题目：Fast convolution-type nonlocal potential solvers in Nonlinear Schroedinger equation and Lightning simulation

报告人：张勇博士（University of Vienna）

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 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 $O(N /log N )$ fast algorithm achieving spectral accuracy. Applications to NLSE, together with A useful recently-developed sum-of-exponential algorithm are reviewed. Tree-algorithm to compute the one-dimensional convolutions in lighting-shield simulation is also covered in the last section.

时间：1月3日（周三）下午 5：00--5:50

地点：首师大校本部新教二楼527

欢迎全体师生积极参加！