In this paper, electromagnetic scattering problems are analyzed using an electric field integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation which is based on loop star-basis functions. Because the matrix system resulting from the conventional method of moments is a dense matrix, a sparse matrix version of each block matrix is constructed, followed by the inversion of the resultant block sparse matrix using incomplete factorization. Numerical results show that the proposed BMP is efficient in terms of computation time and memory usage.
2. Gibson, W. C., The Method of Moments in Electromagnetics, Chapman & Hall/CRC, 2007.
doi:10.1201/9781420061468
3. Chew, W. C., M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool, 2008.
doi:10.2200/S00102ED1V01Y200807CEM012
4. Wang, W. and N. Nishimura, "Calculation of shape derivatives with periodic fast multipole method with application to shape optimization of metamaterials," Progress In Electromagnetic Research, Vol. 127, 46-64, 2012.
5. Liu, Z.-L. and J. Yang, "Analysis of electromagnetic scattering with higher order moment method and NURBS model," Progress In Electromagnetic Research, Vol. 96, 83-100, 2009.
doi:10.2528/PIER09071704
6. Wang, A.-Q., L.-X. Guo, Y.-W. Wei, and J. Ma, "Higher order method of moments for bistatic scattering from 2D PEC rough surface with geometric modeling by NURBS surface," Progress In Electromagnetic Research, Vol. 130, 85-104, 2012.
7. Liu, Z. H., E. K. Chua, and K. Y. See, "Accurate and efficient evaluation of method of moments matrix based on a generalized analytical approach," Progress In Electromagnetic Research, Vol. 94, 367-382, 2009.
doi:10.2528/PIER09063002
8. Ubeda, E., J. M. Tamayo, and J. M. Rius, "Taylor-orthogonal basis functions for the discretization in method of moments of second kind integral equations in the scattering analysis of perfectly conducting or dielectric objects," Progress In Electromagnetic Research, Vol. 119, 85-105, 2011.
doi:10.2528/PIER11051715
9. Guo, L.-X., A.-Q. Wang, and J. Ma, "Study on EM scattering from 2-D target above 1-D large scale rough surface with low grazing incidence by parallel MoM based on PC clusters," Progress In Electromagnetic Research, Vol. 89, 149-166, 2009.
doi:10.2528/PIER08121002
10. Taflov, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House, 2000.
11. Wang, J. B., B. H. Zhou, L. H. Shi, C. Gao, and B. Chen, "A novel 3D weakly conditionally stable FDTD algorithm," Progress In Electromagnetic Research, Vol. 130, 525-540, 2012.
12. Xiong, R., B. Chen, Y. Mao, B. Li, and Q.-F. Jing, "A simple local approximation FDTD model of short apertures with a finite thickness," Progress In Electromagnetics Research, Vol. 131, 153-167, 2012.
13. Chen, C.-Y., Q. Wu, X.-J. Bi, Y.-M. Wu, and L. W. Li, "Characteristic analysis for FDTD based on frequency response," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 2-3, 283-292, 2010.
doi:10.1163/156939310790735796
14. Sirenko, K., V. Pazynin, Y. K. Sirenko, and H. Bagci, "An FFT-accelerated FDTD scheme with exact absorbing conditions for characterizing axially symmetric resonant structures," Progress In Electromagnetics Research, Vol. 111, 331-364, 2011.
doi:10.2528/PIER10102707
15. Kusiek, A. and J. Mazur, "Analysis of scattering from arbitrary configuration of cylindrical objects using hybrid finite-difference mode-matching method," Progress In Electromagnetics Research, Vol. 97, 105-127, 2009.
doi:10.2528/PIER09072804
16. Jin, J. M., The Finite Element Method in Electromagnetics, Wiley, 2002.
17. Ping, X. W. and T.-J. Cui, "The factorized sparse approximate inverse preconditioned conjugate gradient algorithm for finite element analysis of scattering problems," Progress In Electromagnetics Research, Vol. 98, 15-31, 2009.
doi:10.2528/PIER09071703
18. Fotyga, G., K. Nyka, and M. Mrozowski, "Efficient model order reduction for FEM analysis of waveguide structures and resonators," Progress In Electromagnetic Research, Vol. 127, 259-275, 2012.
