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

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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:
CreatorsEmailORCID
Heinlein, Alexanderalexander.heinlein@uni-koeln.deUNSPECIFIED
Lanser, Martinmartin.lanser@uni-koeln.deUNSPECIFIED
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
Subjects: Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
Nonlinear Domain Decomposition MethodsEnglish
Overlapping SchwarzEnglish
Energy minimizing coarse spaceEnglish
ASPINEnglish
RASPENEnglish
MsFEMEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Central Institutions / Interdisciplinary Research Centers > Center for Data and Simulation Science
Language: English
Date: 16 November 2018
URI: http://kups.ub.uni-koeln.de/id/eprint/9015

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