Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T20:38:08.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Study of Two Sparse AMG-methods

Published online by Cambridge University Press:  15 March 2003

Janne Martikainen
Janne Martikainen*
Affiliation:
University of Jyväskylä, Department of Mathematical Information Technology, P.O. Box 35 (Agora), 40351 Jyväskylä, Finland. Janne.Martikainen@mit.jyu.fi.
Get access

Abstract

A sparse algebraic multigrid method is studied as a cheap and accurateway to compute approximations of Schur complements of matricesarising from the discretization of some symmetric and positive definitepartial differential operators. The construction of such a multigrid isdiscussed and numerical experiments are used to verify the propertiesof the method.

Keywords

Algebraic multigridSchur complementLagrange multipliers.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 133 - 142
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 20 (1972/73) 179-192.
C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XI, Paris (1989-1991) 13-51. Longman Sci. Tech., Harlow (1994).
Bramble, J.H., Pasciak, J.E. and Schatz, A.H., The construction of preconditioners for elliptic problems by substructuring. I. Math. Comp. 47 (1986) 103-134. CrossRef
Bramble, J.H., Pasciak, J.E. and Jinchao Xu, Parallel multilevel preconditioners. Math. Comp. 55 (1990) 1-22. CrossRef
Chang, Qianshun, Wong, Yau Shu and Fu, Hanqing, On the algebraic multigrid method. J. Comput. Phys. 125 (1996) 279-292. CrossRef
Dryja, M., A capacitance matrix method for Dirichlet problem on polygon region. Numer. Math. 39 (1982) 51-64. CrossRef
R. Glowinski, T. Hesla, D.D. Joseph, T.-W. Pan and J. Periaux, Distributed Lagrange multiplier methods for particulate flows, in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Periaux and M.F. Wheeler Eds., Wiley (1997) 270-279.
Glowinski, R., Tsorng-Whay Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. CrossRef
G.H. Golub and D. Mayers, The use of preconditioning over irregular regions, in Computing methods in applied sciences and engineering VI, Versailles (1983) 3-14. North-Holland, Amsterdam (1984).
A. Greenbaum, Iterative methods for solving linear systems. SIAM, Philadelphia, PA (1997).
F. Kickinger, Algebraic multi-grid for discrete elliptic second-order problems, in Multigrid methods V, Stuttgart (1996) 157-172. Springer, Berlin (1998).
Kuznetsov, Yu.A., Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187-211.
Kuznetsov, Yu.A., Overlapping domain decomposition with non-matching grids. East-West J. Numer. Math. 6 (1998) 299-308.
Mäkinen, R.A.E., Rossi, T. and Toivanen, J., A moving mesh fictitious domain approach for shape optimization problems. ESAIM: M2AN 34 (2000) 31-45. CrossRef
J. Martikainen, T. Rossi and J. Toivanen, Multilevel preconditioners for Lagrange multipliers in domain imbedding. Electron. Trans. Numer. Anal. (to appear).
Meurant, G., A multilevel AINV preconditioner. Numer. Algorithms 29 (2002) 107-129. CrossRef
J.W. Ruge and K. Stüben, Algebraic multigrid. SIAM, Philadelphia, PA, Multigrid methods (1987) 73-130.
Silvester, D. and Wathen, A., Fast iterative solution of stabilised Stokes systems. II. Using general block preconditioners. SIAM J. Numer. Anal. 31 (1994) 1352-1367. CrossRef
Tong, C.H., Chan, T.F., and Kuo, C.-C. Jay, A domain decomposition preconditioner based on a change to a multilevel nodal basis. SIAM J. Sci. Statist. Comput. 12 (1991) 1486-1495. CrossRef