EFIE analysis of low-frequency problems with loop-star decomposition and Calderón multiplicative preconditioner

IEEE Transactions on Antennas and Propagation

Volumn 58, Issue 3, 2010, Pages 857-867

  Yan, Su ^a,b   Jin, Jian Ming ^b   Nie, Zaiping ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Buffa Christiansen basis functions; Calder n multiplicative preconditioner; Electric field integral equation (EFIE); Loop star decomposition; Low frequency problems; Method of moments

Indexed keywords

BASIS FUNCTIONS; ELECTRIC FIELD INTEGRAL EQUATION; LOW FREQUENCY; LOW-FREQUENCY PROBLEMS; PRECONDITIONERS; STAR DECOMPOSITIONS;

CONVERGENCE OF NUMERICAL METHODS; ELECTRIC FIELDS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; METHOD OF MOMENTS;

PHYSICAL OPTICS;

EID: 77749307678     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2009.2039336     Document Type: Article

References (25)

1. D. R. Wilton and A. W. Glisson, "On improving the electric field integral equation at low frequencies," in Proc. URSI Radio Sci. Meet. Dig., Los Angeles, CA, Jun. 1981, pp. 24-24.
2. J. S. Zhao and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propag., vol. 48, pp. 1635-1645, Oct. 2000.
3. J. F. Lee, R. Lee, and R. J. Burkholder, "Loop star basis functions and a robust preconditioner for EFIE scattering problems," IEEE Trans. Antennas Propag., vol. 51, pp. 1855-1863, Aug. 2003.
4. F. P. Andriulli, K. Cools, H. Ba' gci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, "A multiplicative Calderón preconditioner for the electric field integral equation," IEEE Trans. Antennas Propag., vol. 56, pp. 2398-2412, Aug. 2008.
5. G. C. Hsiao and R. E. Kleinman, "Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics, " IEEE Trans. Antennas Propag., vol. 45, pp. 316-328, Mar. 1997.
6. R. J. Adams, "Physical and analytical properties of a stabilized electric field integral equation," IEEE Trans. Antennas Propag., vol. 52, pp. 362-372, Feb. 2004.
7. R. J. Adams and N. J. Champagne, "A numerical implementation of a modified form of the electric field integral equation," IEEE Trans. Antennas Propag., vol. 52, pp. 2262-2266, Sep. 2004.
8. S. H. Christiansen and J. C. Nedelec, "A preconditioner for the electric field integral equation based on Calderón formulas," SIAM J. Numer. Anal., vol. 40, no. 3, pp. 1100-1135, Aug. 2002.
9. A. Buffa and S. H. Christiansen, "A dual finite element complex on the barycentric refinement," Mathematics of Computation, vol. 76, no. 260, pp. 1743-1769, Oct. 2007.
10. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., vol. 30, pp. 409-418, May 1982.
11. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propag., vol. 45, pp. 329-342, Mar. 1997.
12. T. A. Davis, UMFPACK: Unsymmetric Multifrontal Sparse LU Factorization Package 2007 [Online]. Available: http://www.cise.ufl.edu/research/sparse/ umfpack/
13. S. Yan, J.-M. Jin, and Z. Nie, "EFIE analysis of low-frequency problems with loop-star decomposition and Calderón multiplicative preconditioner," University of Illinois at Urbana-Champaign, 2009, Tech. Rep. CCEML 1-09.
14. J. S. Zhao, W. C. Chew, T. J. Cui, and Y. H. Zhang, "Cancellations of surface loop basis functions," in Proc. IEEE Antennas Propag. Symp., 2002, pp. 58-61.
15. G. Alléon, M. Benzi, and L. Giraud, "Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics," Numer. Algorithms, vol. 16, pp. 1-15, 1997.
16. B. Carpentieri, I. S. Duff, and L. Giraud, "Experiments with sparse preconditioning of dense problems from electromagnetic applications," CERFACS, Toulouse, France, 2000, Tech. Rep. TR/PA/00/04.
17. K. Cools, F. P. Andriulli, F. Olyslager, and E. Michielssen, "On Calderón techniques in time-domain integral equation solvers," in Proc. Int. Conf. on Electromagnetics in Advanced Applications, Sep. 2007, pp. 360-363.
18. S. Yan, J.-M. Jin, and Z. Nie, "Implementation of the Calderón multiplicative preconditioner for the EFIE solution with curvilinear triangular patches," in Proc. IEEE Antennas Propag. Symp., North Charleston, SC, Jun. 2009.
19. F. Valdés, F. P. Andriulli, K. Cools, and E. Michielssen, "High-order quasi-curl conforming functions for multiplicative Calderón preconditioning of the EFIE," in Proc. IEEE Antennas Propag. Symp., North Charleston, SC, Jun. 2009.
20. T. F. Eibert, "Interative-solver convergence for loop-star and loop-tree decompositions in method-of-moments solutions of the electric-field integral equation," IEEE Antennas Propag. Mag., vol. 46, no. 3, pp. 80-85, Jun. 2004.
21. R. F. Harrington, Field Computation by Moment Methods. New York: MacMillan, 1968.
22. G. L. G. Sleijpen and D. R. Fokkema, "BiCGstab(1) for linear equations involving unsymmetric matrices with complex spectrum," Electro. Transa. Numer. Analys., vol. 1, pp. 11-32, Sep. 1993.
23. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia, PA: SIAM, 1994.
24. Y. Saad and M. H. Schultz, "GMRes: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. Stat. Comput., vol. 7, no. 3, pp. 856-869, Jul. 1986.
25. M. B. Stephanson and J. F. Lee, "Preconditioned electric field integral equation using Calderón identities and dual loop/star basis functions," IEEE Trans. Antennas Propag., vol. 57, pp. 1274-1279, Apr. 2009.