Universität zu Köln

Heinlein, Alexander and Lanser, Martin (2018). Coarse Spaces for Nonlinear Schwarz Methods on Unstructured Grids. Technical Report.

Preview

PDF CDS_TR-2018-6.pdf Download (2MB) | Preview

Abstract

In recent years, nonlinear domain decomposition (DD) methods for the solution of nonlinear partial differential equations as, e.g., ASPIN (Additive Schwarz Preconditioned Inexact Newton) or Nonlinear-FETI-DP (Nonlinear - Finite Element Tearing and Interconnecting - Dual-Primal), became popular. For several model problems, these approaches outperform classical inexact Newton methods, where a corresponding linear DD method is used to solve the linearized problems, in terms of linear and nonlinear iteration counts and time to solution. As in the linear case, in nonlinear DD methods, an appropriate coarse space is often necessary for robustness and numerical scalability. In this paper, a new multiplicative implementation of a coarse space for ASPIN as well as the related RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) method is suggested. Additionally, several coarse spaces, which are also applicable for unstructured meshes and domain decompositions, are suggested. Robustness and numerical scalability is shown for different homogeneous and heterogeneous p-Laplace problems in two spatial dimensions.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de UNSPECIFIED UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-90158
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2018,6
Date:	16 November 2018
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Nonlinear Domain Decomposition Methods English Overlapping Schwarz English Energy minimizing coarse space English ASPIN English RASPEN English MsFEM English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9015