PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 155 > pp. 39-52

FAST DOMAIN DECOMPOSITION METHODS OF FE-BI-MLFMA FOR 3D SCATTERING/RADIATION PROBLEMS (Invited Paper)

By M.-L. Yang, H.-W. Gao, X.-M. Sun, and X.-Q. Sheng

Full Article PDF (834 KB)

Abstract:
It has been widely verified that the hybrid finite element - boundary integral - multilevel fast multipole algorithm (FE-BI-MLFMA) is a general, efficient and accurate method for the analysis of unbounded electromagnetic problems. A variety of fast methods of FE-BI-MLFMA have been developed since 1998. In particular, the domain decomposition methods have been applied to FE-BI-MLFMA and significantly improve the efficiency of FE-BI-MLFMA in recent years. A series of fast domain decomposition methods (DDMs) of FE-BI-MLFMA have been developed. These fast DDMs can be roughly classified into two types: Schwarz DDMs and dual-primal finite element tearing and interconnecting (FETI-DP) DDMs. This paper will first give an overview of the DDMs development of FE-BI-MLFMA. Then a uniform, consistent, and efficient formulation is presented and discussed for these fast DDMs of FE-BI-MLFMA. Their computational complexities are analyzed and studied numerically.

Citation:
M.-L. Yang, H.-W. Gao, X.-M. Sun, and X.-Q. Sheng, "Fast Domain Decomposition Methods of FE-BI-MLFMA for 3D Scattering/Radiation Problems (Invited Paper)," Progress In Electromagnetics Research, Vol. 155, 39-52, 2016.
doi:10.2528/PIER15102802
http://www.jpier.org/PIER/pier.php?paper=15102802

References:
1. Sheng, X. Q., J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, "On the formulation of hybrid finite element and boundary integral methods for 3-D scattering," IEEE Transactions on Antennas and Propagation, Vol. 46, 303-311, 1998.
doi:10.1109/8.662648

2. Sheng, X. Q. and E. K. N. Yung, "Implementation and experiments of a hybrid algorithm of the MLFMA-Enhanced FE-BI method for open-region inhomogeneous electromagnetic problems," IEEE Transactions on Antennas and Propagation, Vol. 50, No. 2, 163-167, 2002.
doi:10.1109/8.997987

3. Botha, M. M. and J. M. Jin, "On the variational formulation of hybrid finite element-boundary integral techniques for electromagnetic analysis," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 11, 3037-3047, 2004.
doi:10.1109/TAP.2004.835140

4. Vouvakis, M. N., S. C. Lee, K. Zhao, and J. F. Lee, "A symmetric FEM-IE formulation with a single-level IE-QR algorithm for solving electromagnetic radiation and scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 11, 3060-3070, 2004.
doi:10.1109/TAP.2004.837525

5. Liu, J. and J. M. Jin, "A special higher-order finite-element method for scattering by deep cavities," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 5, 694-703, 2000.
doi:10.1109/8.855487

6. Jin, J. M., J. Liu, Z. Lou, and C. S. T. Liang, "A fully high-order finite-element simulation of scattering by deep cavities," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 9, 2420-2429, 2003.
doi:10.1109/TAP.2003.816354

7. Peng, Z. and X. Q. Sheng, "A flexible and efficient higher-order FE-BI-MLFMA for scattering by a large body with deep cavities," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 7, 2031-2042, 2008.
doi:10.1109/TAP.2008.924725

8. Yang, M. L. and X.-Q. Sheng, "Parallel high-order FE-BI-MLFMA for scattering by large and deep coated cavities loaded with obstacles," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 13, 1813-1823, 2009.
doi:10.1163/156939309789566932

9. Liu, J. and J. M. Jin, "A highly effective preconditioner for solving the finite element-boundary integral matrix equation for 3-D scattering," IEEE Transactions on Antennas and Propagation, Vol. 50, 1212-1221, 2002.

10. Hu, F. G. and C. F. Wang, "Preconditioned formulation of FE-BI equations with domain decomposition method for calculation of electromagnetic scattering from cavities," IEEE Transactions on Antennas and Propagation, Vol. 57, 2506-2511, 2009.

11. Lee, J., J. Zhang, and C. C. Lu, "Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 9, 2277-2287, 2004.
doi:10.1109/TAP.2004.834084

12. Lee, J. F. and D. K. Sun, "p-type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 3, 864-870, 2004.
doi:10.1109/TMTT.2004.823554

13. Yang, M. L. and X. Q. Sheng, "Hybrid h-and p-type multiplicative Schwarz (h-p-MUS) preconditioned algorithm of higher-order FE-BIMLFMA for 3D scattering," IEEE Transactions on Magnetics, Vol. 48, 187-190, 2012.
doi:10.1109/TMAG.2011.2174033

14. Despres, B., P. Joly, and J. E. Roberts, "A domain decomposition method for the harmonicMaxwell equations," Iterative Methods in Linear Algebraic Amsterdam, 475-484, The Netherlands, 1992.

