Fast multi-particle scattering: A hybrid solver for the Maxwell equations in microstructured materials

Journal of Computational Physics

Volumn 232, Issue 1, 2013, Pages 22-32

  Gimbutas, Z ^a   Greengard, L ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Fast multipole method; Maxwell equations; Meta materials; Multiple scattering

Indexed keywords

DIELECTRIC MATERIALS; FORWARD SCATTERING; HYBRID MATERIALS; INTEGRAL EQUATIONS; MICROSTRUCTURE; MULTIPLE SCATTERING; NANOTECHNOLOGY;

DEVICE DESIGN; FAST-MULTIPOLE METHODS; FORWARD MODELING; HIGH-ORDER; MATERIALS DESIGN; META-MATERIALS; MICROSTRUCTURED MATERIALS; MULTIPLE-SCATTERING; PARTICLE SCATTERING; STRUCTURED MATERIALS;

MAXWELL EQUATIONS;

EID: 84868459717     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.01.041     Document Type: Article

References (28)

1. Biedenharn L.C., Louck J.D. Angular Momentum in Quantum Physics: Theory and Application 1981, Addison-Wesley, Reading, Mass.
2. Bohren C.F., Huffman D.R. Absorption and Scattering of Light by Small Particles 1983, Wiley, New York.
3. Born M., Wolf E. Principles of Optics: Electromagnetic Theory of Propagation. Interference and Diffraction of Light 1999, Cambridge University Press.
4. Chen Y., Hesthaven J.S., Maday Y., Rodriguez J. " Certified reduced basis methods and output bounds for the harmonic Maxwell's equations. SIAM J. Sci. Comput. 2010, 32:970-996.
5. Cheng H., Crutchfield W.Y., Gimbutas Z., Greengard L., Ethridge F., Huang J., Rokhlin V., Yarvin N., Zhao J. " A wideband fast multipole method for the Helmholtz equation in three dimensions. J. Comput. Phys. 2006, 216:300-325.
6. Debye P. " Der Lichtdruck auf Kugeln von beliebigen Material. Ann. Phys. (Leipzig) 1909, 30:57-136.
7. Edmonds A.R. Angular Momentum in Quantum Mechanics 1957, Princeton University Press, Princeton.
8. Epton M.A., Dembart B. " Multipole translation theory for the three-dimensional Laplace and Helmholtz equations. SIAM J. Sci. Comput. 1995, 16:865-897.
9. Greengard L., Huang J. " A new version of the fast multipole method for screened Coulomb interactions in three dimensions" J. Comput. Phys. 2002, 180:642-658.
10. Greengard L., Gueyffier D., Martinsson P.-G., Rokhlin V. " Fast direct solvers for integral equations in complex three-dimensional domainsó. Acta Numer. 2009, 18:245-275.
11. Gumerov N., Duraiswami R. " A scalar potential formulation and translation theory for the time-harmonic Maxwell equations. J. Comput. Phys. 2007, 225:206-236.
12. Gumerov N., Duraiswami R. " Computation of scattering from clusters of spheres using the fast multipole method. J. Acoust. Soc. Am. 2005, 117:1744-1761.
13. Hafner CH. The Generalized Multipole Technique for Computational Electromagnetics 1990, Artech House Books, Boston.
14. Hesford A.J., Astheimer J.P., Greengard L., Waag R.C. " A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators. J. Acoust. Soc. Am. 2010, 127:850-861.
15. K.L. Ho, L. Greengard, " A fast direct solvers for structured linear systems by recursive linearization. (2012). arxiv:1110.3105.
16. Ioannidou M.P., Chrissoulidis D.P. " Electromagnetic-wave scattering by a sphere with multiple spherical inclusions. J. Opt. Soc. Am. A. 2002, 19:505-512.
17. Jackson J.D. Classical Electrodynamics 1975, Wiley, New York.
18. Lorenz L.V. " Lysvevxgelsen i og uden for en af plane lysbolger belyst kugle. K. Dan. Vidensk. Selsk. Forh. 1890, 6:1-62.
19. P.A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles, Cambridge U. Press, Cambridge, 2006.
20. Mie G., Medien " Beiträge zur Optik trüber speziell kolloidaler Metallösungen. Ann. Phys. (Leipzig) 1908, 25:377-445.
21. M.I. Mishchenko, L.D. Travis, A.A. Lacis, Scattering Absorption and Emission of Light by Small Particles, Cambridge U. Press, Cambridge, 2002.
22. Müller C. Foundations of the Mathematical Theory of Electromagnetic Waves 1969, Springer-Verlag, Berlin.
23. Papas C.H. Theory of Electromagnetic Wave Propagation 1988, Dover, New York.
24. Rokhlin V. " Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions. Appl. Comput. Harm. Anal. 1993, 1:82-93.
25. Rose M.E. Elementary Theory of Angular Momentum 1957, John Wiley & Sons, Inc.
26. Saad Y., Schultz M.H. " GMRESA generalized minimal residual algorithm for solving nonsymmetric linear-systems. SIAM J. Sci. Stat. Comput. 1986, 7:856-869.
27. Xu Y. " Electromagnetic scattering by an aggregate of spheres. Appl. Opt. 1995, 34:4573-4588.
28. Yla-Oijala P., Taskinen M. " Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects. IEEE Trans. Antennas Propagat. 2005, 53:3316-3323.