报告题目: 科学计算与人工智能

报告人: Jinchao Xu（许进超）Peking University and Penn State University
报告主持人：王汉权

时间地点: 2018年7月4日(周三)下午3:00--4:00， 统数学院会议室307

摘要: 实验、理论、计算与数据通常被认为科学研究的四大主要方法。此报告通过一些简单的例子与数学分析，由浅入深的介绍科学计算与大数据的一些基本方法与应用。科学计算从求解大规模线性代数方程组入手，介 绍现代科学与工程计算中最有效的算法之一“多层网格法”的基本思想与技巧。数据科学从图像识别入手，简单介绍以深度神经网络为基础的人工智能方法。最后，我们介绍科学计算中的方法与人工智能建模与计算之间的联系以及因此带来的相关研究课题。

报告人简介:许进超教授是美国宾州州立大学Verne M.Willaman讲席教授、计算数学与应用研究中心主任、北京大学长江讲座教授、北京国际数学研究中心计算方法与应用实验室主任、中组部“海外高层次人才引进计划”入选者。许进超教授的主要研究方向为偏微分方程快速算法，是该研究领域国际知名学术带头人，取得了一系列奠基性的科研成果（比如著名的子空间矫正算法，BPX算法，以及XZ恒等式等）。迄今发表学术论文170余篇，其论文Google引用次数近超过10000次。他与合作者提出的求解Maxwell方程组的HX-算法，被美国能源部评为近年来计算科学领域中的十大突破之一。他还担任了十多种国际计算数学权威期刊的编委。许进超教授曾于1995获得首届冯康科学计算奖，于2005年获得德国“洪堡”资深科学家奖，2006年获得中国杰出青年基金（B类）,于2007年应邀在第6届国际工业与应用数学学会大会上作特邀报告，2010年应邀在世界数学家大会上作45分钟报告。他是美国工业与应用数学学会、美国数学学会会士。


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

报告时间：2018年7月4日下午4：00至5：00点
报告地点：统计与数学学院307会议室

报告人：张勇教授（天津大学应用数学中心）
报告主持人：王汉权教授（统计与数学学院副院长）

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 e_ciency. 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, 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.
References
[1] W. Bao, S. Jiang, Q. Tang and Y. Zhang, Computing the ground state and dynamics of the nonlinear Schr?dinger equation with nonlocal interactions via the nonuniform FFT, J. Comput. Phys., 296 (2015), pp. 72–89.
[2] L. Exl, N. Mauser and Y. Zhang, Accurate and e_cient computation of nonlocal potentials based on Gaussian-sum approximation, J. Comput. Phys., 327 (2016), pp. 629–642.
[3] X. Antoine, Q. Tang and Y. Zhang, On the ground states and dynamics of space fractional nonlinear Schr?dinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions, J. Comput. Phys., 325 (2016), pp. 74–97.
[4] C. Zhuang, Y. Zhang, X.Zhou, R. Zeng and L. Liu, A fast tree algorithm for electrical field calculation in electrical discharge simulations, IEEE Transactions on Magnetics (2017).
[5] X. Antoine, Q. Tang, Y. Zhang A Preconditioned Conjugated Gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via Kernel Truncation method for Dipole-Dipole Interaction evaluation, Communication in Computational Physics, 2017.
[6] L. Greengard, S. Jiang and Y. Zhang, A generic anisotropic kernel truncation method for convolution of free-space Green’s function, submitted.

张勇教授简介见网页：http://cam.tju.edu.cn/faculty/teacherDetail.php?id=81