19. Tian, J., Z.-Q. Lv, X.-W. Shi, L. Xu, and F. Wei, "An efficient approach for multifrontal algorithm to solve non-positive definite finite element equations in electromagnetic problems," Progress In Electromagnetics Research, Vol. 95, 121-133, 2009.
doi:10.2528/PIER09070207
20. Gomez-Revuelto, I., L. E. Garcia-Castillo, and M. Salazar-Palma, "Goal-oriented self-adaptive HP-strategies for finite element analysis of electromagnetic scattering and radiation problems," Progress In Electromagnetics Research, Vol. 125, 459-482, 2012.
doi:10.2528/PIER11121606
21. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antenna and Propagation, Vol. 30, 409-418, 1982.
doi:10.1109/TAP.1982.1142818
22. Giuseppe Vecchi, G., "Loop-star decomposition of basis functions in the discretization of the EFIE," IEEE Transaction on Antenna and Propagation, Vol. 47, No. 2, 339-346, 1999.
doi:10.1109/8.761074
23. Zhao, J. S. and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Transactions on Antenna and Propagation, Vol. 48, 1635-1645, 2000.
doi:10.1109/8.899680
24. Lee, J. F., R. Lee, and R. J. Burkholder, "Loop star basis functions and a robust preconditioner for EFIE scattering problems," IEEE Transactions on Antenna and Propagation, Vol. 51, No. 8, 1855-1863, 2003.
doi:10.1109/TAP.2003.814736
25. Eibert, T. F., "Iterative-solver convergence for loop-star and loop-tree decompositions in method of moments solutions of the electric-field integral equation," IEEE Antenna and Propagation Magazine, Vol. 46, No. 3, 2004.
doi:10.1109/MAP.2004.1374101
26. Hestenes, M. R. and E. Steilfel, "Method of conjugate gradients for solving linear systems," Journal of Research of the National Bureau of Standards, Vol. 49, 409-436, 1952.
doi:10.6028/jres.049.044
27. Saad, Y., "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, Vol. 7, 856-869, 1986.
doi:10.1137/0907058
28. Lee, J. F. and D. K. Sun, "p-type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities," IEEE Transactions on Microwave Theory and Technology, Vol. 52, No. 3, 864-870, 2004.
doi:10.1109/TMTT.2004.823554
29. Lee, J. F., R. Lee, and F. Teixeira, "Hierarchical vector finite elements with p-type non-overlapping Schwarz method for modeling waveguide discontinuities," CEMS - Computer Modeling in Engineering & Sciences, Vol. 5, No. 5, 423-434, 2004.
30. Malas, T. and L. Gurel, "Schur complement preconditioners for surface integral equation formulation of dielectric problems solved with the multilevel fast multipole algorithm," SIAM Journal on Scientific Computing, Vol. 33, No. 5, 2440-2467, 2011.
doi:10.1137/090780808
31. Saad, Y., Iterative Methods for Sparse Linear Systems, 2nd Edition, PWS, 2003.
32. Benzi, M., C. D. Meyer, and M. Tuma, "A sparse approximate inverse preconditioner for the conjugate gradient method," SIAM Journal on Scientific and Statistical Computing, Vol. 17, 1135-1149, 1996.
doi:10.1137/S1064827594271421
33. Benzi, M., "A sparse approximate inverse preconditioner for nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, Vol. 19, 968-994, 1998.
doi:10.1137/S1064827595294691
34. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York, 1989.
35. Jin, J. M., Theory and Computation of Electromagnetic Fields, Wiley, 2010.
36. Li, N., B. Suchomel, D. O. Kuffuor, R. Li, and Y. Saad, "ZITSOL: Iterative solvers package version 1.0,", Department of Computer Science and Engineering,-University of Minnesota, Minneapolis MN55455, 2010, http://www-user.cs.umn.edu/»saad/software/.
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