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Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell’s Equations

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Abstract

We propose two schemes [AVF(2) and AVF(4)] for Maxwell’s equations, by discretizing the Hamiltonian formulation with Fourier pseudospectral method for spatial discretization and average vector field method for time integration. Both AVF(2) and AVF(4) hold the two Hamiltonian energies automatically, while being energy-, momentum- and divergence-preserving, unconditionally stable, non-dissipative and spectral accurate. Rigorous error estimates are obtained for the proposed schemes. The numerical dispersion relations are also investigated. Numerical experiments support well the theoretical analysis results. The proposed schemes are valid for the regular domain, but invalid for the domain with complex geometries.

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Acknowledgments

The authors would like to express sincere gratitude to the referees for their insightful comments and suggestions.

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Authors and Affiliations

  1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Jiaxiang Cai, Yushun Wang & Yuezheng Gong

  2. School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, Jiangsu, People’s Republic of China

    Jiaxiang Cai

Authors
  1. Jiaxiang Cai
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  2. Yushun Wang
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  3. Yuezheng Gong
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Corresponding author

Correspondence to Jiaxiang Cai.

Additional information

The work was supported by the National Natural Science Foundation of China (11201169, 41231173 and 11271195) and the Graduate Education Innovation Project of Jiangsu Province of China (CXLX13_366).

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Cai, J., Wang, Y. & Gong, Y. Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell’s Equations. J Sci Comput 66, 141–176 (2016). https://doi.org/10.1007/s10915-015-0016-5

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  • DOI: https://doi.org/10.1007/s10915-015-0016-5

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