QUADRATURE OF SINGULAR INTEGRANDS OVER SURFACES
QUADRATURE OF SINGULAR INTEGRANDS OVER SURFACES
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曲面上奇异积分的求积
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
K. Atkinson
中科院分区：
文献类型：
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作者：
K. Atkinson
考虑R 3中一个简单闭光滑曲面上的积分，该曲面与单位球面同胚，并假设被积函数有一个点奇点。我们提出了一个数值积分方法的基础上使用的转换，导致积分问题的单位球的被积函数，这是平滑得多。在这一点上，梯形规则被应用到球坐标表示的问题。该方法应用简单，收敛速度快。预期的应用程序是在潜在的理论和辐射度方程的边界积分方程方法中产生的边界积分的评估。
Consider integration over a simple closed smooth surface in R 3 , one that is homeomorphic to the unit sphere, and suppose the integrand has a point singularity. We propose a numerical integration method based on using transformations that lead to an integration problem over the unit sphere with an integrand that is much smoother. At this point, the trapezoidal rule is applied to the spherical coordinate representation of the problem. The method is simple to apply and it results in rapid convergence. The intended application is to the evaluation of boundary integrals arising in boundary integral equation methods in potential theory and the radiosity equation.