Nystrom-type techniques for solving electromagnetics integral equations with smooth and singular kernels

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Volumn 25, Issue 5-6, 2012, Pages 490-511

  Balaban, M V ^a   Smotrova, E I ^a   Shapoval, O V ^a   Bulygin, V S ^a   Nosich, A I ^a  

^a A USIKOV INSTITUTE OF RADIO PHYSICS AND ELECTRONICS   (Ukraine)

Author keywords

eigenvalue problem; generalized boundary conditions; integral equations; method of analytical regularization

Indexed keywords

DIELECTRIC CYLINDER; DISCRETE MODELS; EIGENVALUE PROBLEM; ELECTROMAGNETICS; EXACT SOLUTION; GENERALIZED BOUNDARY CONDITIONS; KERNEL FUNCTION; KERNEL SINGULARITY; METALLIC OBJECTS; METHOD OF ANALYTICAL REGULARIZATION; NUMERICAL RESULTS; PERFECTLY ELECTRICALLY CONDUCTING; PRACTICAL ACCURACY; QUADRATURE FORMULA; SINGULAR KERNEL; THIN MATERIALS;

BOUNDARY INTEGRAL EQUATIONS; DIELECTRIC DEVICES; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; TWO DIMENSIONAL;

DIELECTRIC MATERIALS;

EID: 84865477296     PISSN: 08943370     EISSN: 10991204     Source Type: Journal    
DOI: 10.1002/jnm.1827     Document Type: Article

References (36)

