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A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations

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Abstract

In this paper we are concerned with plane wave discretizations of nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. To this end, we design a plane wave method combined with local spectral elements for the discretization of such nonhomogeneous equations. This method contains two steps: we first solve a series of nonhomogeneous local problems on auxiliary smooth subdomains by the spectral element method, and then apply the plane wave method to the discretization of the resulting (locally homogeneous) residue problem on the global solution domain. We derive error estimates of the approximate solutions generated by this method. The numerical results show that the resulting approximate solutions possess high accuracy.

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Acknowledgments

The authors wish to thank the anonymous referee for many insightful comments which led to great improvement in the results and the presentation of the paper.

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientic/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qiya Hu

  2. College of Mathematics and Systems Science, Shan Dong University of Science and Technology, 579 Qian Wan Gang Road, Qingdao, 266590, China

    Long Yuan

  3. University of Chinese Academy of Sciences, Beijing, China

    Qiya Hu

Authors
  1. Qiya Hu
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  2. Long Yuan
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Corresponding authors

Correspondence to Qiya Hu or Long Yuan.

Additional information

Communicated by: Karsten Urban

The first author was supported by the Natural Science Foundation of China G11571352. The second author was supported by China NSF under the grant 11501529 and Qingdao applied basic research project under the grant 17-1-1-9-jch.

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Hu, Q., Yuan, L. A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. Adv Comput Math 44, 245–275 (2018). https://doi.org/10.1007/s10444-017-9542-z

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  • DOI: https://doi.org/10.1007/s10444-017-9542-z

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