Universität zu Köln

Bevilacqua, Tommaso ORCID: 0000-0002-0828-5018, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin ORCID: 0000-0002-4232-9395 (2026). Highly scalable two-level monolithic overlapping Schwarz preconditioners for thermo-elastoplastic laser beam welding problems. Computational Mechanics, 77 (2). pp. 485-499. Springer Nature. ISSN 0178-7675

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Abstract

A thermo-elastoplastic finite element approach is used to perform the simulation of a Laser Beam Welding (LBW) process. This results in a nonlinear, nonsymmetric saddle point multiphysics system, for which the nonlinearity is handled via the Newton method. The iterative solution of the arising linear system is accelerated by using robust and highly scalable, overlapping Schwarz domain decomposition preconditioners. It is well-known that a one-level method of this type is not scalable and therefore a second level has to be added. Therefore, the construction and numerical analysis of monolithic, two-level overlapping Schwarz preconditioners with different variants of the GDSW (Generalized Dryja–Smith–Widlund) coarse space are presented here. A new and parallel efficient implementation of several variants of GDSW, that is, GDSW, RGDSW, and GDSW*, in PETSc (Portable, Extensible Toolkit for Scientific Computing), is introduced, which is usable for multiphysics problems, as, for example, the thermo-mechanical LBW problem considered here. Different combinations of the GDSW variants for the different fields (temperature and displacements) are compared and parallel scalability for realistic problems is shown.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Bevilacqua, Tommaso UNSPECIFIED https://orcid.org/0000-0002-0828-5018 UNSPECIFIED Klawonn, Axel UNSPECIFIED https://orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED https://orcid.org/0000-0002-4232-9395 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-801945
Identification Number:	10.1007/s00466-025-02674-6
Journal or Publication Title:	Computational Mechanics
Volume:	77
Number:	2
Page Range:	pp. 485-499
Number of Pages:	15
Date:	5 February 2026
Publisher:	Springer Nature
ISSN:	0178-7675
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers Faculty of Mathematics and Natural Sciences
Divisions:	Center for Data and Simulation Science Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science
Uncontrolled Keywords:	Keywords Language Laser beam welding ; Saddle point problems ; Schwarz methods ; GDSW ; RGDSW ; GDSW* ; Thermo-elastoplasticity ; Monolithic preconditioner English
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/80194