1. Colton D, Kress R,. Integral Equation Methods in Scattering Theory. Wiley: New York, 1983.
2. Peterson AF,. The 'interior resonance' problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies. Electromagnetics 1990; 10: 293-312.
3. Valdés F, Andriulli FP, Bagci H, Michielssen E,. A Calderón-preconditioned single source combined field integral equation for analyzing scattering from homogeneous penetrable objects. IEEE Trans. Antenn. Propag. 2011; 59 (6): 2315-2328.
4. Hanson GW, Yakovlev AB,. Operator Theory for Electromagnetics. Springer-Verlag: New York, 2001.
5. Nosich AI,. Method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions. IEEE Antenn. Propag. Mag. 1999; 42 (3): 34-49.
6. Nazarchuk ZT,. Numerical Investigation of Wave Diffraction by Cylindrical Structures. Naukova Dumka: Kyiv, 1989 in Russian.
7. Gandel YV,. Introduction to the Methods of Computation of Singular and Hyper-Singular Integrals. KhNU Press: Kharkiv, 2001 in Russian.
8. Tsalamengas J,. Exponentially converging Nystrom's methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures. IEEE Trans. Antenn. Propag. 2006; 54 (5): 1549-1558.
9. Tsalamengas J,. Exponentially converging Nystrom methods in scattering from infinite curved smooth strips. Pt. 2-TE case. IEEE Trans. Antenn. Propag 2010; 58 (10): 3275-3281.
10. Nosich AA, Gandel YV, Magath T, Altintas A,. Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization. J. Opt. Soc. Am. A 2007; 24 (9): 2831-2836.
11. Boriskina SV, Sewell P, Benson TM, Nosich AI,. Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization. J. Opt. Soc. Am. A 2004; 21: 393-402.
12. Smotrova EI, Nosich AI,. Mathematical study of the 2D lasing problem for the whispering-gallery modes in a circular dielectric microcavity. Opt. Quant. Electron. 2004; 36 (1-3): 213-221.
13. Smotrova EI, Nosich AI, Benson TM, Sewell P,. Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis. IEEE J. Sel. Top. Quant. Electron. 2005; 11 (5): 1135-1142.
14. Smotrova EI, Byelobrov VO, Benson TM, Sewell P, Ctyroky J, Nosich AI,. Optical theorem helps understand thresholds of lasing in microcavities with active regions. IEEE J. Quant. Electron. 2011; 47 (1): 20-30.
15. Muller C,. Foundations of the Mathematical Theory of Electromagnetic Waves. Springer: Berlin, 1969.
16. Wang L, Cox JA, Friedman A,. Modal analysis of homogeneous optical waveguides by the boundary integral formulation and the Nyström method. J. Opt. Soc. Am. A 1998; 15 (1): 92-100.
17. Colton D, Kress R,. Inverse Acoustic and Electromagnetic Scattering Theory. Springer: Berlin, 1998.
18. Abramowitz M, Stegun I,. Handbook of Mathematical Functions. Nat. Bureau of Standards Publ, Washington DC 1964.
19. Kouznetsov D, Moloney J,. Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry. J. Opt. Soc. Am. B 2002; 19 (6): 1259-1263.
20. Smotrova EI, Benson TM, Sewell P, Ctyroky J, Sauleau R, Nosich AI,. Optical fields of the lowest modes in a uniformly active thin sub-wavelength spiral microcavity. Opt. Lett. 2009; 34 (24): 3773-3775.
21. Smotrova EI, Nosich AI,. Simulation of lasing modes in a kite-shaped microcavity laser. Proc. Int. Conf. Advanced Optoelectronics and Lasers (CAOL-10), Sebastopol, 2010; 144-146.
22. Smotrova EI, Nosich AI,. Directional light emission from a kite-shaped microcavity laser. Proc. Int. Conf. Transparent Optical Networks (ICTON-11), Stockholm, 2011, We.A4.4.
23. Bleszynski E, Bleszynski M, Jaroszewicz T,. Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets. IEEE Antenn. Propag. Mag. 1993; 35 (6): 14-25.
24. Johnson PB, Christy RW,. Optical constants of the noble metals. Phys. Rev. B 1972; 6 (12): 4370-4379.
25. Shapoval OV, Sauleau R, Nosich AI,. Numerical algorithm for the scattering by imperfect strips using the Nystrom-type discretization. Proc. Int. Conf. Mathematical Methods in Electromagnetic Theory (MMET*10), Kiev, 2010, IET-3.
26. Shapoval OV, Sauleau R, Nosich AI,. Plasmon resonances in the H-wave scattering by a nanosize thin flat silver strip. Proc. Int. Conf. Laser and Fiber-Optic Numerical Modeling (LFNM-10), Sebastopol, 2010, 37-39.
27. Shapoval OV, Sauleau R, Nosich AI,. Scattering and absorption of waves by flat material strips analyzed using generalized boundary conditions and Nystrom-type algorithm. IEEE Trans. Antenn. Propag. 2011; 59 (9): 3339-3346.
28. Balaban MV, Sauleau R, Benson TM, Nosich AI,. Dual integral equations technique in electromagnetic wave scattering by a thin disk. PIER B 2009; 16: 107-126.
29. Balaban MV, Sauleau R, Benson TM, Nosich AI,. Accurate quantification of the Purcell effect in he presence of a dielectric microdisk of nanoscale thickness. Micro and Nano Letters 2011; 6 (6): 393-396.
30. Balaban MV, Sauleau R, Nosich AI,. Complex-source-point beam scattering by a thin high-contrast dielectric disk. Proc. European Conf. on Antennas and Propagation (EuCAP-11), Rome, 2011, 882-885.
31. Vinogradov SS,. Reflectivity of a spherical shield. Radiophys. Quant. Electron. 1983; 26 (1): 78-88.
32. Davydov AG, Zakharov EV, Pimenov YV,. Numerical analysis of fields in the case of electromagnetic excitation of unclosed surfaces. J. Comm. Tech. Electron. 2000; 45, no l.2: 247-259.
33. Berthon A, Bills R,. Integral equation analysis of radiating structures of revolution. IEEE Trans. Antenn. Propag. 1989; 37 (3): 159-170.
34. Vasilyev EN,. Excitation of Bodies of Rotation. Radio i Svyaz: Moscow, 1987 (in Russian).
35. VS Bulygin,: Interpolation-type numerical method for the electromagnetic wave diffraction by a perfectly conducting axially-symmetric screen, Proc. Int. Conf. Mathematical Methods in Electromagnetic Theory (MMET*10), Kiev, 2010, IET-5.
36. VS Bulygin, AI Nosich, YV Gandel,: Near-field focusing and radar cross-section for a PEC paraboloidal screen illuminated by a plane electromagnetic wave, Proc. European Conf. Antennas and Propagation (EuCAP-2011), Rome, 2011, pp. 3836-3840.