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Electromagnetic field representations and computations in complex structures. II: Alternative Green’s functions. (English) Zbl 1001.78028

Summary: In this second paper of the three-part sequence [Part I cf. ibid. 15, 93-107 (2002; Zbl 0992.78037)], we deal with alternative Green’s function (GF) representations for the subdomain (SD) problem in the complexity architecture of Part I [Int. J. Numer. Model. 15, 93-107 (2002)]. The relevant GFs for systematic analytic modelling are those associated with at least partially vector and co-ordinate separable boundary conditions. Such ‘canonical’ GFs, when ‘matched’ to a real problem, can form background kernels which simplify the numerical complexity of real-problem exact integral equations. The analytic machinery involves Sturm-Liouville (SL) theory for the reduced one-dimensional (1D) spectral GF problems resulting from separation of variables in various co-ordinates, set in its most general form in the complex spectral wavenumber domain. Spectral synthesis in the complex spectral wavenumber planes for 2D and 3D co-ordinate-separable full GFs lays the foundation for direct construction (via contour deformations, branch point, and pole residue evaluations) of alternative field representations, and their correspondingly different wave-physical phenomenologies. Illustrative examples show the connection between the canonical GFs and their network representations.
For Part III, see ibid. 15, 127-145 (2002; Zbl 0993.78027).

MSC:

78M25 Numerical methods in optics (MSC2010)
34B27 Green’s functions for ordinary differential equations
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References:

[1] Felsen, International Journal of Numerical Modelling 15 pp 93– (2002) · Zbl 0992.78037
[2] Radiation and Scattering of Waves. Prentice Hall: Englewood Cliffs, NJ, 1973. IEEE Press: Piscataway, NJ, (classic reissue), 1994.
[3] Complexity architecture, phase space dynamics and problem-matched Green’s functions, to be published in the special issue of Wave Motion on Electrodynamics in Complex Environments. Felsen LB. (guest ed.) and Engheta N. (co-guest ed.), 2001; 84:243-262.
[4] Russer, International Journal of Numerical Modelling 15 pp 127– (2002) · Zbl 0993.78027
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