A null space free Jacobi-Davidson iteration for Maxwell's operator

Yin Liang Huang, Tsung Ming Huang, Wen Wei Lin, Wei Cheng Wang

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of time harmonic Maxwell's equations. We focus on a class of spatial discretizations that guarantee the existence of discrete vector potentials, such as Yee's scheme and the edge elements. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential instead. The correction equation is solved approximately as in the standard Jacobi-Davidson approach. The computational cost of the transformation from the vector potential to the corrector is negligible. As a consequence, the expanding subspace automatically stays out of the null space and no extra projection step is needed. Numerical evidence confirms that the proposed scheme indeed outperforms the standard and projection-based Jacobi-Davidson methods by a significant margin.

Original languageEnglish
Pages (from-to)A1-A29
JournalSIAM Journal on Scientific Computing
Volume37
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1

Keywords

  • Discrete deRham complex
  • Discrete vector potential
  • Edge elements
  • Generalized eigenvalue problem
  • Jacobi-Davidson method
  • Poincaré Lemma
  • Time harmonic Maxwell's equations
  • Yee's scheme

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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