报告时间：2025年11月4日（星期二）15:30-16:30

报告地点：翡翠科教楼B座1710

报  告  人：Matthias Schlottbom 教授

工作单位：特文特大学

主办单位：数学学院

报告简介：

The numerical solution of the radiative transfer equation requires the solution of very large linear systems. In the past decades a vast number of iterative schemes has been devised to solve this task. To accelerate convergence of such iterative methods, preconditioners have been developed that solve a diffusion problem, which can be well motivated using arguments from asymptotic analysis. It has been observed that special care needs to be taken in the discretization of such diffusion problems to preserve convergence, leading to so-called consistent schemes. In this talk, we take a slightly different point of view and use preconditioners that are based on residual minimization over suitable subspaces. We prove convergence of the resulting iteration using Hilbert space norms, which allows us to obtain algorithms that converge robustly with respect to finite dimensional realizations via Galerkin projections. We investigate in particular the behavior of the iterative scheme for discontinuous Galerkin discretizations in the angular variable in combination with subspaces that are derived from related diffusion problems. The performance of the resulting schemes is investigated in numerical examples for highly anisotropic scattering problems with heterogeneous parameters.

报告人简介：

Matthias Schlottbom教授于2011年获亚琛工业大学博士学位，其关于光学断层扫描正问题与反问题研究的卓越贡献，被授予博谢纪念奖。他先后在慕尼黑工业大学（2011–2012）、达姆施塔特工业大学（2012–2014）与明斯特大学（2014–2016）从事博士后研究工作。自2016年起，他任职于特文特大学，担任计算科学数学研究中心主任。此外，Matthias Schlottbom教授是荷兰-佛拉芒计算数学学会理事，并自2025年起受聘为中国科学技术大学国际访问教授。

他的研究聚焦于偏微分方程数值分析及反问题理论，尤其在辐射传输方程相关应用方面开展深入工作。至今已在SIAM系列期刊、《计算数学基础》、《微分方程杂志》及《反问题》等多类权威期刊上合作发表论文40余篇。