Comptes Rendus
no. 6
Fast algorithms for layered media
[Algorithmes rapides pour des milieux en couches]
Weng Cho Chew1  ; Bin Hu2 ; Y.C. Pan2 ; L.J. Jiang3
1 Center for Computational Electromagnetics and Electromagnetics Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USA
2 Intel Corporation, Hillsboro, OR 97214, USA
3 IBM, Yorktown Heights, NY 10598, USA
Comptes Rendus. Physique, Volume 6 (2005) no. 6, pp. 604-617.

Cet article présente une vue d'ensemble de l'électromagnétisme en vue du calcul pour la simulation de structures complexes avec un grand nombre d'inconnues à l'aide de méthodes intégrales. Il discute d'abord les avantages et désavantages des codes basés sur la résolution des équations différentielles comparés à ceux sur les équations intégrales. Il donne ensuite une vue d'ensemble des différents algorithmes rapides pour résoudre les équations intégrales. Il discute aussi la difficulté de résoudre les problèmes électromagnétiques dans la « zone d'ombre » entre l'électromagnétisme statique et hautes fréquences. Enfin, il discute les diverses méthodes pour des résolutions rapides de problèmes de diffraction et de couplage impliquant des milieux en couches à la fois pour l'électrostatique et l'électrodynamique, et présente quelques résultats numériques.

This paper gives an overview of computational electromagnetics for simulating complex structures with a large number of unknowns using integral equation method. First, it discusses the pros and cons of differential equation solvers versus integral equation solvers. Then it gives an overview of different fast algorithms for solving integral equations. It also discusses the difficulty of solving electromagnetic problems in the “twilight zone” between static and full-wave electromagnetics. Finally, it discusses various methods for fast solutions of scattering and coupling problems involving layered media both for statics and dynamic problems, and presents some numerical results.

Publié le :
DOI : 10.1016/j.crhy.2005.06.004
Keywords: Computational electromagnetics, Integral equations solvers, Layered media
Mot clés : Électromagnétisme numérique, Équations intégrales, Milieux en couches
Weng Cho Chew 1 ; Bin Hu 2 ; Y.C. Pan 2 ; L.J. Jiang 3

1 Center for Computational Electromagnetics and Electromagnetics Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USA
2 Intel Corporation, Hillsboro, OR 97214, USA
3 IBM, Yorktown Heights, NY 10598, USA 
@article{CRPHYS_2005__6_6_604_0,
     author = {Weng Cho Chew and Bin Hu and Y.C. Pan and L.J. Jiang},
     title = {Fast algorithms for layered media},
     journal = {Comptes Rendus. Physique},
     pages = {604--617},
     publisher = {Elsevier},
     volume = {6},
     number = {6},
     year = {2005},
     doi = {10.1016/j.crhy.2005.06.004},
     language = {en},
}
TY  - JOUR
AU  - Weng Cho Chew
AU  - Bin Hu
AU  - Y.C. Pan
AU  - L.J. Jiang
TI  - Fast algorithms for layered media
JO  - Comptes Rendus. Physique
PY  - 2005
SP  - 604
EP  - 617
VL  - 6
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crhy.2005.06.004
LA  - en
ID  - CRPHYS_2005__6_6_604_0
ER  - 
%0 Journal Article
%A Weng Cho Chew
%A Bin Hu
%A Y.C. Pan
%A L.J. Jiang
%T Fast algorithms for layered media
%J Comptes Rendus. Physique
%D 2005
%P 604-617
%V 6
%N 6
%I Elsevier
%R 10.1016/j.crhy.2005.06.004
%G en
%F CRPHYS_2005__6_6_604_0
Weng Cho Chew; Bin Hu; Y.C. Pan; L.J. Jiang. Fast algorithms for layered media. Comptes Rendus. Physique, Volume 6 (2005) no. 6, pp. 604-617. doi : 10.1016/j.crhy.2005.06.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2005.06.004/

[1] Fast and Efficient Algorithms in Computational Electromagnetics (W.C. Chew; J. Jin; E. Michielssen; J.M. Song, eds.), Artech House, Norwood, MA, July 2001

