Efficiency improvements in wave and kinetic transport simulations

：李凤艳（美国伦斯勒理工学院）
：2023-12-18 16:00
：海韵园实验楼106报告厅

报告人：李凤艳（美国伦斯勒理工学院）

时  间：2023年12月18日16:00

地  点：海韵园实验楼106报告厅

内容摘要:

In this two-part talk, we will  present some recent efforts in improving the computational efficiency in simulating wave and kinetic transport models. In Part I, we will review the numerical stiffness of the standard discontinuous Galerkin (DG) methods of very high order accuracy, and the resulting stringent requirement for time step size in explicitly solving time dependent PDEs. We then report our work in overcoming such stiffness by devising energy-stable staggered DG methods for linear wave equations. In Part II, we consider the radiative transfer equation, a fundamental kinetic description of energy or particle transport through media involving scattering and absorption processes. One prominent computational challenge comes from the high dimensionality of the phase space. By leveraging the existence of a low-rank structure in the solution manifold induced by the angular variable in the scattering dominating regime, we propose and test a new reduced basis method.

个人简介：

Prof. Fengyan Li serves as a Professor in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. She obtained a Ph.D. in Applied Mathematics from Brown University in 2004. Prior to that, Prof. Li earned an M.Sc. and a B.Sc. in Computational Mathematics from Peking University in 2000 and 1997 respectively. Prof. Li's research interests encompass a wide range of topics within numerical methods for partial differential equations (PDEs). She is particularly focused on the design, analysis, implementation, and application of accurate, robust, and efficient numerical methods. Her expertise includes finite element methods, discontinuous Galerkin methods, WENO methods, central schemes, and structure-preserving high order methods, such as divergence-free, well-balanced, energy-stable/conservative, and positivity-preserving methods. Additionally, Prof. Li is actively involved in research on reduced order modeling for transport models, utilizing cutting-edge learning techniques and reduced basis methods. Her research also extends to various equations, such as ideal magnetohydrodynamics (MHD) equations, Hamilton-Jacobi equations, Maxwell's equations, shallow water models, kinetic models in rarefied gas dynamics and plasma physics, wave equations, and eigenvalue problems. She has published more than 50 articles in top-ranked international journals, including Math. Comput., SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys., etc.

 

联系人：邱建贤