报告题目 (Title)：Reduced Order Model Enhanced Preconditioner for Parametric Radiative Transfer Equation（参数化散射输运方程的降阶模型预条件子）
报告人 (Speaker)：彭志超 助理教授（香港科技大学）
报告时间 (Time)：2025年6月2日 (周一) 9:30
报告地点 (Place)：校本部GJ403
邀请人(Inviter)：纪丽洁
主办部门：理学院数学系
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.
