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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 17 — Aug. 25, 2014
  • pp: 20481–20499

A fast solver for multi-particle scattering in a layered medium

Jun Lai, Motoki Kobayashi, and Leslie Greengard  »View Author Affiliations


Optics Express, Vol. 22, Issue 17, pp. 20481-20499 (2014)
http://dx.doi.org/10.1364/OE.22.020481


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Abstract

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of microstructured composite materials, and the evaluation of the scattered field requires a suitable fast solver for either a single configuration or for a sequence of configurations as part of a design or optimization process. We have developed an algorithm for problems of this type by combining the Sommerfeld integral representation, high order integral equation discretization, the fast multipole method and classical multiple scattering theory. The efficiency of the solver is illustrated with several numerical experiments.

© 2014 Optical Society of America

OCIS Codes
(290.4210) Scattering : Multiple scattering
(290.5825) Scattering : Scattering theory
(160.2710) Materials : Inhomogeneous optical media

ToC Category:
Scattering

History
Original Manuscript: July 15, 2014
Revised Manuscript: August 3, 2014
Manuscript Accepted: August 4, 2014
Published: August 15, 2014

Virtual Issues
Vol. 9, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Jun Lai, Motoki Kobayashi, and Leslie Greengard, "A fast solver for multi-particle scattering in a layered medium," Opt. Express 22, 20481-20499 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-17-20481


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References

  1. G. Bao and J. Lai, “Radar cross section reduction of a cavity in the ground plane,” Commun. Comput. Phys. 15, 895–910 (2014).
  2. W. J. Parnell, I. D. Abrahams, and P. R. Brazier-Smith, “Effective properties of a composite half-space: Exploring the relationship between homogenization and multiple-scattering theories,” Quantum J. Mech. Appl. Math. 63, 145–175 (2010). [CrossRef]
  3. Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009). [CrossRef]
  4. Z. Gimbutas and L. Greengard, “Fast multi-particle scattering: A hybrid solver for the Maxwell equations in microstructured materials,” J. Comput. Phys. 232, 22–32 (2013). [CrossRef]
  5. D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley-Interscience, 1983).
  6. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).
  7. M. O’Neil, L. Greengard, and A. Pataki, “On the efficient representation of the half-space impedance green’s function for the helmholtz equation,” Wave Motion 51, 1–13 (2014). [CrossRef]
  8. A. Barnett and L. Greengard, “A new integral representation for quasi-periodic scattering problems in two dimensions,” BIT Numer. Math. 51, 67–90 (2011). [CrossRef]
  9. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences 93 (Springer-Verlag, 1998). [CrossRef]
  10. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).
  11. R. Kress and G. F. Roach, “Transmission problems for the helmholtz equation,” J. Math. Phys. 19, 1433–1437 (1978). [CrossRef]
  12. V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414–439 (1990). [CrossRef]
  13. Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear-systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
  14. H. Cheng, W. Crutchfield, Z. Gimbutas, L. Greengard, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao, “Remarks on the implementation of the wideband fmm for the helmholtz equation in two dimensions,” Contemp. Math. 408, 99–110 (2006). [CrossRef]
  15. L. L. Foldy, “The multiple scattering of waves. i. general theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107–119 (1945). [CrossRef]
  16. N. A. Gumerov and R. Duraiswami, “A scalar potential formulation and translation theory for the time-harmonic maxwell equations,” J. Comput. Phys. 225, 206–236 (2007). [CrossRef]
  17. K. Huang, P. Li, and H. Zhao, “An efficient algorithm for the generalized Foldy–Lax formulation,” J. Comput. Phys. 234, 376–398 (2013). [CrossRef] [PubMed]
  18. B. K. Alpert, “Hybrid Gauss-trapezoidal quadrature rules,” SIAM J. Sci. Comput. 20, 1551–1584 (1999). [CrossRef]
  19. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969). [CrossRef]
  20. M. Haider, S. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances,” SIAM J. Appl. Math. 62, 2129–2148 (2002). [CrossRef]
  21. V. Rokhlin, “Solution of acoustic scattering problems by means of second kind integral equations,” Wave Motion 5, 257–272 (1983). [CrossRef]
  22. A. A. Lacis, L. D. Travis, and M. I. Mishchenko, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  23. A. Dutt and V. Rokhlin, “Fast fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. 14, 1368–1393 (1993). [CrossRef]
  24. A. Dutt and V. Rokhlin, “Fast fourier transforms for nonequispaced data, II,” Appl. Comput. Harmon. Anal. 2, 85–100 (1995). [CrossRef]
  25. L. Greengard and J. Lee, “Accelerating the nonuniform fast fourier transform,” SIAM Rev. 46, 443–454 (2004). [CrossRef]
  26. J. Lee and L. Greengard, “The type 3 nonuniform FFT and its applications,” J. Comput. Phys. 206, 1–5 (2005). [CrossRef]
  27. J.-P. Berrut and L. N. Trefethen, “Barycentric lagrange interpolation,” SIAM Rev. 46, 501–517 (2004). [CrossRef]
  28. H. Cheng, J. Huang, and T. J. Leiterman, “An adaptive fast solver for the modified helmholtz equation in two dimensions,” J. Comput. Phys. 211, 616–637 (2006). [CrossRef]
  29. J. Bremer, V. Rokhlin, and I. Sammis, “Universal quadratures for boundary integral equations on two-dimensional domains with corners,” J. Comput. Phys. 229, 8259–8280 (2010). [CrossRef]
  30. J. Helsing and R. Ojala, “Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning,” J. Comput. Phy. 227, 8820–8840 (2008). [CrossRef]
  31. M. H. Cho and W. Cai, “A parallel fast algorithm for computing the Helmholtz integral operator in 3-d layered media,” J. Comput. Phys. 231, 5910–5925 (2012). [CrossRef]
  32. K. L. Greengard, L. Ho, and J.-Y. Lee, “A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions,” J. Comput. Phys. 258, 738–751 (2014). [CrossRef]

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