Commun. Comput. Phys., 5 (2009), pp. 667-682.


p-Multigrid Method for Fekete-Gauss Spectral Element Approximations of Elliptic Problems

Richard Pasquetti 1*, Francesca Rapetti 1

1 Laboratoire J.A. Dieudonne, UMR 6621 CNRS, Universite de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 02, France.

Received 28 September 2007; Accepted (in revised version) 8 January 2008
Available online 1 August 2008

Abstract

An efficient p-multigrid method is developed to solve the algebraic systems which result from the approximation of elliptic problems with the so-called Fekete-Gauss Spectral Element Method, which makes use of the Fekete points of the triangle as interpolation points and of the Gauss points as quadrature points. A multigrid strategy is defined by comparison of different prolongation/restriction operators and coarse grid algebraic systems. The efficiency and robustness of the approach, with respect to the type of boundary condition and to the structured/unstructured nature of the mesh, are highlighted through numerical examples.

AMS subject classifications: 65N30, 65N35, 65N55

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Key words: Spectral elements, Fekete points, multigrid methods.

*Corresponding author.
Email: richard.pasquetti@unice.fr (R. Pasquetti), francesca.rapetti@unice.fr (F. Rapetti)
 

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