Potential-based numerical solution of Dirichlet problems for the Helmholtz equation

DOI10.1134/S0965542512080052zbMath1274.35065MaRDI QIDQ2836645

A. A. Kashirin, S. I. Smagin

Publication date: 3 July 2013

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemHelmholtz equationintegral operatorssingle-layer potential

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fredholm integral equations (45B05)

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ИССЛЕДОВАНИЕ ПРИБЛИЖЕННОГО РЕШЕНИЯ НЕКОТОРЫХ КЛАССОВ ПОВЕРХНОСТНЫХ ИНТЕГРАЛЬНЫХ УРАВНЕНИЙ ПЕРВОГО РОДА ⋮ Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form ⋮ On the existence of mosaic-skeleton approximations for discrete analogues of integral operators ⋮ Justification of the collocation method for a class of surface integral equations ⋮ Application of boundary integral equation method to numerical solution of elliptic boundary-value problems in R3 ⋮ Investigation of an approximate solution of the integral equation of the exterior Dirichlet boundary value problem for the Helmholtz equation in the two-dimensional space ⋮ Parallel mosaic-skeleton algorithm for the numerical solution of a three-dimensional scalar scattering problem in integral form ⋮ Substantiation of the collocation method for one class of systems of integral equations ⋮ On an approximate solution of a class of surface singular integral equations of the first kind ⋮ Unnamed Item ⋮ On an approximate solution of a class of boundary integral equations of the first kind ⋮ Numerical solution of scalar diffraction problems in integral statements on spectra of integral operators ⋮ Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation ⋮ Numerical solution of integral equations for a scalar diffraction problem ⋮ Constructive method for solving a boundary value problem with impedance boundary condition for the Helmholtz equation ⋮ Justification of the collocation method for an integral equation of the exterior Dirichlet problem for the Laplace equation ⋮ Approximate solution of the boundary value problem for the Helmholtz equation with impedance condition ⋮ On numerical solution of a first kind integral equation with a weak singularity in the kernel on a closed surface

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