On the multilevel preconditioning of Crouzeix-Raviart elliptic problems

Numerical Linear Algebra with Applications

Volumn 15, Issue 5 SPEC. ISS., 2008, Pages 395-416

  Kraus, J ^a   Margenov, S ^b   Synka, J ^c  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

^b BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^c JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Anisotropy; CBS constant; Differences and aggregates; First reduce; Hierarchical splittings; Multilevel preconditioning; Non conforming finite elements

Indexed keywords

EID: 51349137357     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.543     Document Type: Conference Paper

References (19)

1. Axelsson O. Vassilevski PS. Algebraic multilevel preconditioning methods. I. Numerische Mathematik 1989: 56:157-177.
2. Axelsson O, Margenov S. An optimal order multilevel preconditioner with respect to problem and discretization parameters. In Advances in Computations. Theory and Practice, Minev P. Wong YS, Lin Y (eds), vol. 7. Nova Science: New York, 2001; 2-18.
3. Blaheta R. Margenov S, Neytcheva M. Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non-conforming FEM systems. Numerical Linear Algebra with Applications 2004; 11:309-326.
4. Margenov S, Synka J. Generalized aggregation-based multilevel preconditioning of Crouzeix-Raviart FEM elliptic problems. RICAM Report 2006-23, 2006.
5. Margenov S, Vassilevski PS. Two-level preconditioning of non-conforming FEM systems. In Large-scale Scientific Computations of Engineering and Environmental Problems, Notes on Numerical Fluid Mechanics. Griebel M. Iliev O, Margenov S, Vassilevski PS (eds), vol. 2. VIEWEG, 1998; 239-248.
6. Axelsson O. Iterative Solution Methods. Cambridge University Press: Cambridge, MA, 1994.
7. Axelsson O. Stabilization of algebraic multilevel iteration methods; additive methods. Numerical Algorithms 1999; 21:23-47.
8. Axelsson O, Gustafsson I. Preconditioning and two-level multigrid methods of arbitrary degree of approximations. Mathematics of Computation 1983; 40:219-242.
9. Axelsson O, Padiy A. On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems. SIAM Journal on Scientific Computing 1999; 20(5): 1807-1830.
10. Axelsson O, Vassilevski PS. Algebraic multilevel preconditioning methods, II. SIAM Journal on Numerical Analysis 1990;27:1569-1590.
11. Blaheta R, Margenov R, Neytcheva M. Robust optimal multilevel preconditioners for non-conforming finite element systems. Numerical Linear Algebra with Applications 2005; 12:495-514.
12. Axelsson O, Vassilevski PS. A black box generalized conjugate gradient solver with linear iterations and variable-step preconditioning. SIAM Journal on Matrix Analysis and Applications 1991; 12:625-644.
13. Axelsson O, Vassilevski PS. Variable-step multilevel preconditioning methods, I: Self-adjoint and positive definite elliptic problems. Numerical Linear Algebra with Applications 1994; 1:75-101.
14. Kraus J. An algebraic preconditioning method for M-matrices: linear versus nonlinear multilevel iteration. Numerical Linear Algebra with Applications 2002; 9:599-618.
15. Notay Y. Robust parameter-free algebraic multilevel preconditioning. Numerical Linear Algebra with Applications 2002; 9:409-428.
16. Georgiev I, Kraus J, Margenov S. Multilevel preconditioning of rotated bilinear non-conforming FEM problems. Computers and Mathematics with Applications 2008, to appear.
17. Kraus J. Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Numerical Linear Algebra with Applications 2006; 13:49-70.
18. Georgiev I, Kraus J, Margenov S. Multilevel Preconditioning of 2D Rannacher-Turek FE Problems: Additive and Multiplicative Methods. Lecture Notes in Computer Science (LNCS) 4310, 2007; 56-64.
19. Saad Y Iterative Methods for Sparse Linear Systems. PWS Publishing Company: Boston. 1996.