The factorized sparse approximate inverse preconditioned conjugate gradient algorithm for finite element analysis of scattering problems

Progress in Electromagnetics Research

Volumn 98, Issue , 2009, Pages 15-31

  Ping, X W ^a   Cui, T J ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONJUGATE GRADIENT METHOD; ELECTROMAGNETIC WAVE SCATTERING; INVERSE PROBLEMS; ITERATIVE METHODS; LINEAR SYSTEMS;

ITERATIVE SOLUTIONS; LARGE SPARSE LINEAR SYSTEMS; LARGE-SCALE ELECTROMAGNETIC SCATTERINGS; MODEL PROBLEMS; PRECONDITIONED CONJUGATE GRADIENT ALGORITHMS; PRECONDITIONERS; SCATTERING PROBLEMS; SPARSE APPROXIMATE INVERSE;

FINITE ELEMENT METHOD;

EID: 70749152736     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER09071703     Document Type: Article

References (29)

1. Liu, H. and H. W. Yang, "FDTD analysis of magnetized ferrite sphere, " Journal of Electromagnetic Waves and Applications, Vol. 22, No. 17-18, 2399-2406, 2008.
2. Ali, M. and S. Sanyal, "FDTD analysis of rectangular waveguide in receiving mode as EMI sensors, " Progress In Electromagnetics Research B, Vol. 2, 291-303, 2008.
3. Sabri, M. M., J. Rashed-Mohassel, and N. Masoumi, "Application of FDTD-based macromodeling for signal integrity analysis in practical PCBs, " Progress In Electromagnetics Research Letters, Vol. 5, 45-55, 2008.
4. Liu, Y. W., J. Wang, and K. K. Mei, "A simple MoM loading technique used in microstrip circuits, " Journal of Electromagnetic Waves and Applications, Vol. 16, No. 12, 1695-1709, 2002.
5. Hassani, H. R. and M. Jahanbakht, "Method of moment analysis of finite phased array of aperture coupled circular microstrip patch antennas, " Progress In Electromagnetics Research B, Vol. 4, 197-210, 2008.
6. Jin, J. M., The Finite Element Method in Electromagnetics, 2nd edition, John Wiley & Sons, Inc., New York, 2002.
7. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetic, IEEE Press, New York, 1998.
8. Sun, X. Y. and Z. P. Nie, "Vector finite element analysis of multicomponent induction response in anisotropic formations, " Progress In Electromagnetics Research, PIER 81, 21-39, 2008.
9. Aubourg, M. and P. Guillon, "A mixed finite element formulation for microwave devices problems. Application to MIS structure, " Journal of Electromagnetic Waves and Applications, Vol. 5, No. 4-5,371-386, 1991.
10. Irons, B. M., "A frontal method solution program for finite element analysis, " International Journal for Numerical Methods in Engineering, Vol. 2, 5-32, 1970.
11. Mittra, R. and O. Ramahi, "Absorbing boundary conditions for the direct solution of partial differential equations arising in electromagnetic scattering problems, " Progress In Electromagnetics Research, PIER 02, 133-173, 1990.
12. Hadi, M. F., "Wide-angle absorbing boundary conditions for low and high-order FDTD algorithms, " Applied Computational Electromagnetics Society Journal, Vol. 24, No. 1, 9-15, 2009.
13. 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 Trans. Microwave Theory Tech., Vol. 44, 15-23, 1996.
14. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, 1995.
15. Benzi, M., "Preconditioning techniques for large linear systems: A survey, " Journal of Computational Physics, Vol. 182, 418-477, 2002.
16. Carpentieri, B., "Fast iterative solution methods in electro-magnetic scattering, " Progress In Electromagnetics Research, PIER 79, 151-178, 2008.
17. Lahaye, D., H. D. Gersem, S. Vandewalle, and K. Hameyer, "Algebraic multigrid for complex symmetric systems, " IEEE Trans. Magn., Vol. 36, No. 4, 1535-1538, 2000.
18. Sheng, Y. J., R. S. Chen, and X. W. Ping, "An efficient p-version multigrid solver for fast hierarchical vector finite element analysis, " Finite Elements in Analysis and Design, Vol. 44, 732-737,2008.
19. Li, S. S., X. W. Ping, and R. S. Chen, "A kind of preconditioners based on shifted operators to solve three-dimensional TVFEM equations, " IEEE 2007 International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, 842-844, 2007.
20. Chen, Y., S. Yang, S. He, and Z. P. Nie, "Design and analysis of wideband planar monopole antennas using the multilevel fast multipole algorithm, " Progress In Electromagnetics Research B, Vol. 15, 95-112, 2009.
21. Benzi, M. and M. Tuma, "A comparative study of sparse approximate inverse preconditioners, " Applied Numerical Mathematics, Vol. 30, 305-340, 1999.
22. Axelsson, O., "On the rate of convergence of the preconditioned conjugate gradient method, " Numerical Mathematics, Vol. 48, 499-523, 1986.
23. Mardochee Magolu Monga Made, "Incomplete factorization-based preconditionings for solving the Helmholtz equation, " International Journal for Numerical Methods in Engineering, Vol. 50, 1077-1101, 2001.
24. 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 Trans. Antennas Propagat., Vol. 54, No. 5, 1604-1608, May 2006.
25. Huang, Z. and J. P. Webb, "Iterative solvers for hierarchal vector finite element analysis of microwave problems, " IEEE Trans. Magn., Vol. 37, No. 5, 3285-3288, Sep. 2001.
26. Benzi, M. and M. Tuma, "A sparse approximate inverse preconditioner for nonsymmetric linear systems, " SIAM Journal of Sci. Comput., Vol. 19, 968-994, 1998.
27. Yeremin, A., L. Kolotilina, and A. Nikishin, "Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising effciency, " Numerical Linear Algebra with Applications, Vol. 6, 515-531, 1999.
28. Ping, X. W., T.-J. Cui, and W. B. Lu, "The combination of Bcgstab with multifrontal algorithm to solve Febi-MLFMA linear systems arising from inhomogeneous electromagnetic scattering problems, " Progress In Electromagnetics Research, PIER 93, 91-105,2009.
29. Medgyesi-Mitschang, L. N. and J. M. Putnam, "Electromagnetic scattering from axially inhomogeneous bodies of revolution, " IEEE Trans. Antennas Propagat., Vol. 32, No. 8, 797-806, 1984.