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An algebraic multigrid method for finite element discretizations with edge elements
Author(s) -
Reitzinger S.,
Schöberl J.
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.271
Subject(s) - mathematics , finite element method , multigrid method , discretization , kernel (algebra) , grid , curl (programming language) , regular grid , operator (biology) , algebraic number , transfer operator , mathematical analysis , geometry , pure mathematics , partial differential equation , computer science , biochemistry , chemistry , physics , repressor , transcription factor , gene , thermodynamics , programming language
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 (curl,Ω). The finite element spaces are generated by Nédélec's edge elements. 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 Hiptmair and Arnold, Falk and Winther are directly used in the algebraic framework. Numerical studies are presented for 3D problems to show the high efficiency of the proposed technique. Copyright © 2002 John Wiley & Sons, Ltd.