Closed-form evaluation of potential integrals in the Boundary Element Method

Michael Carley

doi:10.1142/S2591728519500142

Closed-form evaluation of potential integrals in the Boundary Element Method

Michael Carley

Department of Mechanical Engineering

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Abstract

A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

Original language	English
Article number	1950014
Journal	Journal of Theoretical and Computational Acoustics
Volume	28
Issue number	2
Early online date	3 Mar 2020
DOIs	https://doi.org/10.1142/S2591728519500142
Publication status	Published - 30 Jun 2020

Keywords

Boundary element method
Helmholtz equation
layer potentials
numerical integration
scattering

ASJC Scopus subject areas

Acoustics and Ultrasonics
Computer Science Applications
Applied Mathematics

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10.1142/S2591728519500142

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lectronic version of an article published as [Journal of Theoretical and Computational Acoustics https://doi.org/10.1142/S2591728519500142 © [copyright World Scientific Publishing Company] https://www.worldscientific.com/doi/abs/10.1142/S2591728519500142
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abstract = "A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.",

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AB - A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

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Closed-form evaluation of potential integrals in the Boundary Element Method

Abstract

Keywords

ASJC Scopus subject areas

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