Multigrid transfers for nonsymmetric systems based on Schur complements and Galerkin projections

2013 ◽  
Vol 21 (3) ◽  
pp. 415-438 ◽  
Author(s):  
T. A. Wiesner ◽  
R. S. Tuminaro ◽  
W. A. Wall ◽  
M. W. Gee
Keyword(s):  
Schur Complements ◽  
Galerkin Projections ◽  
Nonsymmetric Systems

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach
Keyword(s):  
Condition Number ◽  
Three Dimensional ◽  
Schur Complement ◽  
Decomposition Methods ◽  
Stiffness Matrices ◽  
Spectral Bounds ◽  
Schur Complements ◽  
Linear Problems ◽  
Primal Method ◽  
Large Clusters

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.

Aberration Characteristics Of Nonsymmetric Systems

1986 ◽  
Author(s):  
John W. Figoski
Keyword(s):  
Nonsymmetric Systems

scholarly journals Nonsymmetric systems on nonsmooth planar domains

1997 ◽  
Vol 349 (11) ◽  
pp. 4501-4535 ◽  
Author(s):  
G. C. Verchota ◽  
A. L. Vogel
Keyword(s):  
Planar Domains ◽  
Nonsymmetric Systems

A scalable parallel factorization of finite element matrices with distributed Schur complements

2016 ◽  
Vol 23 (5) ◽  
pp. 848-864
Author(s):  
Daniel Maurer ◽  
Christian Wieners
Keyword(s):  
Finite Element ◽  
Parallel Factorization ◽  
Schur Complements

scholarly journals Some inequalities for eigenvalues of Schur complements of Hermitian matrices

2006 ◽  
Vol 196 (2) ◽  
pp. 439-451 ◽  
Author(s):  
Jianzhou Liu ◽  
Yunqing Huang ◽  
Anping Liao
Keyword(s):  
Hermitian Matrices ◽  
Schur Complements

scholarly journals A new proof of Haynsworth's quotient formula for Schur complements

1971 ◽  
Vol 4 (4) ◽  
pp. 389-392 ◽  
Author(s):  
Alexander Ostrowski
Keyword(s):  
Schur Complements
Sign in / Sign up

Export Citation Format

Share Document