Numerical methods and programming
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Num. Meth. Prog.: Year: Volume: Issue: Page: Find

 Num. Meth. Prog., 2015, Volume 16, Issue 3, Pages 421–435 (Mi vmp552)

On the numerical solution of the Neumann boundary value problem for the Helmholtz equation using the method of hypersingular integral equations

S. G. Daevaa, A. V. Setukhab

a Vega Concern, Moscow
b Lomonosov Moscow State University, Research Computing Center

Abstract: A numerical method for solving a boundary hypersingular integral equation arising from the Neumann boundary value problem for the Helmholtz equation is proposed. The proposed numerical method is based on the explicit separation of the hypersingular main part in the kernel of the integral equation. After discretization, this boundary integral equation is reduced to a system of linear algebraic equations. The coefficients of this system are represented as the sums of hypersingular and weakly singular integrals. The hypersingular integrals are understood in the sense of the finite Hadamard value and are calculated analytically. A number of quadrature formulas for the weakly singular integrals are developed using the smoothing procedures for singularity. The proposed numerical scheme is tested on the basis of the following model examples: a hypersingular integral equation on a sphere and the problems of diffraction of acoustic waves on inelastic spheres and discs. The numerical solutions obtained are compared with existing analytical and numerical data.

Keywords: boundary integral equations, hypersingular integrals, discrete singularity method, Helmholtz equation, diffraction of acoustic waves.

Full text: PDF file (1180 kB)
UDC: 519.64+534.6

Citation: S. G. Daeva, A. V. Setukha, “On the numerical solution of the Neumann boundary value problem for the Helmholtz equation using the method of hypersingular integral equations”, Num. Meth. Prog., 16:3 (2015), 421–435

Citation in format AMSBIB
\Bibitem{DaeSet15} \by S.~G.~Daeva, A.~V.~Setukha \paper On the numerical solution of the Neumann boundary value problem for the Helmholtz equation using the method of hypersingular integral equations \jour Num. Meth. Prog. \yr 2015 \vol 16 \issue 3 \pages 421--435 \mathnet{http://mi.mathnet.ru/vmp552} 

• http://mi.mathnet.ru/eng/vmp552
• http://mi.mathnet.ru/eng/vmp/v16/i3/p421

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. V. Boikov, V. A. Rudnev, A. I. Boikova, N. S. Stepanov, “Primenenie nepreryvnogo metoda resheniya nelineinykh operatornykh uravnenii k pryamym i obratnym zadacham rasseyaniya”, Zhurnal SVMO, 23:3 (2021), 247–272