报告题目：Fast convolution-type nonlocal potential solvers in Nonlinear Schrödinger equation and Lightning simulation

报告人：Dr. Yong ZHANG (Wolfgang Pauli Institute, University of Vienna)

主持人：鞠红杰

报告时间：2017年11月17日10：30-11：30

报告地点：主楼1214

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 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 a O(N log N) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed. Tree-algorithm to compute the onedimensional convolutions in lighting-shield simulation is also covered in the last section.

报告人简介：

Yong ZHANG（张勇），清华大学博士，先后在沃尔夫冈泡利研究所/维也纳大学、法国雷恩第一大学从事博士后研究工作，期间作为访问学者访问美国库朗数学科学研究所。他的研究方向主要包括Bose-Einstein 凝聚问题的数值计算、快速算法与积分方程、高震荡系统的数值分析等。目前已在J. Comput. Phys.，SIAM等期刊发表SCI论文二十余篇，并是J. Comput. Phys、Comput. Phys. Commun.等多个国际知名期刊的审稿人。