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.
Mots-clés : algebraic multigrid, Schur complement, Lagrange multipliers
@article{M2AN_2003__37_1_133_0, author = {Martikainen, Janne}, title = {Numerical study of two sparse {AMG-methods}}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {133--142}, publisher = {EDP-Sciences}, volume = {37}, number = {1}, year = {2003}, doi = {10.1051/m2an:2003016}, mrnumber = {1972654}, zbl = {1030.65128}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2003016/} }
TY - JOUR AU - Martikainen, Janne TI - Numerical study of two sparse AMG-methods JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 133 EP - 142 VL - 37 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003016/ DO - 10.1051/m2an:2003016 LA - en ID - M2AN_2003__37_1_133_0 ER -
%0 Journal Article %A Martikainen, Janne %T Numerical study of two sparse AMG-methods %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 133-142 %V 37 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003016/ %R 10.1051/m2an:2003016 %G en %F M2AN_2003__37_1_133_0
Martikainen, Janne. Numerical study of two sparse AMG-methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 133-142. doi : 10.1051/m2an:2003016. http://archive.numdam.org/articles/10.1051/m2an:2003016/
[1] The finite element method with Lagrangian multipliers. Numer. Math. 20 (1972/73) 179-192. | Zbl
,[2] 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). | Zbl
, and ,[3] The construction of preconditioners for elliptic problems by substructuring. I. Math. Comp. 47 (1986) 103-134. | Zbl
, and ,[4] Zbl
, and Jinchao Xu, Parallel multilevel preconditioners. Math. Comp. 55 (1990) 1-22. |[5] Qianshun Chang, Yau Shu Wong and Hanqing Fu, On the algebraic multigrid method. J. Comput. Phys. 125 (1996) 279-292. | Zbl
[6] A capacitance matrix method for Dirichlet problem on polygon region. Numer. Math. 39 (1982) 51-64. | Zbl
,[7] 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. | Zbl
, , , and ,[8] Tsorng-Whay Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | Zbl
,[9] The use of preconditioning over irregular regions, in Computing methods in applied sciences and engineering VI, Versailles (1983) 3-14. North-Holland, Amsterdam (1984). | Zbl
and ,[10] Iterative methods for solving linear systems. SIAM, Philadelphia, PA (1997). | MR | Zbl
,[11] Algebraic multi-grid for discrete elliptic second-order problems, in Multigrid methods V, Stuttgart (1996) 157-172. Springer, Berlin (1998). | Zbl
,[12] Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187-211. | Zbl
,[13] Overlapping domain decomposition with non-matching grids. East-West J. Numer. Math. 6 (1998) 299-308. | Zbl
,[14] A moving mesh fictitious domain approach for shape optimization problems. ESAIM: M2AN 34 (2000) 31-45. | Numdam | Zbl
, and ,[15] Multilevel preconditioners for Lagrange multipliers in domain imbedding. Electron. Trans. Numer. Anal. (to appear). | MR | Zbl
, and ,[16] A multilevel AINV preconditioner. Numer. Algorithms 29 (2002) 107-129. | Zbl
,[17] Algebraic multigrid. SIAM, Philadelphia, PA, Multigrid methods (1987) 73-130.
and ,[18] Fast iterative solution of stabilised Stokes systems. II. Using general block preconditioners. SIAM J. Numer. Anal. 31 (1994) 1352-1367. | Zbl
and ,[19] A domain decomposition preconditioner based on a change to a multilevel nodal basis. SIAM J. Sci. Statist. Comput. 12 (1991) 1486-1495. | Zbl
, , and ,Cité par Sources :