15. Farhat, C. and F. X. Roux, "A method of finite element tearing and interconnecting and its parallel solution algorithm," International Journal for Numerical Methods in Engineering, Vol. 32, 1205-1227, 1991.
doi:10.1002/nme.1620320604

16. Wolfe, C. T., U. Navsariwala, and S. D. Gedney, "An efficient implementation of the finite-element time-domain algorithm on parallel computers using finite-element tearing and interconnecting algorithm," Microwave and Optical Technology Letters, Vol. 16, No. 4, 1997.

17. Farhat, C., P. Avery, and R. Tezaur, "FETI-DPH: A dual-primal domain decomposition method for acoustic scattering," Journal of Computational Acoustics, Vol. 13, 499-524, 2005.
doi:10.1142/S0218396X05002761

18. Li, Y. J. and J. M. Jin, "A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems," IEEE Transactions on Antennas and Propagation, Vol. 54, 3000-3009, 2006.
doi:10.1109/TAP.2006.882191

19. Li, Y. J. and J. M. Jin, "A new dual-primal domain decomposition approach for finite element simulation of 3-D large-scale electromagnetic problems," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 10, 2803-2810, 2007.
doi:10.1109/TAP.2007.905954

20. Yang, M. L. and X. Q. Sheng, "On the finite element tearing and interconnecting method for scattering by large 3D inhomogeneous targets," International Journal of Antennas and Propagation, Vol. 2011, 2012, [Online], available: http://www.hindawi.com/journals/ijap/2012/898247/.

21. Zhao, K., V. Rawat, S. C. Lee, and J. F. Lee, "A domain decomposition method with nonconformal meshes for finite periodic and semi-periodic structures," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 9, 2559-2570, 2007.
doi:10.1109/TAP.2007.904107

22. Peng, Z. and J. F. Lee, "Non-conformal domain decomposition method with mixed true second order transmission condition for solving large finite antenna arrays," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 5, 1638-1651, 2011.
doi:10.1109/TAP.2011.2123067

23. Xue, M. F. and J. M. Jin, "Nonconformal FETI-DP methods for large-scale electromagnetic simulation," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 9, 4291-4304, 2012.
doi:10.1109/TAP.2012.2207076

24. Xue, M. F. and J. M. Jin, "A hybrid conformal/nonconformal domain decomposition method for multi-region electromagnetic modeling," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 2009-2021, 2014.
doi:10.1109/TAP.2014.2300149

25. Vouvakis, M. N., K. Zhao, S. M. Seo, and J. F. Lee, "A domain decomposition approach for nonconformal couplings between finite and boundary elements for unbounded electromagnetic problems in R3," Journal of Computational Physics, Vol. 225, No. 1, 975-994, 2007.
doi:10.1016/j.jcp.2007.01.014

26. Zhao, K. Z., V. Rawat, S. C. Lee, and J. F. Lee, "Hybrid domain decomposition method and boundary element method for the solution of large array problems," IEEE Antennas and Propagation Society International Symposium, 2007.

27. Xue, M. F., Y. J. Li, and J. M. Jin, "Acceleration and accuracy improvement of FEM computation by using FETI-DP and BI hybrid algorithm," IEEE Antennas and Propagation Society International Symposium, 2010.

28. Yang, M. L., H. W. Gao, and X. Q. Sheng, "Parallel domain-decomposition-based algorithm of hybrid FE-BI-MLFMA method for 3D scattering by large inhomogeneous objects," IEEE Transactions on Antennas and Propagation, Vol. 61, 4675-4683, 2013.
doi:10.1109/TAP.2013.2271232

29. Yang, M. L., H. W. Gao, W. Song, and X. Q. Sheng, "An effective domain-decomposition-based preconditioner for the FE-BI-MLFMA method for 3D scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 2263-2268, 2014.
doi:10.1109/TAP.2014.2300159

30. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, 409-418, 1982.
doi:10.1109/TAP.1982.1142818

31. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 10, 1488-1493, 1997.
doi:10.1109/8.633855

32. Amestoy, P. R., I. S. Duff, J. Koster, and J.-Y. L’Excellent, "A fully asynchronous multifrontal solver using distributed dynamic scheduling," SIAM Journal of Matrix Analysis and Applications, Vol. 23, 15-41, 2001.
doi:10.1137/S0895479899358194


© Copyright 2014 EMW Publishing. All Rights Reserved