Volume 40, Number 1, January-February 2006
|Page(s)||99 - 122|
|Published online||23 February 2006|
A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101,
8092 Zürich, Switzerland. Xavier.Vasseur@cerfacs.fr
Revised: 3 July 2005
Revised: 8 September 2005
In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal. 24 (2004) 123–156]. They confirm that the condition numbers are independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients. Good results are also obtained for certain singularly perturbed problems. The condition numbers only grow polylogarithmically with the polynomial degree, as in the case of p approximations on shape-regular meshes [Pavarino, RAIRO: Modél. Math. Anal. Numér. 31 (1997) 471–493]. This paper follows [Toselli and Vasseur, Comput. Methods Appl. Mech. Engrg. 192 (2003) 4551–4579] on two dimensional problems.
Mathematics Subject Classification: 65N22 / 65N35 / 65N55
Key words: Domain decomposition / preconditioning / hp finite elements / spectral elements / anisotropic meshes.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.