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Zbl 1071.65170
Reitzinger, S.; Schöberl, J.
An algebraic multigrid method for finite element discretizations with edge elements.
(English)
[J] Numer. Linear Algebra Appl. 9, No. 3, 223-238 (2002). ISSN 1070-5325; ISSN 1099-1506/e

Summary: This paper presents an algebraic multigrid method for the efficient solution of the linear system arising from a finite element discretization of variational problems in $H_0 (\text {curl},\,\Omega )$. The finite element spaces are generated by Nédélec's edge elements. \par A coarsening technique is presented, which allows the construction of suitable coarse finite element spaces, corresponding transfer operators and appropriate smoothers. The prolongation operator is designed such that coarse grid kernel functions of the curl-operator are mapped to fine grid kernel functions. Furthermore, coarse grid kernel functions are `discrete' gradients. The smoothers proposed by {\it R.\ Hiptmair} [SIAM J.\ Numer. Anal. 36, 204--225 (1998; Zbl 0922.65081)] and {\it D. Arnold, R. Falk} and {\it R. Winther} [Numer. Math. 85, 197--217 (2000; Zbl 0974.65113)] are directly used in the algebraic framework. \par Numerical studies are presented for 3D problems to show the high efficiency of the proposed technique.
MSC 2000:
*65N55 Multigrid methods; domain decomposition (BVP of PDE)
78M10 Finite element methods (optics)
65Y20 Complexity and performance of numerical algorithms

Keywords: Maxwell's equation; finite element method; Nédélec's edge element; iterative solver

Citations: Zbl 0922.65081; Zbl 0974.65113

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