Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Professor Yong Zhang,Center for Applied Mathematics, Tianjin University
Inviter:	Professor Hehu Xie
Title:	Fast convolution-type nonlocal potential solvers in Nonlinear Schro?dinger equation and Lightning simulation
Language:	Chinese
Time & Venue:	2023.07.06 14:00-15:00 Z301
Abstract:	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 the kernel truncation method (KTM), NonUniform-FFT based method (NUFFT) and Gaussian-Sum based method (GauSum). 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.