volume | PIER Journals

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.

1. Jin, J. M., The Finite Element Method in Electromagnetics, Second edition, 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. Google Scholar

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 Google Scholar

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. Google Scholar

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

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

Dr. Xing-Chang Wei

Professor Er Ping Li

Dr. Yao Jiang Zhang