Axel
Lanser, Martin
author_facet Heinlein, Alexander
Ho, Kyrill
Klawonn, Axel
Lanser, Martin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_24138
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch
Heinlein, Alexander
Ho, Kyrill
Klawonn, Axel
Lanser, Martin
Numerical Analysis
65F08, 65F10, 65H10, 65N22, 65N55
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.
title Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch
topic Numerical Analysis
65F08, 65F10, 65H10, 65N22, 65N55
url https://arxiv.org/abs/2410.24138