Comparison of two discontinuous spectral element methods

Zhang Yang; Wang Xianghui; Zhang Jie; Wang Jianguo; Qi Hongxin

doi:10.11884/HPLPB201830.170169

Volume 30 Issue 2

Feb. 2018

Turn off MathJax

Article Contents

Article Navigation > High Power Laser and Particle Beams > 2018 > 30(2): 023004

Zhang Yang, Wang Xianghui, Zhang Jie, et al. Comparison of two discontinuous spectral element methods[J]. High Power Laser and Particle Beams, 2018, 30: 023004. doi: 10.11884/HPLPB201830.170169

Citation:

Zhang Yang, Wang Xianghui, Zhang Jie, et al. Comparison of two discontinuous spectral element methods[J]. High Power Laser and Particle Beams, 2018, 30: 023004. doi: 10.11884/HPLPB201830.170169

Zhang Yang, Wang Xianghui, Zhang Jie, et al. Comparison of two discontinuous spectral element methods[J]. High Power Laser and Particle Beams, 2018, 30: 023004. doi: 10.11884/HPLPB201830.170169

Citation:

Zhang Yang, Wang Xianghui, Zhang Jie, et al. Comparison of two discontinuous spectral element methods[J]. High Power Laser and Particle Beams, 2018, 30: 023004. doi: 10.11884/HPLPB201830.170169

PDF( 3335 KB)

Comparison of two discontinuous spectral element methods

doi: 10.11884/HPLPB201830.170169

1.
Institute of Biophysics, Department of Physics, East China Normal University, Shanghai 200241, China
2.
Northwest Institute of Nuclear Technology, P. O. Box 69-1, Xi'an 710024, China

Received Date: 2017-09-26
Rev Recd Date: 2017-10-11
Publish Date: 2018-02-15

Abstract

Abstract

This paper is concerned with the comparison of two spectral Discontinuous Galerkin Time-Domain (DGTD) methods for the solution of Maxwell's equations in two-dimensional space. The first scheme is based on the conventional mass-lumping technique, where the same set of points are chosen for both the interpolation base functions and the numerical integration of coefficients. The second scheme is a newly proposed approach, called the Weight-Adjusted discontinuous Galerkin (WADG) method. Several numerical examples are presented to evaluate the performance of the two methods. It is shown that although the two methods need the same storage capacity, the WADG method has higher accuracy.
- discontinuous Galerkin method,
- Maxwell equations,
- mass-lumping,
- spectral method

FullText(HTML)

References(12)

References

[1]	Stephane D, Clement D, Stephane L, et al. Recent advances on a DGTD method for time-domain electromagnetics[J]. Photonics and Nanostructures Fundamentals and Applications, 2013, 11(4): 291-302. doi: 10.1016/j.photonics.2013.06.005
[2]	Stephane D, Stephane L, Ludovic M. Temporal convergence analysis of a locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media[J]. Journal of Computational and Applied Mathematics, 2017, 316(15): 122-132.
[3]	Xiong Meng, Jennifer K R. Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement[J]. Numerische Mathematik, 2017, 136(1): 27-73.
[4]	Zhu Jun, Zhong Xinghui, Shu Chiwang, et al. Runge-Kutta discontinuous Galerkin method with a simple and compact hermite WENO limiter on unstructured meshes[J]. Communications in Computational Physics, 2017, 21(3): 623-649.
[5]	Demirel A, Niegemann J, Busch K, et al. Efficient multiple time-stepping algorithms of higher order[J]. Journal of Computational Physics, 2015, 285(15): 133-148.
[6]	夏轶栋, 伍贻兆, 吕宏强. 高阶间断有限元法的并行计算研究[J]. 空气动力学报, 2011, 29(5): 537-541. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201105000.htm Xia Yidong, Wu Yizhao, Lü Hongqiang. Parallel computation of a high-order discontinuous Galerkin method on unstructured grids. Acta Aerodynamica Sinica, 2011, 29(5): 537-541 https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201105000.htm
[7]	Liu Xiang, Kameni A, Serhir M, et al. 3D modeling with discontinuous Galerkin time domain method for ground penetration radar application[C]//GDR Ondes, Assemblee Generale Interferences d'Ondes, 2015.
[8]	Su Yan, Andrew D G, Jin Jianming. Modeling of plasma formation during high-power microwave breakdown in air using the discontinuous Galerkin time-domain method[J]. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 2016, 27(1): 2-13.
[9]	Nikolai S, Claire S, Stephane L, et al. A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects[J]. Journal of Computational Physics, 2016, 316(7): 396-415.
[10]	Chan J, Hewett R J, Warburton T. Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media[OL]. arXiv, 2016.
[11]	Anderson W K, Wang Li, Kapadia S, et al. Petrov-Galerkin and discontinuous Galerkin methods for time-domain and frequency-domain electromagnetic simulations[J]. Journal of Computational Physics, 2011, 230(23): 8360-8385.
[12]	Liu Meilin, Sirenko K, Bagci H. An efficient discontinuous Galerkin finite element method for highly accurate solution of Maxwell equations[J]. IEEE Trans Antennas and Propagation, 2012, 60(8): 3992-3998.