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

Yin-Liang Huang National University of Tainan Tsung-Ming Huang National Taiwan Normal University Wen-Wei Lin National Chiao Tung University Wei-Cheng Wang National Tsing Hua University

Numerical Analysis and Scientific Computing mathscidoc:1702.25083

SIAM J. Sci. Comput., 37, A1-A29, 2015
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.
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@inproceedings{yin-liang2015a,
  title={A null space free Jacobi-Davidson iteration for Maxwell's operator},
  author={Yin-Liang Huang, Tsung-Ming Huang, Wen-Wei Lin, and Wei-Cheng Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170223082934458606509},
  booktitle={SIAM J. Sci. Comput.},
  volume={37},
  pages={A1-A29},
  year={2015},
}
Yin-Liang Huang, Tsung-Ming Huang, Wen-Wei Lin, and Wei-Cheng Wang. A null space free Jacobi-Davidson iteration for Maxwell's operator. 2015. Vol. 37. In SIAM J. Sci. Comput.. pp.A1-A29. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170223082934458606509.
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