2014-02-24
Simple Methods to Raise the Robustness and Efficiency of the Incomplete Cholesky Preconditioners for FEM Simulation of Electromagnetic Problems
By
Progress In Electromagnetics Research M, Vol. 35, 49-56, 2014
Abstract
In this paper, the finite element method (FEM) is applied to the analysis of three-dimensional (3D) electromagnetic structures. The incomplete Cholesky (IC) preconditioner based on shifted operators is used to solve the finite element linear systems. Several strategies are adopted to raise the efficiency and robustness of the preconditioner. Numerical experiments for several microwave devices demonstrate the superior numerical convergence and robustness of the proposed preocnditioner.
Citation
Xue Wei Ping, Caixia Bian, Xinghui Yin, and Jiaqi Chen, "Simple Methods to Raise the Robustness and Efficiency of the Incomplete Cholesky Preconditioners for FEM Simulation of Electromagnetic Problems," Progress In Electromagnetics Research M, Vol. 35, 49-56, 2014.
doi:10.2528/PIERM13111401
References

1. Jin, J. M., The Finite Element Method in Electromagnetics, 2nd Ed., John Wiley & Sons, Inc., New York, 2002.

2. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetic, IEEE Press, New York, 1998.
doi:10.1109/9780470544655

3. Zhang, Y. Q. and D. B. Ge, "A unified FDTD approach for electromagnetic analysis of dispersive objects," Progress In Electromagnetics Research, Vol. 96, 155-172, 2009.
doi:10.2528/PIER09072603        Google Scholar

4. Harrington, R. F., Field Computation by Moment Methods Malabar, Krieger Publishing Company, Florida, 1983.

5. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, and Z. Masouri, "A moment method simulation of electromagnetic scattering from conducting bodies," Progress In Electromagnetics Research, Vol. 81, 99-119, 2008.
doi:10.2528/PIER07122502        Google Scholar

6. Hano, M., T. Miyamura, and M. Hotta, "Three-dimensional finite element eddy current analysis by using high-order vector elements," Electrical Engineering in Japan, Vol. 147, No. 4, 60-67, 2004.
doi:10.1002/eej.10306        Google Scholar

7. Holmgaard, T. and S. I. Bozhevolnyi, "Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides," Physical Review B, Vol. 75, 245405, 2007.
doi:10.1103/PhysRevB.75.245405        Google Scholar

8. Politano, A., "Interplay of structural and temperature e®ects on plasmonic excitations at noble-metal interfaces," Philosophical Magazine, Vol. 92, No. 6, 768-778, 2012.
doi:10.1080/14786435.2011.634846        Google Scholar

9. Politano, A. and G. Chiarello, "Unravelling suitable graphene-metal contacts for graphene-based plasmonic devices," Nanoscale, Vol. 5, No. 17, 8215-8220, 2013.
doi:10.1039/c3nr02027d        Google Scholar

10. Politano, A., V. Formoso, and G. Chiarello, "Dispersion and damping of gold surface plasmon," Plasmonics, Vol. 3, 165-170, 2008.
doi:10.1007/s11468-008-9070-2        Google Scholar

11. Politano, A., V. Formoso, and G. Chiarello, "Evidence of composite plasmon{phonon modes in the electronic response of epitaxial graphene," Journal of Physics: Condensed Matter, Vol. 25, 345303, 2013.
doi:10.1088/0953-8984/25/34/345303        Google Scholar

12. Cajan, H., L. Pichon, and C. Marchand, "Finite element method for radiated emissions in EMC analysis," IEEE Transactions on Magnetics, Vol. 36, No. 4, 964-967, 2000.
doi:10.1109/20.877602        Google Scholar

13. An, X. and Z.-Q. Lu, "An efficient finite element-boundary integral method solving electromagnetic scattering problems," Microwave and Optical Technology Letters, Vol. 51, No. 9, 2065-2071, 2009.
doi:10.1002/mop.24538        Google Scholar

14. Wei, X. C., E. P. Li, and Y. J. Zhang, "Efficient solution to the large scattering and radiation problem using the improved finite-element fast multipole method," IEEE Transactions on Magnetics, Vol. 41, No. 5, 1684-1687, 2005.
doi:10.1109/TMAG.2005.846083        Google Scholar

15. Chen, R. S., X. W. Ping, E. K. N. Yung, C. H. Chan, et al. "Application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite element analysis of Helmholtz equations," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 5, 1604-1608, 2006.
doi:10.1109/TAP.2006.874358        Google Scholar

16. Chen, X., K. C. Toh, and K. K. Phoon, "A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations," International Journal for Numerical Methods in Engineering, Vol. 65, No. 6, 785-807, 2006.
doi:10.1002/nme.1461        Google Scholar

17. Ping, X. W. and T. J. Cui, "The factorized sparse approximate inverse preconditioned conjugate gradient algorithm for ¯nite element analysis of scattering problems," Progress In Electromagnetics Research, Vol. 98, 15-31, 2009.
doi:10.2528/PIER09071703        Google Scholar

18. Dyczij-Edlinger, R. and O. Biro, "A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements," IEEE Transactions on Microwave Theory and Techniques, Vol. 44, No. 1, 15-23, 1996.
doi:10.1109/22.481380        Google Scholar

19. Zhu, J., X. W. Ping, R. S. Chen, Z. H. Fan, and D. Z. Ding, "An incomplete factorization preconditioner based on shifted Laplace operators for FEM analysis of microwave structures," Microwave and Optical Technology Letters, Vol. 52, No. 5, 1036-1042, 2010.
doi:10.1002/mop.25111        Google Scholar

20. Teixeira, F. L. and W. C. Chew, "Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves," Microwave and Optical Technology Letters, Vol. 17, No. 4, 231-236, Mar. 1998.
doi:10.1002/(SICI)1098-2760(199803)17:4<231::AID-MOP3>3.0.CO;2-J        Google Scholar

21. George, A. and J. W. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall, Englewood Cliffs, NJ, 1981.

22. Sieverding, T. and F. Arndt, "Field theoretical CAD of open or aperture matched T-junction coupled rectangular waveguide structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 2, 353-363, 1992.
doi:10.1109/22.120109        Google Scholar

23. Ise, K., K. Inoue, and M. Koshiba, "Three-dimensional finite-element method with edge elements for electromagnetic waveguide discontinuities," IEEE Transactions on Microwave Theory and Techniques, Vol. 39, No. 8, 1289-1295, 1991.
doi:10.1109/22.85402        Google Scholar