Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the <i>x = t<sup>p</sup></i>Substitution

• 作者: George Papazafeiropoulos Javad Yazdani Stephen M. Kirkup
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Boundary Element Method SINGULAR INTEGRAL Numerical Integration
• 年，卷（期）: 2019,（4）
• 页码范围: 282-301
• 页数: 20页
• 分类号: O17

摘要

Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.