spectral bounds
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2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.



2021 ◽  
Vol 280 (1) ◽  
pp. 108804
Author(s):  
Jean-Claude Cuenin ◽  
Orif O. Ibrogimov
Keyword(s):  


2021 ◽  
pp. 507-524
Author(s):  
Matthias Keller ◽  
Daniel Lenz ◽  
Radosław K. Wojciechowski
Keyword(s):  


2020 ◽  
Vol 18 (1) ◽  
pp. 486-495
Author(s):  
Mohammad Abudayah ◽  
Omar Alomari ◽  
Torsten Sander

Abstract Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalues of the matrix AA T , where A is the adjacency matrix of D. In this study, we relate the classical spectrum of undirected graphs to the N-spectrum of their oriented counterparts, permitting us to derive spectral bounds. Moreover, we study the spectral effects caused by certain modifications of a given digraph.



2020 ◽  
Vol 279 ◽  
pp. 12-24
Author(s):  
Miguel F. Anjos ◽  
José Neto
Keyword(s):  




2020 ◽  
Vol 53 (4) ◽  
pp. 993-1035
Author(s):  
Te LI ◽  
Dongyi WEI ◽  
Zhifei ZHANG
Keyword(s):  


2019 ◽  
Vol 269 ◽  
pp. 200-210
Author(s):  
Miguel F. Anjos ◽  
José Neto




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