Fast algorithm for convolution-type potential evaluation in different dimensions
报告题目(Title)：Fast algorithm for convolution-type potential evaluation in different dimensions
报告人(Speaker)：张勇 教授（天津大学，应用数学中心）
地点(Place)：电子楼 103 & 腾讯会议 ID：182 564 287
时间(Time)：2020年10月12日13:30 -14：30
邀请人(Inviter)：蔡勇勇
报告摘要
Convolution-type potentials 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) algorithm achieving spectral accuracy. For the one-dimensional convolutions, we shall introduce the tree and sum-of-exponential based fast algorithm.
References
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