A Novel Finite Element Mesh Truncation Technology Accelerated by Parallel Multilevel Fast Multipole Algorithm and its Applications
Keywords:
Finite element method (FEM), integral equation, mesh truncation technique, multilevel fast multipole algorithm (MLFMA)Abstract
In order to meet the highly accurate requirements of nowadays scattering and antenna problems, the finite element method requires the use of very accurate mesh truncations techniques able to absorb any outgoing wave completely. In this paper a novel implementation of the finite element mesh truncation technique called Finite Element-Iterative Integral Equation Evaluation (FE-IIEE) is studied. This method can provide a numerical exact radiation boundary condition while the original sparse and banded structure of the finite element method (FEM) matrix is retained. Also, an efficient parallel multilevel fast multipole algorithm (MLFMA) is included to drastically accelerate the time-consuming near field calculation process required by the truncation technique. In order to achieve a high parallel efficiency, both algorithms have been implemented together from scratch, being able to run over several thousands of CPU cores. Through comparisons with commercial software such as HFSS, the accuracy and efficiency of the method are validated showing excellent performance. Finally, a large 100- elements array antenna with more than 24 million unknowns is effectively analyzed using 2560 CPU cores.
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References
J. Jianming, The Finite Element Method in Electromagnetics. New Jersey: John Wiley & Sons, 2002.
M. Salazar-Palma, T. K. Sarkar, L. E. GarciaCastillo, T. Roy, and A. R. Djordjevic, Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling. Norwood, MA: Artech House Publishers, Inc., 1998.
B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proceedings of the National Academy of Sciences, vol. 74, no. 5, pp. 1765-1766, 1977.
J. Y. Wu, D. M. Kingsland, J. F. Lee, et al., “A comparison of anisotropic PML to Berenger's PML and its application to the finite-element method for EM scattering,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 1, pp. 40-50, 1997.
X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integralmultilevel fast multipole algorithm,” IET Microwaves, Antennas & Propagation, vol. 4, no. 4, pp. 492-0, 2010.
J. L. Volakis, J. Gong, and A. Alexanian “A finite element boundary integral method for antenna RCS analysis,” Electromagnetic, vol. 14, no. 1, pp. 63-85, 1994.
H. Hu, Y. Tan, B. Zhu, and L. Zhou, “A hybrid FEBI method using in antenna radiation analysis,” 2008 8th International Symposium on Antennas, Propagation and EM Theory, Kunming, pp. 898- 901, 2008
. [8] R. Fernandez-Recio, L. E. Garcia-Castillo, I. Gomez-Revuelto, et al. “Fully coupled multihybrid FEM-PO/PTD-UTD method for the analysis of radiation problems,” IEEE Transactions on Magnetics, vol. 43, no. 4, pp. 1341-1344, 2007.
R. Fernandez-Recio, L. E. Garcia-Castillo, I. Gomez-Revuelto, et al., “Fully coupled hybrid FEM-UTD method using NURBS for the analysis of radiation problems,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 3, pp. 774- 783, 2008.
R. Fernandez-Recio, L. E. Garcia-Castillo, I. Gomez-Revuelto, and M. Salazar-Palma, “Convergence study of a non-standard Schwarz domain decomposition method for finite element mesh truncation in electromagnetics,” Progress In Electromagnetics Research (PIER), vol. 120, pp. 439-457, 2011.
D. Garcia-Donoro, S. Ting, A. Amor-Martin, et al., “Analysis of planar microwave devices using higher order curl-conforming triangular prismatic finite elements,” Microwave and Optical Technology Letters, vol. 58, no. 8, pp. 1794-1801, 2016.
D. Garcia-Donoro, L. E. Garcia-Castillo, T. K. Sarkar, et al., “A non-standard Schwarz domain decomposition method for finite element mesh truncation of infinite arrays,” IEEE Transactions on Antennas and Propagation, vol. 66, no. 11, pp. 6179-6190, 2018.
A. Tzoulis, T. F. Eibert, “Efficient electromagnetic near-field computation by the multilevel fast multipole method employing mixed near-field/farfield translations,” IEEE Antennas & Wireless Propagation Letters, vol. 4, no. 1, pp. 449-452, 2005.
A. Amor-Martin, D. Garcia-Donoro, L. E. GarciaCastillo, et al., “A finite element mesh truncation technique for scattering and radiation problems in HPC environments,” Computing & Electromagnetics International Workshop, IEEE, 2017.
L. E. Garcia-Castillo and M. Salazar-Palma, “Second-order Nédélec tetrahedral element for computational electromagnetics,” International Journal of Numerical Modelling: Electronic Networks. Devices and Fields (John Wiley & Sons, Inc.), vol. 13, no. 2-3, pp. 261-287, Mar.-June 2000.
C. W. Chew, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, 2001.
X. Zhao, S. W. Ting, and Y. Zhang, “Parallelization of half-space MLFMA using adaptive direction partitioning strategy,” IEEE Antennas and Wireless Propagation Letters, vol. 13, pp. 1203-1206, 2014.
HFSS. Accessed: 01/06/2019. [Online]. Available: https://www.ansys.com/products/electronics/ansys -hfss, 2019.
FEKO. Accessed: 01/06/2019. [Online]. Available: https://altairhyperworks.com/product/FEKO, 2019.
Y. Zhang, T. K. Sarkar, Y. Zhao, et al., Higher Order Basis Based Integral Equation Solver (HOBBIES). Wiley Press, USA: New Jersey, 2012.
