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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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APPLICATION OF THE IMPROVED FINITE ELEMENT-FAST MULTIPOLE METHOD ON LARGE SCATTERING PROBLEMS

By X.-C. Wei, E. P. Li, and Y. J. Zhang

Full Article PDF (263 KB)

Abstract:
The finite element hybridized with the boundary integral method is a powerful technique to solve the scattering problem, especially when the fast multipole method is employed to accelerate the matrix-vector multiplication in the boundary integral method. In this paper, the multifrontal method is used to calculate the triangular factorization of the ill conditioned finite element matrix in this hybrid method. This improves the spectral property of the whole matrix and makes the hybrid method converge very fast. Through some numerical examples including the scattering from a real-life aircraft with an engine, the accuracy and efficiency of this improved hybrid method are demonstrated.

Citation:
X.-C. Wei, E. P. Li, and Y. J. Zhang, "Application of the Improved Finite Element-Fast Multipole Method on Large Scattering Problems," Progress In Electromagnetics Research, Vol. 47, 49-60, 2004.
doi:10.2528/PIER03092501
http://www.jpier.org/PIER/pier.php?paper=0309251

References:
1. Jin, J. M., The Finite Element Method in Electromagnetics, Second edition, Wiley, New York, 2002.

2. Xiang, X. and Y. Lu, "A hybrid FEM/BEM/WTM approach for fast solution of scattering from cylindrical scatters with arbitrary cross sections," J. Electromag. Wave Applicat., Vol. 13, No. 6, 811-812, 1999.

3. Wei, X. C., E. P. Li, and C. H. Liang, "Fast solution for large scale electromagnetic scattering problems using wavelet transform and its precondition," J. Electromag. Wave Applicat., Vol. 17, No. 4, 611-613, 2003.
doi:10.1163/15693930360681965

4. Canning, F. X., "The impedance matrix localization method (IML) for MM calculation," IEEE Trans. Antennas Propagat. Mag., Vol. 32, No. 5, 8-30, 1990.

5. Canning, F. X., "Transformations that produce a sparse moment method matrix," J. Electromag. Wave Applicat., Vol. 4, No. 9, 893-913, 1990.

6. Rokhlin, V., "Rapid solution of integral equations of scattering theory in two dimensions," J. Comput. Phys., Vol. 86, No. 2, 414-439, 1990.
doi:10.1016/0021-9991(90)90107-C

7. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Micro. and Opt. Tech. Lett., Vol. 10, No. 1, 14-19, 1995.

8. Topsakal, E., R. Kindt, K. Sertel, and J. Volakis, "Evaluation of the BICGSTAB(l) algorithm for the finite-element/boundaryintegral method," IEEE Trans. Antennas Propagat. Mag., Vol. 43, No. 6, 124-131, 2001.
doi:10.1109/74.979531

9. 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.
doi:10.1109/8.997987

10. Jian, L. and J. M. Jin, "A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering," IEEE Trans. Antennas Propagat., Vol. 50, No. 9, 1212-1221, 2002.
doi:10.1109/TAP.2002.801377

11. Liu, J. W. H., "The multifrontal method for sparse matrix solution: theory and practice," SIAM Review, Vol. 34, No. 1, 82-109, 1992.
doi:10.1137/1034004

12. Graglia, R. D., "On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle," IEEE Trans. Antennas Propagat., Vol. 41, No. 10, 1448-1455, 1993.
doi:10.1109/8.247786

13. Sheng, X. Q., J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, "On the formulation of hybrid finite-element and boundaryintegral methods for 3-D scattering," IEEE Trans. Antennas Propagat., Vol. 46, No. 3, 303-311, 1998.
doi:10.1109/8.662648


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