Lecture:Fast Convolution-Type Nonlocal Potential Solvers in Nonlinear Schrödinger Equation and Lightning Simulation
Lecturer: Zhang Yong(Professor, under Thousand Young Talents Program, Tianjin University)
Time:16:00-18:00 PM, Sept. 3rd, 2021.
Avenue:Tencent Meeting (ID:394 782 695)
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 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 aO(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 are also covered as the last application.
Professor Zhang Yong received his Bachelor's Degree from Tianjin University in 2007 and his PhD degree from Tsinghua University in 2012. He worked as a postdoctoral fellow at the Wolfgang Pauli Institute at the University of Vienna in Austria, Rennes I in France, and the Krahn Institute at New York University in the United States. Zhang was rewarded Schrodinger Foundation, supported by the Natural Science Foundation of Austria in July 2015, and was selected into the National "Thousand Young Talents" Program in 2018. His research interests are numerical computation and analysis of partial differential equations, especially the design and application of fast algorithms. So far, he has published more than 20 papers. Major publications includeSIAM Journal on Scientific Computing,SIAM Journal on Applied Mathematics,SIAM Multiscale Modeling and Simulation,Journal of Computational Physics,Mathematics of Computation,Computer Physics Communication and other top journal of computational mathematics.
Organizer and sponsor:Scientific Research Department
School of Sciences
Artificial Intelligence Institute
Institute of Nonlinear Dynamic Systems
Research Center for Mathematical Mechanics