A Smoother Based on Nonoverlapping Domain Decomposition Methods for H(div) Problems: A Numerical Study
- 327 Downloads
The purpose of this paper is to introduce a V-cycle multigrid method for vector field problems discretized by the lowest order Raviart-Thomas hexahedral element. Our method is connected with a smoother based on a nonoverlapping domain decomposition method. We present numerical experiments to show the effectiveness of our method.
- 5.S.C. Brenner, D.-S. Oh, Multigrid methods for H(div) in three dimensions with nonoverlapping domain decomposition smoothers. Numer. Linear Algebra Appl. https://doi.org/10.1002/nla.2191
- 7.V. Girault, P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer Series in Computational Mathematics, vol. 5 (Springer, Berlin, 1986)Google Scholar
- 8.R. Hiptmair, Multigrid method for H(div) in three dimensions. Electron. Trans. Numer. Anal. 6(Dec), 133–152 (1997), Special issue on multilevel methods (Copper Mountain, CO, 1997)Google Scholar
- 9.R. Hiptmair, A. Toselli, Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions, in Parallel Solution of Partial Differential Equations (Minneapolis, MN, 1997). IMA Volumes in Mathematics and Its Applications, vol. 120 (Springer, New York, 2000), pp. 181–208Google Scholar
- 14.P.-A. Raviart, J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical Aspects of Finite Element Methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975). Lecture Notes in Mathematics, vol. 606 (Springer, Berlin, 1977), pp. 292–315Google Scholar