[2] J. Needham Science and Civilization in China, Cambridge Univ. Press, Cambridge, UK, 2005

[3] R. Cooke The History of Mathematics: A Brief Course, Wiley Interscience, New York, 1997

[4] A.R. Choudhuri The Physics of Fluids and Plasma, Cambridge Univ. Press, Cambridge, UK, 1998

[5] G. Cookson The Cable: The Wire That Changed the World, Tempus Publishing, Ltd., 2003

[6] J.C. Maxwell A Treatise of Electricity and Magnetism, 2 vols. (P.M. Harman, ed.), The Scientific Letters and Papers of James Clerk Maxwell, vol. II, 1862–1873, Clarendon Press, Oxford, 1873 (Also, see, 1995, Cambridge Univ. Press, Cambridge, UK)

[7] J.J. Bowman; T.B.A. Senior; P.L.E. Uslenghi Electromagnetic and Acoustic Scattering by Simple Shapes, North-Holland, Amsterdam, 1969 (and references therein)

[8] Geometric Theory of Diffraction (R.C. Hansen, ed.), IEEE Press, Piscataway, NJ, 1981

[9] P.E. Ceruzzi A History of Modern Computing, MIT Press, Cambridge, MA, 1998

[10] J.C. Tannehill; D.A. Anderson; R.H. Pletcher Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing, Washington, DC/New York, 1984

[11] K.S. Yee Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Ant. Propagat., Volume 14 (1966), pp. 302-307

[12] R.F. Harrington Field Computation by Moment Method, Krieger Publ., Malabar, FL, 1982

[13] A. Taflove Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Norwood, MA, 1995

[14] P.P. Silvester; R.L. Ferrari Finite Elements for Electrical Engineers, Cambridge Univ. Press, Cambridge, UK, 1990

[15] J.M. Jin The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 1993

[16] J.L. Volakis; A. Chatterjee; L.C. Kempel Finite Element Method for Electromagnetics, IEEE Press, New York, 1998

[17] S.M. Rao; D.R. Wilton; A.W. Glisson Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. Antennas Propagat., Volume 30 (1982) no. 3, pp. 409-418

[18] E.J. Nyström Uber die praktische auflosung von linearen integralgleichungen mit anwendungen auf randwertaufgaben der potentialtheorie, Commentationes Physico-Mathematicae, Volume 4 (1928) no. 15

[19] L.S. Canino; J.J. Ottusch; M.A. Stalzer; J.L. Visher; S. Wandzura Numerical solution of the Helmholtz equation in 2D and 3D using a higher order Nyström discretization, J. Comput. Phys., Volume 146 (1998), pp. 627-663

[20] R. Lee; A.C. Cangellaris A study of discretization error in the finite element approximation of wave solution, IEEE Trans. Ant. Propagat., Volume 40 (1992) no. 5, pp. 542-549

[21] J.M. Jin; J. Liu; Z. Lou; C.S. Liang A fully high-order finite element simulation of scattering by deep cavities, IEEE Trans. Antennas Propagat., Volume 51 ( September 2003 ) no. 9, pp. 2420-2429

[22] D.T. Borup; O.P. Gandhi Fast-Fourier transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies, IEEE Trans. Microwave Theory Tech., Volume 32 (1984) no. 4, pp. 355-360

[23] C.Y. Shen; K.J. Glover; M.I. Sancer; A.D. Varvatsis The discrete Fourier transform method of solving differential-integral equations in scattering theory, IEEE Trans. Ant. Propagat., Volume 37 (1989) no. 8, pp. 1032-1041

[24] H. Gan; W.C. Chew A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems, J. Electromag. Waves Appl., Volume 9 (1995) no. 10, pp. 1339-1357

[25] J.R. Phillips, J.K. White, Efficient capacitance computation of 3D structures using generalized pre-corrected FFT methods, in: Proceedings of the 3rd Topical Meeting on Electric Performance of Electronic Packaging, November 2–4, Monterey, CA, 1994

[26] E. Bleszynski; M. Bleszynski; T. Jaroszewicz A fast integral-equation solver for electromagnetic scattering problems, IEEE APS Int. Symp. Dig. (1994), pp. 416-419

