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

報告人：張勇（教授、“青年千人”計劃）

報告人單位：天津大學

報告時間：2021年9月3日下午16:00-18:00

騰訊會議：會議ID：394 782 695

報告內容簡介：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.

報告人簡介：張勇教授2007年本科畢業于天津大學，2012年在清華大學獲得博士學位。他先后在奧地利維也納大學的Wolfgang Pauli研究所，法國雷恩一大和美國紐約大學克朗所從事博士后研究工作。2015年7月獲得奧地利自然科學基金委支持的薛定諤基金，2018年入選國家“青年千人”計劃。研究興趣主要是偏微分方程的數值計算和分析工作，尤其是快速算法的設計和應用。迄今發表論文20余篇，主要發表在包括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等計算數學頂尖雜志。

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主辦單位：科研處、理學院、人工智能研究院、非線性動力系統研究所、

數理力學研究中心