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New variable transformations for evaluating nearly singular integrals in 3D boundary element method

机译：用于评估3D边界元方法中几乎奇异积分的新变量转换

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摘要

This work presents new variable transformations for accurate evaluation of the nearly singular integrals arising in the 3D boundary element method (BEM). The proposed method is an extension of the variable transformation method in Ref. [4] for 2D BEM to 3D BEM. In this paper, first a new system denoted as (α, β) is introduced compared with the polar coordinate system. So the original transformations in Ref. [4] can be developed to 3D in (α, β) or the polar coordinate system. Then, the new transformation is performed by four steps in case the source point coincides with the projection point or five steps otherwise. For each step, a new transformation is proposed based on the approximate distance function, so that all steps can finally be unified into a uniform formation. To perform integration on irregular elements, an adaptive integration scheme combined with the transformations is applied. Numerical examples compared with other methods are presented. The results demonstrate that our method is accurate and effective.
机译：这项工作提出了新的变量转换，以准确评估3D边界元方法（BEM）中出现的几乎奇异的积分。所提出的方法是对Ref中变量转换方法的扩展。 [4]从2D BEM到3D BEM。在本文中，与极坐标系相比，首先引入了一个新的系统（α，β）。因此，参考文献中的原始转换。文献[4]可以发展为（α，β）或极坐标系的3D。然后，在源点与投影点重合的情况下，通过四个步骤执行新的转换，否则以五个步骤执行新的转换。对于每个步骤，都基于近似距离函数提出了一个新的变换，以便最终可以将所有步骤统一为一个统一的形式。为了对不规则元素执行积分，应用了与转换结合的自适应积分方案。给出了与其他方法比较的数值示例。结果表明，该方法是准确有效的。

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  • 来源
    《Engineering analysis with boundary elements》 |2013年第9期|1169-1178|共10页
  • 作者

    Guizhong Xie; Fenglin Zhou; Jianming Zhang; Xingshuai Zheng; Cheng Huang;

  • 作者单位

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Nearly singular integrals; Numerical integration; Boundary element method; Variable transformations;

    机译：几乎奇异的积分;数值积分;边界元法;变量转换;

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