报告题目：Fast algorithm for convolution-type potential evaluation in quantum mechanics and engineering problems

报 告 人：张勇 教授 天津大学

报告时间：2020年11月17日 9:00-10:00

报告地点：腾讯会议 ID：905 849 419  会议密码：123456

会议链接：https://meeting.tencent.com/s/EfXXFyu5HNfJ

校内联系人：许志国 xuzg2014@jlu.edu.cn

报告摘要：

Convolution-type potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations. In this serial-talk, I will focus on those arising from quantum physics/chemistry and lightning-shield protection, including Coulomb, dipolar and Yukawa potential that are generated by isotropic and anisotropic smooth and fast-decaying density, as well as convolutions defined on a one-dimensional adaptive finite difference grid. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and efficiency. The state-of-art fast algorithms include Wavelet based Method( WavM), kernel truncation method(KTM), NonUniform-FFT based method(NUFFT) and Gaussian-Sum based method(GSM). Gaussian-sum/exponential-sum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to O(N log N) algorithm achieving spectral accuracy. For the one-dimensional convolutions, we shall introduce the tree and sum-of-exponential based fast algorithm.

报告人简介：

张勇教授，2007年本科毕业于天津大学，2012年在清华大学获得博士学位。他先后在奥地利维也纳大学的Wolfgang pauli 研究所，法国雷恩一大和美国纽约大学克朗所从事博士后研究工作。2015年7月获得奥地利自然科学基金委支持的薛定谔基金。研究兴趣主要是偏微分方程的数值计算和分析工作，尤其是快速算法的设计和应用。迄今发表论文20余篇，主要发表在包括SIAM Journal on Scientific Computing, SIAM journal on Applied Mathematics, Journal of Computational Physics, Mathematics of Computation, Computer Physics Communication 等计算数学顶尖杂志。