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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7, Pages 1078–1095 (Mi zvmmf10060)  

On an algorithm for calculating diffraction integrals

A. F. Albua, V. I. Zubovab

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Moscow Institute of Physics and Technology

Abstract: n algorithm for calculating integrals of rapidly oscillating functions given on a smooth two-dimensional surface is proposed. The surface is approximated by a collection of flat triangles with the values of the integrand known at their vertices. These values are used as reference ones to extend the function to other points of a triangle. The integral of the extended function over the surface of a triangle is calculated exactly. The desired value of the full diffraction integral is determined as the sum of the integrals calculated over the surfaces of all triangles. The resulting formulas for integral calculation involve singularities (indeterminate forms). Much attention is given to representations of these formulas in such a way that the indeterminate forms are automatically evaluated. Numerical results are presented.

Key words: diffraction integral, rapidly oscillating function, algorithm for computing two-dimensional integrals of rapidly oscillating functions.

DOI: https://doi.org/10.7868/S0044466914070035

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1079–1095

Bibliographic databases:

UDC: 519.644
MSC: 6M55,65Z05
Received: 12.02.2014

Citation: A. F. Albu, V. I. Zubov, “On an algorithm for calculating diffraction integrals”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1078–1095; Comput. Math. Math. Phys., 54:7 (2014), 1079–1095

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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