[27] W.C. Chew, G.L. Wang, Anterpolation precorrected FFT for integral equations, in: PIERS 2003, Hawaii, October 13, 2003

[28] A. Aydiner; W.C. Chew; J.M. Song; T.J. Cui A Sparse Data Fast Fourier Transform (SDFFT), IEEE Antennas Propagat., Volume 51 ( November 2003 ) no. 11, pp. 3161-3170

[29] A.W. Appel An efficient program for many-body simulation, SIAM J. Sci. Stat. Comput., Volume 6 (1985) no. 1, pp. 85-103

[30] J. Barnes; P. Hut A hierarchical O(NlogN) force calculation algorithm, Nature, Volume 324 (1986), pp. 446-449

[31] L. Greengard; V. Rokhlin A fast algorithm for particle simulations, J. Comput. Phys., Volume 73 (1987), pp. 325-348

[32] R.L. Wagner; W.C. Chew A study of wavelets for the solution of electromagnetic integral equations, IEEE Trans. Ant. Propagat., Volume 43 (1995) no. 8, pp. 802-810

[33] W.C. Chew Computational electromagnetics—the physics of smooth versus oscillatory fields, Philos. Trans. Royal Soc. London Ser. A, Math., Phys. Eng. Sci. Theme Issue Short Wave Scattering, Volume 362 ( March 15, 2004 ) no. 1816, pp. 579-602

[34] W.K. Tung Group Theory in Physics, World Scientific Publ., Philadelphia, PA, 1985

[35] V. Rokhlin Rapid solution of integral equations of scattering theory in two dimensions, J. Comput. Phys., Volume 86 (1990), pp. 414-439

[36] A. Brandt Multilevel computations of integral transforms and particle interactions with oscillatory kernels, Comp. Phys. Comm., Volume 65 (1991), pp. 24-38

[37] C.C. Lu; W.C. Chew A multilevel algorithm for solving boundary-value scattering, Micro. Opt. Tech. Lett., Volume 7 ( July 1994 ) no. 10, pp. 466-470

[38] J.M. Song; W.C. Chew Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering, Micro. Opt. Tech. Lett., Volume 10 ( September 1995 ) no. 1, pp. 14-19

[39] J.S. Zhao; W.C. Chew Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies, IEEE Trans. Antennas Propagat., James R. Wait Memorial Special Issue, Volume 48 ( October 2000 ) no. 10, pp. 1635-1645

[40] L.J. Jiang; W.C. Chew Low frequency inhomogeneous plane wave algorithm—LF-FIPWA, Micro. Opt. Tech. Lett., Volume 40 ( January 2004 ) no. 2, pp. 117-122

[41] Y. Chu; W.C. Chew; S. Chen; J. Zhao A surface integral equation method for low-frequency scattering from a composite object, IEEE Trans. Antennas Propagat., Volume 51 ( October 2003 ) no. 10, pp. 2837-2844

[42] Y.H. Chu, W.C. Chew, Large-scale computation for electrically small structures using surface integral equation method, Micro. Opt. Tech. Lett., 2005, in press

[43] R.E. Collin Foundation for Microwave Engineering, McGraw–Hill, New York, 1992

[44] H. Contopanagos; B. Dembart; M. Epton; J.J. Ottusch; V. Rokhlin; J.L. Visher; S.M. Wandzura Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering, IEEE Trans. Antennas Propagat., Volume 50 ( December 2002 ), pp. 1824-1830

[45] Y. Zhang; T.J. Cui; W.C. Chew; J.S. Zhao Magnetic field integral equation at very low frequencies, IEEE Trans. Antennas Propagat., Volume 51 ( August 2003 ) no. 8, pp. 1864-1871

[46] R.J. Adams Physical and analytical properties of a stabilized electric field integral equation, IEEE Trans. Antennas Propagat., Volume 52 (2004) no. 2, pp. 362-372

[47] D.R. Wilton, A.W. Glisson, On improving the electric field integral equation at low frequencies, in: URSI Radio Science Meeting Digest, Los Angeles, CA, June 1981, p. 24

[48] D. Colton; R. Kress Integral Equation methods in Scattering Theory, Wiley, New York, 1983

