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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >ON THE EFFICIENT COMPUTATION OF SINGULAR AND NEARLY SINGULAR SURFACE INTEGRALS ARISING IN 3D-GALERKIN BEM
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ON THE EFFICIENT COMPUTATION OF SINGULAR AND NEARLY SINGULAR SURFACE INTEGRALS ARISING IN 3D-GALERKIN BEM

机译：3D-Galerkin BEM中奇异面和近奇异面积分的有效计算

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摘要

We will present efficient techniques to approximate singular and nearly singular surface integrals arising massively in Galerkin boundary element discretizations of Fredholm integral equations on two-dimensional surfaces. The technique is based on a new representation of the functionals which arise by computing the so-called focal element matrices, i.e., integrals over pairs of panels. The remaining integrals are approximated by introducing relative co-ordinates which fix the location of the singularity. These integrals can be integrated using polar co-ordinates. It turns out that the number of kernel evaluations which is needed to compute the integrals up to the required accuracy is independent of the order of the singularity. This enables us to use the hypersingular formulation of integral equations which is the method of choice from the theoretical point of view, i. e., stability, robustness with respect to non-smooth surfaces, etc. [References: 6]
机译：我们将提出有效的技术，以近似近似在二维表面上Fredholm积分方程的Galerkin边界元离散化中大量产生的奇异和近奇异表面积分。该技术基于对功能的新表示，该功能是通过计算所谓的焦点元素矩阵（即，成对的面板上的积分）而产生的。通过引入固定奇点位置的相对坐标来近似剩余的积分。可以使用极坐标对这些积分进行积分。事实证明，计算积分直至达到所需精度所需的内核评估次数与奇异性顺序无关。这使我们能够使用积分方程的超奇异公式，这是从理论角度出发选择的方法。例如，相对于非光滑表面的稳定性，鲁棒性等。[参考：6]

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