報告題目：Fast algorithm for convolution-type potential evaluation in quantum mechanics and engineering problems（系列講座）
主講人：張勇教授（天津大學應用數學中心）
時間：
系列講座之一：2020年10月19日（周一）10:30 a.m.
系列講座之二：2020年10月26日（周一）10:30 a.m.
系列講座之三：2020年11月2日（周一）10:30 a.m.
形式：線上講座
主辦單位：統計與數學學院
會議鏈接：
系列講座之一：https://meeting.tencent.com/s/S2218JFQTYCq
系列講座之二：https://meeting.tencent.com/s/UjDyv201PWNB
系列講座之三：https://meeting.tencent.com/s/UjDyv201PWNB
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 a 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.
Part I：The series topic will cover the following topics
Spectral method on bounded domain and PDE-based algorithm
Part II：The series topic will cover the following topics
（1）NUFFT-based fast convolution solver and related application
（2） GauSum approximation and Fast Convolution Solver
Part III：The series topic will cover the following topics
1) Kernel truncation method and Anisotropic Kernel Truncation method
2) Fast one-dimensional Solver based on Sum-Of-Exponentials
主講人簡介：
張勇，男，天津大學應用數學中心。2012年于清華大學數學學院取得博士學位后，于奧地利維也納大學Wolfgang Pauli研究所、美國著名的數學研究所——克朗數學研究所等地進行博士后研究。近年來，張勇博士在快速算法設計與相關物理應用取得了不少先進的研究成果。
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