Integral equation method

This method occupies a particular place among the methods of solution of diffraction problems. It is a general approach where using the Green functions the boundary-value problem is transformed into the integral form including the boundary conditions and the radiation conditions at infinity [83,401,506]. Therefore, this method is not only a numerical approach, but in fact a basis for formulation of other methods (e.g., the method of moments [243,495], the T-matrix method [147,463], Rayleigh-Debye-Gans theory [25,441]).

Pioneer rigid calculations using this method were performed in 1964-1965 [136,137,424]. A detailed discussion of the questions connected with the application of the integral equations to light scattering problems can be found in [24,401,464]. For solution of the integral equations one uses different methods: method of moments, Galerkin method, etc. [228,243,265,380,434,467,495,500]. From the integral equations one can calculate scattering and absorption by particles of different shape and structure: cubes [272], disks [301,500], cylinders of any shape (cross-section) [380,424,434], finite thin rods [476], any structure aggregates of spherical particles [175,265] and so on.

In 1972-1973 in a series of two papers A.R. Holt and V. Santoso [258] formulated the quantum mechanics problem of scattering by a central potential (Schroedinger equation) in the form of the Fredholm equation of the 2nd kind. It was shown that the algorithm is stable, since it automatically satisfies the variational principle. In the subsequent papers applications to the problems of light scattering by cylinders [257,476,478] and spheroids [260,477,478] were developed. In 1990 this method was formulated in general case for anisotropic spheroids [387], but numerical results were presented only for anisotropic single axis sphere.
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Created by V.I.
Last modified: 12/08/03, V.I.