On optimal zero-padding of kernel truncation method
数学专题报告
报告题目(Title)：On optimal zero-padding of kernel truncation method
报告人(Speaker)：刘欣 （天津大学）
地点(Place)：教八楼405
时间(Time)：2025 年 4 月 21 日（周一） 14:00--15:00
邀请人(Inviter)：熊云丰
报告摘要
The kernel truncation method (KTM) is a commonly used algorithm to compute the convolution-type nonlocal potential, where the convolution kernel might be singular at the origin and/or far-field and the density function is smooth and fast-decaying. In KTM, in order to capture the Fourier integrand's oscillations brought by the kernel truncation, one needs to carry out a zero-padding of the density, which means a larger physical computation domain and a finer mesh in the Fourier space by duality. In this talk, we first derive the optimal zero-padding factor in a rigorous way for arbitrary space dimension, which helps make the computational time and memory cost greatly reduced. Then, we present the error estimates of the potential and re-investigate the optimal zero-padding factor for the anisotropic density. In addition, we provide details of tensor acceleration, which is an important performance improvement. Extensive numerical results are provided to confirm the accuracy, efficiency, optimal zero-padding factor for the anisotropic density, together with some applications to different types of nonlocal potential.
主讲人简介
刘欣目前是天津大学博士研究生，导师为张勇教授。她主要研究卷积问题的快速算法，目前在SISC、JCP、M3AS等计算数学权威期刊上发表多篇文章。
