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A numerical study on Neumann-Neumann methodsfor hp approximations on geometricallyrefined boundary layer meshes II. Three-dimensional problems

Published online by Cambridge University Press:  23 February 2006

Andrea Toselli  and
Xavier Vasseur
Andrea Toselli
Affiliation:
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Xavier.Vasseur@cerfacs.fr
Xavier Vasseur
Affiliation:
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Xavier.Vasseur@cerfacs.fr
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Abstract

In this paper, we present extensive numerical tests showing the performanceand robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar ellipticproblems on geometrically refined boundary layer meshes inthree 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 theaspect ratio of the mesh and of potentially large jumps of thecoefficients. Good results are also obtained for certain singularly perturbed problems. The condition numbers only grow polylogarithmically with thepolynomial 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.

Keywords

Domain decompositionpreconditioninghp finite elementsspectral elementsanisotropic meshes.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 1 , January 2006 , pp. 99 - 122
Copyright
© EDP Sciences, SMAI, 2006

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