Rigorous Analysis of Double-Negative Materials with the Multilevel Fast Multipole Algorithm


  • Ozg ̈ur Erg ̈ul Department of Mathematics and Statistics University of Strathclyde, G11XH, Glasgow, UK
  • Levent G ̈urel Computational Electromagnetics Research Center (BiLCEM) Bilkent University, TR-06800, Bilkent, Ankara, Turkey


Rigorous Analysis of Double-Negative Materials with the Multilevel Fast Multipole Algorithm


We present rigorous analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of numerical solutions are investigated when DNMs are formulated with two recently developed formulations, i.e., the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Simulation results on canonical objects are consistent with previous results in the literature on ordinary objects. MLFMA is also parallelized to solve extremely large electromagnetics problems involving DNMs.


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G. Monti and L. Tarricone, “Dispersion anal-

ysis of a negative group velocity medium

with MATLAB,” ACES J., vol. 24, no. 5,

pp. 478–486, Oct. 2009.

H. Kettunen, J. Qi, H. Wall ́en, and

A. Sihvola, “Homogenization of thin dielec-

tric composite slabs: techniques and limita-

tions,” ACES J., vol. 26, no. 3, pp. 179–187,

Mar. 2011.

A. J. Poggio and E. K. Miller, “Integral

equation solutions of three-dimensional scat-

tering problems,” in Computer Techniques

for Electromagnetics, R. Mittra, Ed. Oxford:

Pergamon Press, 1973, Chap. 4.

C. M ̈uller, Foundations of the Mathemati-

cal Theory of Electromagnetic Waves. New

York: Springer, 1969.

P. Yl ̈a-Oijala and M. Taskinen, “Applica-

tion of combined field integral equation for

electromagnetic scattering by dielectric and

composite objects,” IEEE Trans. Antennas

Propagat., vol. 53, no. 3, pp. 1168–1173,

Mar. 2005.

Y. A. Liu and W. C. Chew, “Stability of sur-

face integral equation for left-handed materi-

als,” IET Microw. Antennas Propag., vol. 1,

no. 1, pp. 84–89, Mar. 2007.

J. Rivero, J. M. Taboada, L. Landesa,

F. Obelleiro, and I. Garcia-Tunon, “Surface

integral equation formulation for the analysis

of left-handed metamaterials,” Opt. Express,

vol. 18, no. 15, pp. 15876–15886, Jul. 2010.

L. G ̈urel, ̈O. Erg ̈ul, A. ̈Unal, and T. Malas,

“Fast and accurate analysis of large metama-

terial structures using the multilevel fast mul-

tipole algorithm,” Prog. Electromagn. Res.,

vol. 95, pp. 179–198, 2009.

J. Song, C.-C. Lu, and W. C. Chew, “Multi-

level fast multipole algorithm for electromag-

netic scattering by large complex objects,”

IEEE Trans. Antennas Propag., vol. 45,

no. 10, pp. 1488–1493, Oct. 1997.

J. Lee, J. Zhang, and C.-C. Lu, “Perfor-

mance of preconditioned Krylov iterative

methods for solving hybrid integral equations

in electromagnetics,” ACES J., vol. 18, no. 4,

pp. 54–61, Nov. 2003.

R. J. Burkholder, P. H. Pathak, K. Sertel,

R. J. Marhefka, and J. L. Volakis, “A hy-

brid framework for antenna/platform analy-

sis,” ACES J., vol. 21, no. 3, pp. 177–195,

Nov. 2006.

M. Vikram and B. Shanker, “An incom-

plete review of fast multipole methods–from

static to wideband–as applied to problems

in computational electromagnetics,” ACES J.,

vol. 24, no. 2, pp. 79–108, Apr. 2009.

H. Fangjing, N. Zaiping, and H. Jun, “An

efficient parallel multilevel fast multipole

algorithm for large-scale scattering prob-

lems,” ACES J., vol. 25, no. 4, pp. 381–387,

Apr. 2010.

P. Yl ̈a-Oijala, M. Taskinen, and S. J ̈arvenp ̈a ̈a,

“Surface integral equation formulations for

solving electromagnetic scattering problems

with iterative methods,” Radio Sci., vol. 40,

RS6002, doi:10.1029/2004RS003169,

Nov. 2005.

S. M. Rao, D. R. Wilton, and A. W. Glisson,

“Electromagnetic scattering by surfaces of

arbitrary shape,” IEEE Trans. Antennas

Propag., vol. 30, no. 3, pp. 409–418,

May 1982.

̈O. Erg ̈ul and L. G ̈urel, “Comparison of

integral-equation formulations for the fast and accurate solution of scattering problems

involving dielectric objects with the multi-

level fast multipole algorithm,” IEEE Trans.

Antennas Propag., vol. 57, no. 1, pp. 176–

, Jan. 2009.

̈O. Erg ̈ul and L. G ̈urel, “A hierarchical

partitioning strategy for an efficient paral-

lelization of the multilevel fast multipole

algorithm,” IEEE Trans. Antennas Propag.,

vol. 57, no. 6, pp. 1740–1750, Jun. 2009.

̈O. Erg ̈ul and L. G ̈urel, “Discretization error

due to the identity operator in surface integral

equations,” Comput. Phys. Comm., vol. 180,

no. 10, pp. 1746–1752, Oct. 2009.

H. van der Vorst, “Bi-CGSTAB: A fast and

smoothly converging variant of Bi-CG for

the solution of nonsymmetric linear sys-

tems,” SIAM J. Sci. Stat. Comput., vol. 13,

no. 2, pp. 631–644, Mar. 1992.




How to Cite

Erg ̈ul O. . ̈. ., & G ̈urel L. . (2022). Rigorous Analysis of Double-Negative Materials with the Multilevel Fast Multipole Algorithm. The Applied Computational Electromagnetics Society Journal (ACES), 27(2), 161–168. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/15133