Results 31 to 40 of about 614 (179)

Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D [PDF]

, 2014
summary:We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator.
Zapletal, Jan, Bouchala, Jiří
core   +1 more source

Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

, 2021
IET Microwaves, Antennas &Propagation, Volume 15, Issue 10, Page 1127-1132, 12 August 2021.
Mario Lucido, Kazuya Kobayashi, Francisco Medina, Alexander Nosich, Elena Vinogradova   +4 more
wiley   +1 more source

Exact Solution of a Simple Hypersingular Integral Equation [PDF]

Journal of Integral Equations and Applications, 1992
The author considers in a Hölder type space the following linear hypersingular integral equation \(Hf=v\), where \[ \begin{multlined} (Hf)(x)=\int^ 1_{-1}(x-t)^{-2}f(t)dt:=\\ =\lim_{\varepsilon\to 0}\left\{\int^{x-\varepsilon}_{-1}(x-t)^{-2}f(t)dt+\int^ 1_{x+\varepsilon} (x-t)^{-2}f(t)dt+-2\varepsilon^{- 1}f(x)\right\},\quad x\in(-1,1).\end{multlined} \
openaire   +2 more sources

Discrete mathematical model of the scattering process of E-polarized wave on a periodic impedance grating

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2019
The method of numerical modeling of wave scattering by periodic impedance grating is considered. In the case of a harmonic dependence of the field on time and the uniformity of the structure along a certain axis, the three-dimensional problem reduces to ...
Vladimir D. Dushkin, Stanislav Zhuchenko, Oleksii V. Kostenko   +2 more
doaj   +1 more source

Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method [PDF]

, 2010
This paper presents a gradient field representation using an analytical regularization of a hypersingular boundary integral equation for a 2-dimensional time harmonic wave equation called the Helmholtz equation. The regularization is based on cancelation
Tomioka, Satoshi, Nishiyama, Shusuke
core   +1 more source

A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

Sultan Qaboos University Journal for Science, 2000
This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz.
S.I. Zaman
doaj   +1 more source

A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions

, 2008
We study polynomial approximations of vertex singularities of the type $r^\lambda |\log r|^\beta$ on three-dimensional surfaces. The analysis focuses on the case when $\lambda > -\frac 12$.
Bespalov, A, Bespalov, Alexei
core   +1 more source

Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas

, 2020
A mathematical model of sound propagation from a noise source in urban areas is constructed. The exterior Neumann problem for the scalar Helmholtz equation is reduced to a system of hypersingular integral equations.
Gutnikov V.A., Stavtsev S.L., Lifanov I.K., Setukha A.V., Kiryakin V.Yu.   +4 more
core   +2 more sources

On the injectivity property of a hypersingular operator in a scattering problem of electromagnetic waves on a slab, covered with graphene

Известия высших учебных заведений. Поволжский регион: Физико-математические науки
Background. This study focuses on study of a mathematical model describing the scattering of TE-wave on a 2D slab covered with graphene. The purpose of this study is to prove the uniqueness of the scattering problem and the injectivity property of a ...
Stanislav V. Tikhov
doaj   +1 more source

BPX Preconditioner for Hypersingular Integral Equations

Journal of Integral Equations and Applications, 1998
The BPX preconditioner [cf. \textit{J. H. Bramble, J. E. Pasciak} and \textit{J. Xu}, Math. Comput. 55, No. 191, 1-22 (1990; Zbl 0703.65076)] for the Galerkin approximation of hypersingular integral equations is presented. The condition number of the preconditioned matrix is shown to behave as \(O(h^{-\varepsilon})\) where \(\varepsilon\) is small and ...
openaire   +2 more sources