We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy and robustness of our method for quadratic basis functions and quadratic triangles by integrating it into a boundary element code and solving several scattering problems in 3D. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.

翻译：本文提出了基于奇异性消除、延拓方法及移植高斯求积的算法，用于计算曲面三角形片上的强奇异与近奇异面积分。通过将该方法集成至边界元代码并求解多个三维散射问题，我们验证了其在二次基函数与二次三角形情形下的精度与鲁棒性。数值结果同时表明，相较于传统平面单元，采用曲面边界元能够有效提升计算效率。