报告题目： Singularity swapping method for nearly singular integrals based on trapezoidal rule
报 告 人：赖俊 研究员 单位名称 浙江大学
报告时间：2023年 5月 11 日 14:00-15:00
报告地点：腾讯会议 ID：743-787-014
会议链接：https://meeting.tencent.com/dm/c6uZgaquqYoQ
校内联系人：刁怀安 diao @ jlu.edu.cn
报告摘要：Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this talk, we propose a variant of singularity swapping method to accurately evaluate the layer potentials for arbitrarily close targets. Our method is based on the global trapezoidal rule and trigonometric interpolation, resulting in an explicit quadrature formula. The method achieves spectral accuracy for nearly singular integrals on closed analytic curves. In order to extract the singularity from the complexified distance function, an efficient root finding method is proposed based on contour integration. Through the change of variables, we also extend the quadrature method to integrals on the piecewise analytic curves. Numerical examples for Laplace's and Helmholtz equations show that high order accuracy can be achieved for arbitrarily close field evaluation.
报告人简介：赖俊，美国密歇根州立大学应用数学博士毕业，曾任纽约大学柯朗数学研究所博士后及讲师（Courant Instructor），目前任浙江大学数学科学学院“百人计划”研究员，主要研究声波，电磁波及弹性波方程的散射与反散射问题，在数学知名杂志ACHA，SISC，Math Comp，Inverse Problems等发表文章多篇，主持或参与基金委面上项目、基金委重大研究计划，基金委创新群体等研究，曾入选中组部海外高层次青年人才计划，获十一届全国反问题年会“优秀青年学术奖”， 2022年获浙江大学-小米青年学者称号。
