NDLI: Partnership for Advanced Computing in Europe Fixing Nodes Strategies for the Effective Regularization of the Subdomain Stiffness Matrices Arising in Total FETI

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Partnership for Advanced Computing in Europe Fixing Nodes Strategies for the Effective Regularization of the Subdomain Stiffness Matrices Arising in Total FETI

Content Provider	Semantic Scholar
Author	Kozubek, Tomás Vondrák, Vít R̊aback, Peter Ruokolainen, Juha
Copyright Year	2011
Abstract	The bottlenecks related to the numerical solution of many engineering problems are very dependent on the techniques used to solve the systems of linear equations that result from their linearizations and finite element discretizations. The large linearized problems can be solved efficiently using the so-called scalable algorithms based on multigrid or domain decomposition method. In cooperation with the Elmer team two variants of the domain decomposition method have been implemented into Elmer: (i) FETI-1 (Finite Element Tearing and Interconnecting) introduced by Farhat and Roux and (ii) Total FETI introduced by Dostal, Horak, and Kucera. In the latter, the Dirichlet boundary conditions are torn off to have all subdomains floating, which makes the method very flexible. In this paper, we review the results related to the efficient solution of symmetric positive semidefinite systems arising in FETI methods when they are applied on elliptic boundary value problems. More specifically, we show three different strategies to find the so-called fixing nodes (or DOFs degrees of freedom), which enable an effective regularization of the corresponding subdomain system matrices that eliminates the work with singular matrices. The performance is illustrated on an elasticity benchmark computed using ELMER on the French Tier-0 system CURIE.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.prace-ri.eu/IMG/pdf/Fixing_Nodes_Strategies_for_the_Effective_Regularization_of_the_Subdomain_Stiffness_Matrices_Arising_in_Total_FETI-2.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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