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

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Abstract

A method is presented for the analytical 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 languageEnglish
JournalJournal of Theoretical and Computational Acoustics
DOIs
Publication statusAccepted/In press - 7 Aug 2019

Cite this

@article{290a4e35066a418090414e5d8107d69b,
title = "Closed-form evaluation of potential integrals in the Boundary Element Method",
abstract = "A method is presented for the analytical 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.",
author = "Michael Carley",
year = "2019",
month = "8",
day = "7",
doi = "10.1142/S2591728519500142",
language = "English",
journal = "Journal of Theoretical and Computational Acoustics",
issn = "2591-7285",
publisher = "World Scientific Publishing Co. Pte Ltd",

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T1 - Closed-form evaluation of potential integrals in the Boundary Element Method

AU - Carley, Michael

PY - 2019/8/7

Y1 - 2019/8/7

N2 - A method is presented for the analytical 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.

AB - A method is presented for the analytical 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.

U2 - 10.1142/S2591728519500142

DO - 10.1142/S2591728519500142

M3 - Article

JO - Journal of Theoretical and Computational Acoustics

JF - Journal of Theoretical and Computational Acoustics

SN - 2591-7285

ER -