Evaluation of nearly singular integrals in isogeometric boundary element method

Y. P. Gong; C. Y. Dong; Y. Bai

doi:10.1016/j.enganabound.2016.11.005

Evaluation of nearly singular integrals in isogeometric boundary element method

Y. P. Gong, C. Y. Dong^*, Y. Bai

^*Corresponding author for this work

School of Aerospace Engineering

Beijing Institute of Technology

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

20 Citations (Scopus)

Abstract

Isogeometric boundary element method (IGBEM) is a new numerical method that has received a lot of attentions in recent years. However, nearly singular integrals in the IGBEM have not yet received more attention when the IGBEM is used to study thin-body/coating structures. In this paper, the exponential transformation method based on the idea of diminishing the difference of the orders or the scale of change of addition factors in the denominator of the kernels is used to remove or weaken the near singularities of nearly singular integrals appearing in 2D/3D potential problems. Numerical results show that the present method is effective, stable and competitive. We believe that this work clearly presents the power of the IGBEM and provides an efficient approach to investigate the boundary layer effect appearing in thin-body/coating structures.

Original language	English
Pages (from-to)	21-35
Number of pages	15
Journal	Engineering Analysis with Boundary Elements
Volume	75
DOIs	https://doi.org/10.1016/j.enganabound.2016.11.005
Publication status	Published - 1 Feb 2017

Keywords

2D/3D potential problems
Exponential transformation
IGBEM
Nearly singular integrals

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10.1016/j.enganabound.2016.11.005

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title = "Evaluation of nearly singular integrals in isogeometric boundary element method",

abstract = "Isogeometric boundary element method (IGBEM) is a new numerical method that has received a lot of attentions in recent years. However, nearly singular integrals in the IGBEM have not yet received more attention when the IGBEM is used to study thin-body/coating structures. In this paper, the exponential transformation method based on the idea of diminishing the difference of the orders or the scale of change of addition factors in the denominator of the kernels is used to remove or weaken the near singularities of nearly singular integrals appearing in 2D/3D potential problems. Numerical results show that the present method is effective, stable and competitive. We believe that this work clearly presents the power of the IGBEM and provides an efficient approach to investigate the boundary layer effect appearing in thin-body/coating structures.",

keywords = "2D/3D potential problems, Exponential transformation, IGBEM, Nearly singular integrals",

author = "Gong, {Y. P.} and Dong, {C. Y.} and Y. Bai",

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T1 - Evaluation of nearly singular integrals in isogeometric boundary element method

AU - Gong, Y. P.

AU - Dong, C. Y.

AU - Bai, Y.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Isogeometric boundary element method (IGBEM) is a new numerical method that has received a lot of attentions in recent years. However, nearly singular integrals in the IGBEM have not yet received more attention when the IGBEM is used to study thin-body/coating structures. In this paper, the exponential transformation method based on the idea of diminishing the difference of the orders or the scale of change of addition factors in the denominator of the kernels is used to remove or weaken the near singularities of nearly singular integrals appearing in 2D/3D potential problems. Numerical results show that the present method is effective, stable and competitive. We believe that this work clearly presents the power of the IGBEM and provides an efficient approach to investigate the boundary layer effect appearing in thin-body/coating structures.

AB - Isogeometric boundary element method (IGBEM) is a new numerical method that has received a lot of attentions in recent years. However, nearly singular integrals in the IGBEM have not yet received more attention when the IGBEM is used to study thin-body/coating structures. In this paper, the exponential transformation method based on the idea of diminishing the difference of the orders or the scale of change of addition factors in the denominator of the kernels is used to remove or weaken the near singularities of nearly singular integrals appearing in 2D/3D potential problems. Numerical results show that the present method is effective, stable and competitive. We believe that this work clearly presents the power of the IGBEM and provides an efficient approach to investigate the boundary layer effect appearing in thin-body/coating structures.

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KW - Exponential transformation

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JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

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Evaluation of nearly singular integrals in isogeometric boundary element method

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Keywords

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