Efficient Improved Local Time Stepping with the Leapfrog Scheme for Transient 3-D Electromagnetic Analyses
DOI:
https://doi.org/10.13052/2023.ACES.J.380805Keywords:
Antenna transient analysis, discontinuous Galerkin time domain method, high-order time integration, local time steppingAbstract
An alternate boundary local time stepping (ABLTS) method is proposed for the discontinuous Galerkin time domain method for transient electromagnetic simulations to reduce the computation complexity of the local time stepping (LTS) method. The proposed method exhibites lower storage and time complexity than the conventional LF-LTS method . The stability, accuracy, and effectiveness of the ABLTS method are verified by applying it to the simulation of a resonator cavity and multi-layer microstrip antenna. The numerical results revealed that the developed method is effective for the transient electromagnetic simulation of antennas.
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References
J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, New York, NY, USA: Springer, 2008.
A. Bossavit, “Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism,” IEE Proceedings A Physical Science, Measurement and Instrumentation, Management and Education, Reviews, vol. 135, no. 8, pp. 493-500, 1988.
X. Zhao, Z. Lin, Y. Zhang, S. Ting, and T. K. Sarkar, “Parallel Hybrid method of HOMoM–MLFMA for analysis of large antenna arrays on an electrically large platform,” IEEE Transactions on Antennas and Propagation, vol. 64, no. 12, pp. 5501-5506, Dec. 2016, doi:10.1109/TAP.2016.2621029.
L. Zhao, G. Chen, W. Yu, and J. M. Jin, “A fast waveguide port parameter extraction technique for the DGTD method,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 2659-2662, 2017, doi:10.1109/LAWP.2017.2740298.
S. Dosopoulos and J. F. Lee, “Interior penalty discontinuous Galerkin finite element method for the time-dependent first order Maxwell’s equations,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 12, pp. 4085-4090, Dec. 2010, doi:10.1016/j.jcp.2010.07.036.
J. Chen and Q. Liu, “Discontinuous Galerkin time-domain methods for multiscale electromagnetic simulations: A review,” Proceedings of the IEEE, vol. 101, no. 2, pp. 242-254, Feb. 2013, doi: 10.1109/JPROC.2012.2219031.
L. Zhao, G. Chen, W. Yu, and J. M. Jin, “A fast waveguide port parameter extraction technique for the DGTD method,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 2659-2662, 2017, doi:10.1109/LAWP.2017.2740298.
M. J. Grote and M. Teodora. “Explicit local time-stepping methods for time-dependent wave propagation,” arXiv: Numerical Analysi, 2012, doi:10.48550/arXiv.1205.0654.
E. Montseny, S. Pernet, X. Ferrières, and G. Cohen, “Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell’s equations,” Journal of Computational Physics, vol. 227, no. 14, pp. 6795-6820, 2008.
L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM, Mathematical Modelling and Numerical Analysis, vol. 39, no. 6, pp. 1149-1176, 2005.
J. Alvarez, L. D. Angulo, A. R. Bretones, C. M. Coevorden and S. G. Garcia, “Efficient antenna modeling by DGTD: Leap-frog discontinuous Galerkin timedomain method,” IEEE Antennas and Propagation Magazine, vol. 57, no. 3, pp. 95-106, June 2015, doi:10.1109/MAP.2015.2437279.
M. Li, Q. Wu, Z. Lin, Y. Zhang, and X. Zhao, “Novel parallelization of discontinuous galerkin method for transient electromagnetics simulation based on sunway supercomputers,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 37, no. 7, pp. 795-804, Sep. 2021, doi:10.13052/2022.ACES.J.370706.
M. Li, Q. Wu, Z. Lin, Y. Zhang, and X. Zhao, “A minimal round-trip strategy based on graph matching for parallel dgtd method with local Time-stepping,” IEEE Antennas and Wireless Propagation Letters, vol. 22, no. 2, pp. 243-247, Feb. 2023, doi:10.1109/LAWP.2022.3208010.
Z. G. Ban, Y. Shi, and P. Wang, “Advanced parallelism of DGTD method with local time stepping based on novel MPI + MPI unified parallel algorithm,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 5, pp. 3916-3921, 2022, doi:10.1109/TAP.2021.3137455.
G. Cohen, X. Ferrieres, and S. Pernet, “A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell’s equations in time domain,” Journal of Computational Physics, vol. 217, no. 2, pp. 340-363, 2006, doi:10.1016/j.jcp.2006.01.004.
S. Zuo, Z. Lin, D. G. Doñoro, Y. Zhang, and X. Zhao, “A parallel direct domain decomposition solver based on schur complement for electromagnetic finite element analysis,” IEEE Antennas and Wireless Propagation Letters, vol. 20, no. 4, pp. 458-462, Apr. 2021, doi:10.1109/LAWP.2021.3053566.