Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

Qinlong Ren; Cho Lik Chan

doi:10.1016/j.enganabound.2014.11.018

Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

Qinlong Ren, Cho Lik Chan

Aerospace and Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.

Original language	English (US)
Pages (from-to)	1-8
Number of pages	8
Journal	Engineering Analysis with Boundary Elements
Volume	53
DOIs	https://doi.org/10.1016/j.enganabound.2014.11.018
State	Published - Apr 2015

Keywords

Analytical integration
Boundary element method
Coordinate transformation
Laplace's equation
Stokes flow

ASJC Scopus subject areas

Analysis
General Engineering
Computational Mathematics
Applied Mathematics

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10.1016/j.enganabound.2014.11.018

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abstract = "It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.",

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AU - Chan, Cho Lik

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N2 - It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.

AB - It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.

KW - Analytical integration

KW - Boundary element method

KW - Coordinate transformation

KW - Laplace's equation

KW - Stokes flow

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JO - Engineering Analysis with Boundary Elements

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Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

Abstract

Keywords

ASJC Scopus subject areas

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