Fast convolution-type nonlocal potential solvers in Nonlinear Schr?dinger equation and Lightning simulation

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

报告人：张勇（教授、“青年千人”计划）

报告人单位：天津大学

报告时间：2021年9月3日下午16:00-18:00

腾讯会议：会议ID：394 782 695

报告内容简介：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 aO(N log N)fast algorithm achieving spectral accuracy. Applications to NLSE, together with a useful recently-developed sum-of exponential algorithm are reviewed. Tree-algorithm for computing the one-dimensional convolutions in lighting-shield simulation is also covered as the last application.

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，2018年入选国家“青年千人”计划。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, SIAM Multiscale Modeling and Simulation, Journal of Computational Physics, Mathematics of Computation, Computer Physics Communication等计算数学顶尖杂志。

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主办单位：科研处、理学院、人工智能研究院、非线性动力系统研究所、

数理力学研究中心