A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals
A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals
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DOI：
10.1002/nme.1620240509
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发表时间：
1987-05
影响因子：
2.9
通讯作者：
J. Telles
中科院分区：
文献类型：
--
作者：
J. Telles
几乎所有通用的边界元计算机软件包都具备曲面几何建模能力。因此，数值积分方案在该技术的编程效率方面起着重要作用。本文详细讨论了这一问题，并介绍了在二维、轴对称和三维应用中计算奇异或近奇异积分的有效方法。重点介绍了一种新的三次多项式变换，发现它能极大地提高高斯积分方案在近奇异范围内的精度。该方法可以很容易地植入现有的边界元代码中，并具有自适应的重要特性，即根据源点到单元的最小距离，它会使高斯节点朝着奇异点进行可变的聚集。该方案的自适应性还使其在无用（源点距离大）时不发挥作用，这使其在一般使用中非常安全。
Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two-dimensional, axisymmetric and three-dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near-singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self-adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self-adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.