[49] S. Ohnuki; W.C. Chew Truncation error analysis of multipole expansion, SIAM J. Scientific Computing, Volume 25 (2003) no. 4, pp. 1293-1306

[50] M.L. Hastriter; S. Ohnuki; W.C. Chew Error control of the translation operator in 3-D MLFMA, Micro. Opt. Tech. Lett., Volume 37 ( May 2003 ), pp. 184-188

[51] J.S. Zhao; W.C. Chew Three dimensional multilevel fast multipole algorithm from static to electrodynamic, Micro. Opt. Tech. Lett., Volume 26 ( July 2000 ) no. 1, pp. 43-48

[52] W.C. Chew; J. Friedrich; R. Geiger A multiple scattering solution for the effective permittivity of a sphere mixture, IEEE Trans. Geoscience and Remote Sensing, Volume 28 ( March 1990 ) no. 2, pp. 207-214

[53] J.S. Zhao; W.C. Chew Applying LF-MLFMA to solve complex PEC structures, Micro. Opt. Tech. Lett., Volume 28 ( February 5, 2001 ) no. 3, pp. 155-160

[54] L.J. Jiang, W.C. Chew, A mixed-form fast multipole algorithm, IEEE Trans. Antennas Propagat. (2005), in press

[55] B. Hu; W.C. Chew; E. Michielssen; J. Zhao An improved fast steepest descent algorithm for the fast analysis of two-dimensional scattering problems, Radio Science, Volume 34 ( July–August 1999 ) no. 4, pp. 759-772

[56] B. Hu; W.C. Chew Fast inhomogeneous plane wave algorithm for electromagnetic solutions in layered medium structures—2D case, Radio Science, Volume 35 (2000) no. 1, pp. 31-43

[57] B. Hu; W.C. Chew Fast inhomogeneous plane wave algorithm for scattering from objects above the multi-layered medium, IEEE Trans. Geosci. Remote Sensing, Volume 39 ( May 2001 ) no. 5, pp. 1028-1038

[58] B. Hu; W.C. Chew; S. Velamparambil Fast inhomogeneous plane wave algorithm (FIPWA) for analysis of electromagnetic scattering, Radio Science, Volume 36 ( December 2001 ) no. 6, pp. 1327-1340

[59] B. Hu, Fast inhomogeneous plane wave algorithm for electromagnetic scattering problems, Ph.D. Thesis, Dept. Elec. Comp. Engrg., U. Illinois, January 2001

[60] W.C. Chew Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990 (Reprinted by IEEE Press, 1995)

[61] S. Ohnuki; W.C. Chew Error analysis of the fast inhomogeneous plane wave algorithm for 2-D free space cases, Micro. Opt. Tech. Lett., Volume 38 (2003) no. 4, pp. 300-304

[62] H.S. Park, S. Ohnuki, B. Hu, H.T. Kim, W.C. Chew, Error control of the fast inhomogeneous plane wave algorithm for 3-D free space cases, Research Report: CCEM No. 03-05, Ctr Comput. Electromag. and Electromag. Laboratory, U. Illinois, May 20, 2005

[63] Y.C. Pan; W.C. Chew A fast multipole method for embedded structure in a stratified medium, Progress in Electromagnetics Research PIER, Volume 44 (2004), pp. 1-38

[64] Y.C. Pan, Development of fast multipole method for stratified medium, Ph.D. Thesis, Dept. Elec. Comp. Engrg., U. Illinois, May 2002

[65] L.J. Jiang, W.C. Chew, Y.C. Pan, Capacitance extraction in the multilayer medium using DCIM and SMFMA, JEMWA, submitted for publication

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

State of the art in computational methods for the prediction of radar cross-sections and antenna–platform interactions

Frédéric Molinet; Hervé Stève; Jean-Pierre Adam

C. R. Phys (2005)

Some numerical models to compute electromagnetic antenna–structure interactions

Nicolas Zerbib; M'Barek Fares; Thierry Koleck; ...

C. R. Phys (2005)

A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation

Katherine Mer-Nkonga; Michel Mandallena; David Goudin; ...

C. R. Phys (2006)