Numerical study of two sparse AMG-methods

Janne Martikainen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 1, page 133-142
  • ISSN: 0764-583X

Abstract

top
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.

How to cite

top

Martikainen, Janne. "Numerical study of two sparse AMG-methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 133-142. <http://eudml.org/doc/245488>.

@article{Martikainen2003,
abstract = {A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.},
author = {Martikainen, Janne},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {algebraic multigrid; Schur complement; Lagrange multipliers; Laplace equation; finite element; numerical experiments; preconditioning; unstructured grids},
language = {eng},
number = {1},
pages = {133-142},
publisher = {EDP-Sciences},
title = {Numerical study of two sparse AMG-methods},
url = {http://eudml.org/doc/245488},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Martikainen, Janne
TI - Numerical study of two sparse AMG-methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 1
SP - 133
EP - 142
AB - A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
LA - eng
KW - algebraic multigrid; Schur complement; Lagrange multipliers; Laplace equation; finite element; numerical experiments; preconditioning; unstructured grids
UR - http://eudml.org/doc/245488
ER -

References

top
  1. [1] I. Babuška, The finite element method with Lagrangian multipliers. Numer. Math. 20 (1972/73) 179–192. Zbl0258.65108
  2. [2] 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). Zbl0797.65094
  3. [3] J.H. Bramble, J.E. Pasciak and A.H. Schatz, The construction of preconditioners for elliptic problems by substructuring. I. Math. Comp. 47 (1986) 103–134. Zbl0615.65112
  4. [4] J.H. Bramble, J.E. Pasciak and Jinchao Xu, Parallel multilevel preconditioners. Math. Comp. 55 (1990) 1–22. Zbl0703.65076
  5. [5] Qianshun Chang, Yau Shu Wong and Hanqing Fu, On the algebraic multigrid method. J. Comput. Phys. 125 (1996) 279–292. Zbl0857.65037
  6. [6] M. Dryja, A capacitance matrix method for Dirichlet problem on polygon region. Numer. Math. 39 (1982) 51–64. Zbl0478.65062
  7. [7] 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. Zbl0919.76077
  8. [8] R. Glowinski, Tsorng-Whay Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283–303. Zbl0845.73078
  9. [9] 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). Zbl0564.65067
  10. [10] A. Greenbaum, Iterative methods for solving linear systems. SIAM, Philadelphia, PA (1997). Zbl0883.65022MR1474725
  11. [11] F. Kickinger, Algebraic multi-grid for discrete elliptic second-order problems, in Multigrid methods V, Stuttgart (1996) 157–172. Springer, Berlin (1998). Zbl0926.65128
  12. [12] Yu.A. Kuznetsov, Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187–211. Zbl0839.65031
  13. [13] Yu.A. Kuznetsov, Overlapping domain decomposition with non-matching grids. East-West J. Numer. Math. 6 (1998) 299–308. Zbl0918.65075
  14. [14] R.A.E. Mäkinen, T. Rossi and J. Toivanen, A moving mesh fictitious domain approach for shape optimization problems. ESAIM: M2AN 34 (2000) 31–45. Zbl0948.65064
  15. [15] J. Martikainen, T. Rossi and J. Toivanen, Multilevel preconditioners for Lagrange multipliers in domain imbedding. Electron. Trans. Numer. Anal. (to appear). Zbl1030.65129MR1991267
  16. [16] G. Meurant, A multilevel AINV preconditioner. Numer. Algorithms 29 (2002) 107–129. Zbl1044.65036
  17. [17] J.W. Ruge and K. Stüben, Algebraic multigrid. SIAM, Philadelphia, PA, Multigrid methods (1987) 73–130. 
  18. [18] D. Silvester and A. Wathen, Fast iterative solution of stabilised Stokes systems. II. Using general block preconditioners. SIAM J. Numer. Anal. 31 (1994) 1352–1367. Zbl0810.76044
  19. [19] C.H. Tong, T.F. Chan, and C.-C. Jay Kuo, A domain decomposition preconditioner based on a change to a multilevel nodal basis. SIAM J. Sci. Statist. Comput. 12 (1991) 1486–1495. Zbl0744.65084

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.