Seminars on Numerical Algorithms, Analyses, and Applications：Spherical configurations and quadrature methods for integral equations of the second kind

报告人：安聪沛（贵州大学）

时  间：2026年5月14日14:30

地  点：海韵园行政楼C802

内容摘要:

We propose and analyze a product integration method for the second-kind integral equation with weakly singular and continuous kernels on the unit sphere. We employ quadrature rules that satisfy the Marcinkiewicz--Zygmund property to construct hyperinterpolation for approximating the product of the continuous kernel and the solution, in terms of spherical harmonics. By leveraging this property, we significantly expand the family of candidate quadrature rules and establish a connection between the geometrical information of the quadrature points and the error analysis of the method. We then utilize product integral rules to evaluate the singular integral with the integrand being the product of the singular kernel and each spherical harmonic. We derive a practical error bound, which consists of two terms: one controlled by the best approximation of the product of the continuous kernel and the solution, and the other characterized by the Marcinkiewicz--Zygmund property and the best approximation polynomial of this product. Numerical examples validate our numerical analysis.

个人简介：

安聪沛，本科、硕士毕业于中南大学，师从向淑晃，博士毕业于香港理工大学,师从 Chen Xiaojun 和Ian H Sloan,先后工作于暨南大学，西南财经大学，现为贵州大学一流学科特聘教授。研究成果在球 t-设计，振荡积分的近似计算，多项式构造逼近，反问题计算上取得不少同行关注的结果，例如 2022年菲尔兹奖得主 Mayna Viasovska就证明过安聪沛与和作者提出的关于球 t-设计猜想。研究成果发表在SIAM系列杂志、Inverse Problem等期刊上。

联系人：陈黄鑫