報告題目： Singularity swapping method for nearly singular integrals based on trapezoidal rule
報 告 人：賴俊 研究員 單位名稱 浙江大學
報告時間：2023年 5月 11 日 14:00-15:00
報告地點：騰訊會議 ID：743-787-014
會議鍊接：https://meeting.tencent.com/dm/c6uZgaquqYoQ
校内聯系人：刁懷安 diao @ jlu.edu.cn
報告摘要：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.
報告人簡介：賴俊，美國密歇根州立大學應用數學博士畢業，曾任紐約大學柯朗數學研究所博士後及講師（Courant Instructor），目前任浙江大學數學科學學院“百人計劃”研究員，主要研究聲波，電磁波及彈性波方程的散射與反散射問題，在數學知名雜志ACHA，SISC，Math Comp，Inverse Problems等發表文章多篇，主持或參與基金委面上項目、基金委重大研究計劃，基金委創新群體等研究，曾入選中組部海外高層次青年人才計劃，獲十一屆全國反問題年會“優秀青年學術獎”， 2022年獲浙江大學-小米青年學者稱号。
