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Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation

Huangxin Chen, Ronald H. W. Hoppe, Xuejun Xu (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...

Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation∗

Huangxin Chen, Ronald H.W. Hoppe, Xuejun Xu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...

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