Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2015). TOWARD EXTREMELY SCALABLE NONLINEAR DOMAIN DECOMPOSITION METHODS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS. SIAM J. Sci. Comput., 37 (6). S. C667 - 30. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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Abstract

The solution of nonlinear problems, e.g., in material science, requires fast and highly scalable parallel solvers. Finite element tearing and interconnecting dual primal (FETI-DP) domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements. Recently, nonlinear versions of the well-known FETI-DP methods for linear problems have been introduced. In these methods, the nonlinear problem is decomposed before linearization. This approach can be viewed as a strategy to further localize computational work and to extend the parallel scalability of FETI-DP methods toward extreme-scale supercomputers. Here, a recent nonlinear FETI-DP method is combined with an approach that allows an inexact solution of the FETI-DP coarse problem. We combine the nonlinear FETI-DP domain decomposition method with an algebraic multigrid (AMG) method and thus obtain a hybrid nonlinear domain decomposition/multigrid method. We consider scalar nonlinear problems as well as nonlinear hyperelasticity problems in two and three space dimensions. For the first time for a domain decomposition method, weak parallel scalability can be shown beyond half a million cores and subdomains. We can show weak parallel scalability for up to 524 288 cores on the Mira Blue Gene/Q supercomputer for our new implementation and discuss the steps necessary to obtain these results. We solve a heterogeneous nonlinear hyperelasticity problem discretized using piecewise quadratic finite elements with a total of 42 billion degrees of freedom in about six minutes. Our analysis reveals that scalability beyond 524 288 cores depends critically on both efficient construction and solution of the coarse problem.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED orcid.org/0000-0002-4232-9395 UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-415377
DOI:	10.1137/140997907
Journal or Publication Title:	SIAM J. Sci. Comput.
Volume:	37
Number:	6
Page Range:	S. C667 - 30
Date:	2015
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7197
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PRIMAL FETI METHODS; GENERIC GRID INTERFACE; PARALLEL; DP; BDDC; IMPLEMENTATION; PRECONDITIONER Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/41537