We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the reference element's space using Newton's method, singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy of our method for quadratic basis functions and quadratic triangles with several numerical experiments, including the scattering by two half-spheres.

翻译：我们提出在用曲线边界元素解决 3D Helmholtz 方程式时产生的微弱单项和近星系元件计算算法。 这些算法基于使用牛顿的方法、 奇数减法、 持续法和移植高斯方形计算参考元件空间的奇数的预视值。 我们通过若干数字实验, 包括两个半球的散射, 来显示我们四边基函数和二次三角形的方法的准确性 。