Abstract A quadrature formula for the direct value of the normal derivative of the single layer potential with smooth density defined on a closed or nonclosed surface is obtained. Single layer potentials for the Laplace and Helmholtz equations are considered. Numerical tests confirm that our quadrature formula gives considerably higher accuracy than the standard quadrature formula. It can be used when numerically solving boundary value problems for the Laplace and Helmholtz equations by the potential method and the boundary integral equation method.

中文翻译：

---

单层电位正态导数的直接值求积公式

摘要 得到了在封闭或非封闭表面上定义的光滑密度单层势的法向导数的直接值的求积公式。考虑了拉普拉斯方程和亥姆霍兹方程的单层电位。数值测试证实，我们的积分公式比标准积分公式的精度高得多。它可用于通过位势法和边界积分方程法数值求解拉普拉斯方程和亥姆霍兹方程的边值问题。