Two-grid methods for time-harmonic Maxwell equations

Liuqiang Zhong, Shi Shu, Junxian Wang, J. Xu

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

In this paper, we develop several two-grid methods for the Nédélec edge finite element approximation of the time-harmonic Maxwell equations. We first present a two-grid method that uses a coarse space to solve the original problem and then use a fine space to solve a corresponding symmetric positive definite problem. Then, we present two types of iterative two-grid methods, one is to add the kernel of the curl-operator in the fine space to a coarse mesh space to solve the original problem and the other is to use an inner iterative method for dealing with the kernel of the curl-operator in the fine space and the coarse space, separately. We provide the error estimates for the first two methods and present numerical experiments to show the efficiency of our methods.

Original languageEnglish (US)
Pages (from-to)93-111
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume20
Issue number1
DOIs
StatePublished - Jan 1 2013

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Two-grid Method
Maxwell equations
Iterative methods
Maxwell's equations
Harmonic
Curl
Experiments
Edge Finite Elements
kernel
Iteration
Operator
Finite Element Approximation
Positive definite
Error Estimates
Numerical Experiment
Mesh

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

Cite this

Zhong, Liuqiang ; Shu, Shi ; Wang, Junxian ; Xu, J. / Two-grid methods for time-harmonic Maxwell equations. In: Numerical Linear Algebra with Applications. 2013 ; Vol. 20, No. 1. pp. 93-111.
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Two-grid methods for time-harmonic Maxwell equations. / Zhong, Liuqiang; Shu, Shi; Wang, Junxian; Xu, J.

In: Numerical Linear Algebra with Applications, Vol. 20, No. 1, 01.01.2013, p. 93-111.

Research output: Contribution to journalArticle

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