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An efficient algorithm for solution of a scattering problem
Author(s) -
Wang Y. M.,
Chew W. C.
Publication year - 1990
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.4650030309
Subject(s) - operator (biology) , mathematics , scattering , algorithm , algebraic number , algebraic equation , field (mathematics) , mathematical analysis , spherical harmonics , physics , pure mathematics , optics , quantum mechanics , nonlinear system , biochemistry , chemistry , repressor , transcription factor , gene
Abstract An object can always be subdivided into N subobjects. Hence, the scattering solution of an arbitrary‐shape inhomogeneous scatter can be formulated as a scattering solution of N scatterers, each of whose scattered field is approximated by M harmonics. This results in an NM unknown problem. A previously developed recursive operator algorithm, now adapted for wave scattering problems, can be used to solve this N scatterer problem. It is shown that the computational time of such an algorithm scales N 2 M 2 P where P is the number of harmonics used in the translation formulas. The scattered field from the same arbitrary shape scatterer can also be conventionally solved by the method of moments, casting it into an N linear algebraic equation. The solution of the linear algebraic equation via Gauss' elimination will involve order N 3 floating‐point operations. Hence, the complexity of the recursive operator algorithm is of lower order than the method of moments. It is shown that the recursive operator algorithm is more efficient than the method of moments when the number of unknowns is large.