Journal of Integral Equations and Applications

Suppression of spurious frequencies in scattering problems by means of boundary algebraic and combined field equations

J. Poblet-Puig, V.Yu. Valyaev, and A.V. Shanin

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Abstract

A numerical technique for solving scattering problems is presented. It is based on a boundary integral equation idea, so the unknowns are localized on the contour (in 2D case) or the surface (in 3D case) of the scattering object. Two major difficulties of traditional boundary integral methods (the appearance of spurious resonances and the necessity to perform numerical integration of singular functions) are overcome by studying the problem in an approximate discrete formulation from the very beginning. The space is filled by cubic blocks, and the shape of the scatterer is formed by a set of blocks removed from the space. Thus, the formulation of the problem is discrete, and the continuous Green's function is substituted by a discrete mesh Green's function. An analogue of combined field boundary integral equation (CFIE) is developed for this formulation.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 2 (2015), 233-274.

Dates
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1441790288

Digital Object Identifier
doi:10.1216/JIE-2015-27-2-233

Mathematical Reviews number (MathSciNet)
MR3395970

Zentralblatt MATH identifier
1327.65255

Subjects
Primary: 35P25: Scattering theory [See also 47A40] 65N80: Fundamental solutions, Green's function methods, etc. 65R20: Integral equations

Citation

Poblet-Puig, J.; Valyaev, V.Yu.; Shanin, A.V. Suppression of spurious frequencies in scattering problems by means of boundary algebraic and combined field equations. J. Integral Equations Applications 27 (2015), no. 2, 233--274. doi:10.1216/JIE-2015-27-2-233. https://projecteuclid.org/euclid.jiea/1441790288


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