讲座名称：矩量法中奇异值消去法的全新框架

讲座人：朱明达 副教授

讲座时间：1月3日14:30

讲座地点：腾讯会议直播（ID：801 568 833）

讲座人介绍：

朱明达，全球十大赌船网站副教授，分别于2005年、2008年、2012年获上海交通大学学士、硕士和博士学位。2017至2018年在美国Syracuse大学Tapan K. Sarkar教授指导下从事算法研究。2019年至今在陕西省超大规模电磁计算重点实验室工作，主要研究方向为科学计算、积分方程法、以及电磁学中其他相关数值算法。

讲座内容：

The near-singularity and shape-dependence are two main topics in the singularity cancellation methods which have been proposed and widely used for calculating near-singular integrals in method of moments. The shape-dependent problem is that the accuracy of a singularity cancellation scheme decreases vastly when the shape of the sub-triangle is deformed. According to the original theory, these two issues are considered irrelevant. Therefore, a theoretical and numerical investigation on the problem of shape-dependence is necessary to solve the problem.

In this work, the theoretical analysis is carried out, which indicates that the near-singularity is not just affected by the projection height d of the observation point. Similarly, the shape-dependent problem of singularity cancellation methods are not only related to the triangle height a. In other words, the near-singularity and the shape-dependent problem are actually the same thing. We only have one near-singularity problem with relation to a and d, while the level of near-singularity would be dominated by the largest one among a and d. Moreover, we propose a novel framework of singularity cancellation transformations for near-singular integrals. The proposed singularity cancellation transformations have the exponential error convergence even for extremely deformed triangles.

主办单位：电子工程集团