Geodesic
On an algorithm for calculating diffraction integrals
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1078-1095 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. F. Albu; V. I. Zubov. On an algorithm for calculating diffraction integrals. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1078-1095. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a1/

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