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Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem

  • Special Feature: Original Paper
  • The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics (CJK2018), 20-24 August 2018, Kanazawa, Japan
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Abstract

In this paper, we present a semi-analytic approach to enhance the integration of elliptic Dirichlet-to-Neumann (DtN) boundary condition and high order spectral element method in solving scattering problem with slender scatterer. By using appropriate elemental mapping in the spectral element discretization, semi-analytic formulas are obtained for the computation of Mathieu expansion coefficients involved in the global DtN operator. Further, a semi-analytic approach is proposed for the computation of global boundary integral terms in the spectral element discretization. The proposed semi-analytic formulas can also be used to calculate Mathieu expansion coefficients for functions given values on spectral element grids. Numerical examples show that spectral element method with the proposed semi-analytic approach can produce high order numerical solution for scattering problem with slender scatterer.

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Acknowledgements

Rui Zhang acknowledges the financial support provided by NSFC (Grant 11771138 and 11771137). Bo Wang acknowledges the financial support provided by NSFC (Grant 11771137), the Construct Program of the Key Discipline in Hunan Province and a Scientific Research Fund of Hunan Provincial Education Department (No. 16B154). Ziqing Xie is partially supported by NSFC (91430107, 11171104 and 11771138) and the Construct Program of the Key Discipline in Hunan Province.

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  1. LCSM (MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Rui Zhang, Bo Wang & Ziqing Xie

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  1. Rui Zhang
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  2. Bo Wang
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  3. Ziqing Xie
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Correspondence to Bo Wang.

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Zhang, R., Wang, B. & Xie, Z. Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem. Japan J. Indust. Appl. Math. 36, 1129–1148 (2019). https://doi.org/10.1007/s13160-019-00383-1

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  • DOI: https://doi.org/10.1007/s13160-019-00383-1

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