报告题目：Reduced Order Model Enhanced Preconditioner for Parametric Radiative Transfer Equation

报告人：彭志超  香港科技大学

报告时间：7月2日 3:00-4:30

报告地点：五教5106

摘要：

Radiative transfer equation is a kinetic equation providing basic models in medical imaging, nuclear engineering, and astrophysics. In multi-query applications such as sensitivity  analysis, uncertainty quantification and inverse problems, this equation may be needed to solve repeatedly multiple times for various parameters (e.g. material properties).  

Classical diffusion synthetic acceleration (DSA) preconditioner for this equation uses the diffusion limit of this equation to approximate a kinetic error equation. However, when the  scattering effect is not sufficiently strong, this error equation may not be well approximated by this diffusion limit. Moreover, this strategy does not leverage low-rank structures across parameters.  

To address these issues, we utilize data-driven reduced order models, which starts from the kinetic description and exploits low-rank structures across various parameters to design a new preconditioner for parametric RTE. The effectiveness of this preconditioner is demonstrated through a series benchmark problems. 

报告人简介：

彭志超，现为香港科技大学数学系助理教授，在加入香港科技大学之前，他于2020年-2023年在密歇根州立大学做访问助理教授，在2020年于伦斯勒理工获得博士学位，2015年于北大获得学士学位。他的主要研究兴趣是动理学方程和波方程的数值求解，以及数据驱动的模型降阶。