volume | PIER Journals

Abstract

The hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is a powerful method for calculating scattering by inhomogeneous objects. However, the conventional FE-BI-MLFMA often suffers from iterative convergence problems. A non-overlapping domain decomposition method (DDM) is applied to FE-BI-MLFMA to speed up the iterative convergence. Furthermore, a preconditioner based on absorbing boundary condition and symmetric successive over relaxation (ABC-SSOR) is constructed to further accelerate convergence of the DDM-FE-BI-MLFMA. Numerical experiments demonstrate the efficiency of the proposed preconditioned DDM-FE-BI-MLFMA.

1. Yuan, X., "Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method," IEEE Trans. Microwave Theory Tech., Vol. 38, 1053-1058, Aug. 1990.
doi:10.1109/22.57330 Google Scholar

2. Jin, J. M. and J. L. Volakis, "A hybrid finite element method for scattering and radiation by microstrip patch antennas and arrays residing in a cavity," IEEE Trans. Antennas Propagat., Vol. 39, 1598-1604, Nov. 1991.
doi:10.1109/8.102775 Google Scholar

3. Angelini, J. J., C. Soize, and P. Soudais, "Hybrid numerical method for harmonic 3-D Maxwell equations: Scattering by a mixed conducting and inhomogeneous anisotropic dielectric medium," IEEE Trans. Antennas Propagat., Vol. 41, 66-76, May 1993.
doi:10.1109/8.210117 Google Scholar

4. Eibert, T. and V. Hansen, "Calculation of unbounded field problems in free space by a 3-D FEM/BEM-hybrid approach," Journal of Electromagnetic Waves and Applications, Vol. 10, No. 1, 61-77, Apr. 1996.
doi:10.1163/156939396X00216 Google Scholar

5. Shao, H., J. Hu, Z.-P. Nie, G. Han, and S. He, "Hybrid tangential equivalence principle algorithm with MLFMA for analysis of array structures," Progress In Electromagnetics Research, Vol. 113, 127-141, 2011. Google Scholar

6. Ergul, O., "Parallel implementation of MLFMA for homogeneous objects with various material properties," Progress In Electromagnetics Research, Vol. 121, 505-520, 2011.
doi:10.2528/PIER11092501 Google Scholar

7. Pan, X.-M., L. Cai, and X.-Q. Sheng, "An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis," Progress In Electromagnetics Research, Vol. 126, 85-100, 2012.
doi:10.2528/PIER12020203 Google Scholar

8. Sheng, X. Q., J. M. Song, C. C. Lu, and W. C. Chew, "On the formulation of hybrid finite-element and boundary-integral method for 3D scattering," IEEE Trans. Antennas Propagat., Vol. 46, 303-311, Mar. 1998.
doi:10.1109/8.662648 Google Scholar

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 Trans. Antennas Propagat., Vol. 50, 1212-1221, Sep. 2002. Google Scholar

10. 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 Trans. Antennas Propagat., Vol. 50, 163-167, Feb. 2002.
doi:10.1109/8.997987 Google Scholar

11. Peng, Z., X. Q. Sheng, and F. Yin, "An efficient twofold iterative algorithm of FE-BI-MLFMA using multilevel inverse-based ILU preconditioning," Progress In Electromagnetics Research, Vol. 93, 369-384, 2009.
doi:10.2528/PIER09060305 Google Scholar

12. Farhart, C. and F. X. Roux, "A method of finite element tearing and interconnecting and its parallel solution algorithm," Int. J. Numer. Method Eng., Vol. 32, No. 32, 1205-1227, 1991.
doi:10.1002/nme.1620320604 Google Scholar

13. Stupfel, B., "A fast-domain decomposition method for the solution of electromagnetic scattering by large objects," IEEE Trans. Antennas Propagat., Vol. 44, 1375-1385, Oct. 1996. Google Scholar

14. 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, Nov. 1997. Google Scholar

15. Wolfe, C. T., U. Navsariwala, and S. D. Gedney, "A parallel finite-element tearing and interconnecting algorithm for solution of the vectorwave equation with PML absorbing medium," IEEE Trans. Antennas Propagat., Vol. 48, 278-284, Feb. 2000.
doi:10.1109/8.833077 Google Scholar

16. Stupfel, B. and M. Mognot, "A domain decomposition method for the vector wave equation," IEEE Trans. Antennas Propagat., Vol. 48, 653-660, May 2000.
doi:10.1109/8.855483 Google Scholar

17. Vouvakis, M. N. and J.-F. Lee, "A fast non-conforming DP-FETI domain decomposition method for the solution of large EM problems," Proc. Antennas Propag. Soc. Int. Symp., Vol. 1, 623-626, Jun. 2004. Google Scholar

18. Lee, S.-C., M. N. Vouvakis, and J.-F. Lee, "A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays," J. Comput. Phys., Vol. 203, 1-21, Feb. 2005. Google Scholar

19. Vouvakis, M. N., Z. Cendes, and J.-F. Lee, "A FEM domain decomposition method for photonic and electromagnetic band gap structures," IEEE Trans. Antennas Propagat., Vol. 54, 721-733, Feb. 2006.
doi:10.1109/TAP.2005.863095 Google Scholar

20. Lu, Z. Q., X. An, and W. Hong, "A fast domain decomposition method for solving three-dimensional large-scale electromagnetic problems," IEEE Trans. Antennas Propagat., Vol. 56, 2200-2210, Aug. 2008.
doi:10.1109/TAP.2008.926755 Google Scholar

21. 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 Trans. Antennas Propagat., Vol. 54, 3000-3009, Oct. 2006. Google Scholar

22. 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 Trans. Antennas Propagat., Vol. 55, 2803-2810, Oct. 2007. Google Scholar

23. Cui, Z. W., Y. Han, C. Y. Li, and W. J. Zhao, "Efficient analysis of scattering from multiple 3-D cavities by means of a FE-BI-DDM method," Progress In Electromagnetics Research, Vol. 116, 425-439, 2011. Google Scholar

24. 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 Propagat., Vol. 2012, 1-6, 2012. Google Scholar

25. Jin, J. M., The Finite Element Method in Electromagnetics, 2nd Edition, Wiley, New York, 2002.

26. Dziekonski, A., A. Lamecki, and M. Mrozowski, "A memory efficient and fast sparse matrix vector product on a GPU," Progress In Electromagnetics Research, Vol. 116, 49-63, 2011. Google Scholar

27. Amestoy, P. R., I. S. Duff, J.-Y. L'Excellent, and J. Koster, "A full asynchronous multifrontal solver using distributed dynamic scheduling," SIAM J. Matrix Anal. Appl., Vol. 23, No. 1, 15-41, Jan. 2001.
doi:10.1137/S0895479899358194 Google Scholar

Dr. Hong-Wei Gao

Dr. Ming-Lin Yang

Professor Xin-Qing Sheng