Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 93 > pp. 369-384


By Z. Peng, X.-Q. Sheng, and F. Yin

Full Article PDF (337 KB)

It is known that the conventional algorithm (CA) of hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) usually suffers the problem of slow convergence, and the decomposition algorithm (DA) is limited by large memory requirement. An efficient twofold iterative algorithm (TIA) of FE-BI-MLFMA is presented using the multilevel inverse-based incomplete LU (MIB-ILU) preconditioning in this paper. It is shown that this TIA can offer a good balance of efficiency between CPU time and memory requirement. The tree-cotree splitting technique is then employed in the TIA to further improve its efficiency and robustness. A variety of numerical experiments are performed in this paper, demonstrating that the TIA exhibits superior efficiency in memory and CPU time to DA and CA, and greatly improves the computing capability of FE-BI-MLFMA.

Z. Peng, 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.

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, No. 8, 1053-1058, 1990.

2. 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, No. 1, 66-76, 1993.

3. Antilla, G. E. and N. G. Alexopoulos, "Scattering from complex three-dimensional geometries by a curvilinear hybrid finite-element-integral equation approach," J. Opt. Soc. Amer. A, Vol. 11, No. 4, 1445-1457, 1994.

4. Boyes, W. E. and A. A. Seidl, "A hybrid finite element method for 3-D scattering using nodal and edge elements," IEEE Trans. Antennas Propagat., Vol. 42, No. 10, 1436-1442, 1994.

5. Rogier, H., F. Olyslager, and D. De Zutter, "A hybrid finite element integral equation approach for the eigenmode analysis of complex anisotropic dielectric waveguides," Radio Science, Vol. 31, No. 4, 999-1010, 1996.

6. Eibert, T. and V. Hansen, "Calculation of unbounded field problems in free space by a 3D FEM/BEM-hybrid approach,", Vol. 10, No. 1, 61-78, 1996.

7. Cwik, T., C. Zuffada, and V. Jamnejad, "Modeling three-dimensional scatterers using a coupled finite element --- Integral equation formulation," IEEE Trans. Antennas Propagat., Vol. 44, No. 4, 453-459, 1996.

8. Bindiganavale, S. S. and J. L. Volakis, "A hybrid FE-FMM Technique for electromagnetic scattering," IEEE Trans. Antennas Propagat., Vol. 45, No. 1, 180-181, 1997.

9. Soudais, P., H. Steve, and F. Dubois, "Scattering from several test-objects computed by 3-D hybrid IE/PDE methods," IEEE Trans. Antennas Propagat., Vol. 47, No. 4, 646-653, 1999.

10. 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, No. 3, 303-311, 1998.

11. Rogier, H., B. Baekelandt, F. Olyslager, and D. De Zutter, "Application of the FE-BIE technique to problems relevant to electromagnetic compatibility: Optimal choice of mechanisms to take into account periodicity," IEEE Trans. on Electromagnetic Compatibility, Vol. 42, No. 3, 246-256, 2000.

12. 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, No. 2, 163-167, 2002.

13. 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, No. 9, 1212-1221, 2002.

14. Vouvakis, M. N., S. C. Lee, K. Z. 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 Trans. Antennas Propagat., Vol. 52, No. 11, 3060-3070, 2004.

15. Duff, I. S. and J. K. Reid, "The multifrontal solution of indefinite sparse symmetric linear system," ACM Trans. on Mathematical Software, Vol. 9, No. 3, 302-325, 1983.

16. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publishing Company Press, Boston, 1996.

17. Saad, Y. and J. Zhang, "BILUM: Block versions of multielimination and multi-level ILU preconditioner for general sparse linear systems," SIAM J. Sci. Comput., Vol. 20, 2103-2121, 1999.

18. Zhang, J., "A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices," Applied Mathematics and Computation, Vol. 124, No. 1, 95-115, 2001.

19. Bollhofer, M. and Y. Saad, "On the relations between ILUs and factored approximate inverses," SIAM J. Matrix Anal. Appl., Vol. 24, 219-237, 2002.

20. Li, N., Y. Saad, and E. Chow, "Crout versions of ILU for general sparse matrices," SIAM J. Sci. Comput., Vol. 25, No. 2, 716-728, 2003.

21. Bollhofer, M., "A robust and eĀ±cient ILU that incorporates the growth of the inverse triangular factors," SIAM J. Sci. Comput., Vol. 25, No. 1, 86-103, 2003.

22. Bollhofer, M. and Y. Saad, "Multilevel preconditioners constructed from inverse-based ILUs,", Vol. 27, No. 5, 1627-1650, 2006.

23. Albanese, R. and G. Rubinacci, "Solution of three dimensional eddy current problems by integral and differential methods," IEEE Trans. Magn., Vol. 24, No. 1, 98-101, 1988.

24. Lee, S. C., J.-F. Lee, and R. Lee, "Hierarchical vector finite elements for analyzing wave guiding structures," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 8, 1897-1905, 2003.

25. Lee, J. F. and D. K. Sun, "p-Type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 3, 864-870.

26. Duff, I. S. and S. Pralet, "Strategies for scaling and pivoting for sparse symmetric indefinite problems," SIAM J. Matrix Anal. Appl., Vol. 27, No. 2, 313-340, 2005.

27. Karypis, G. and V. Kumar, "A fast and high quality multilevel scheme for partitioning irregular graphs," SIAM J. Sci. Comput., Vol. 20, No. 1, 359-392, 1998.

28. Karypis, G. and V. Kumar, , Metis: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices, available on line at: http://www.cs.umn.edu/~karypis/metis/metis.html, 1998.

© Copyright 2014 EMW Publishing. All Rights Reserved