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：我们提出了基于奇异减除、延拓方法和移植高斯求积的算法，用于计算弯曲三角形单元上的强奇异和近奇异表面积分。通过将算法集成到边界元代码中并求解若干三维散射问题，我们验证了该方法对二次基函数和二次三角形单元的精度与鲁棒性。数值实验表明，与传统平面单元相比，使用弯曲边界元素可提升计算效率。