Choose timezone
Your profile timezone:
Powered by Indico
v3.3.4
Speaker: Weizhu Bao (National University of Singapore)
Title: Computational methods for the dynamics of the nonlinear Schroedinger/Gross-Pitaevskii equations
Abstract: In this talk, I begin wtih the (nonlinear) Schroedinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics, soliton solutions and semiclassical limits. Different numerical methods will be presented including finite difference time domain (FDTD) methods and time-splitting spectral (TSSP) method, and their error estimates and comparison will be discussed. Extensions to NLSE/GPE with an angular momentum rotation term, non-local dipole-dipole interaction, multi-component and logarithmic nonlinearity will be presented. Applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated. Finally, I report our very recent results of energy regularization methods for NLSE with logarithmic nonlinearity and improved uniform error bounds on TSSP for the long-time dynamics of NLSE by using the regularization compensation oscillatory (RCO) technique as well as error estimates on numerical methods for NLSE with low regularity potential and nonlinearity.
Bio: Weizhu Bao is Provost's Chair Professor at Department of Mathematics, and Vice Dean for Graduate Studies and Academic Affairs of Faculty of Science, National University of Singapore (NUS). He had been on the Editorial Board of SIAM Journal on Scientific Computing during 2009--2014 and is currently on the Editorial Board of SIAM Journal of Numerical Analysis.
Bao was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. He has been invited to give plenary and/or invited talks in many international conferences including an Invited Speaker at the International Congress of Mathematicians (ICM) in 2014. He was elected a Fellow of the American Mathematical Society
(AMS Fellow), a Fellow of the Society of Industrial and Applied Mathematics (SIAM Fellow) and a Fellow of Singapore National Academy of Science (SNAS Fellow) in 2022.
For more about Weizhu Bao, see his web page: https://discovery.nus.edu.sg/819-weizhu-bao/about