Computational Aspects of Radiative Transfer: Asymptotics to Uncertainty Quantification

Abstract: 

Thermal radiative transfer (TRT) governs phenomena ranging from supernovas in astrophysics to laser-driven fusion experiments in plasma physics.  The interaction of radiation and matter is characterized by prohibitively small-time scales, nonlinear coupling, and high-dimensional particle dynamics, rendering conventional numerical methods computationally expensive.  Moreover, physical systems are rarely deterministic; uncertainties arising from modelling assumptions, measurement errors, and device imperfections must be incorporated to obtain realistic descriptions of the underlying phenomena.  Quantifying these uncertainties is therefore essential for robustness and reliability in applications.

Dynamical Low-Rank Approximation (DLRA) provides a promising approach for addressing both computational complexity and uncertainty quantification.  The first part of this talk presents strategies for constructing low-rank integrators that remain robust in the presence of prohibitively small-time scales, commonly referred to as asymptotic preserving schemes.  Challenges encountered in real-world applications are discussed along with potential mitigation strategies.  The second part introduces a Low-Rank Multilevel Monte Carlo framework for uncertainty quantifications in TRT equations based on geometric spatial refinement. The efficacy of these methods is demonstrated through a range of test cases and benchmark problems. 

Speaker’s Bio:

Chinmay Patwardhan is a Ph.D. student in the Scientific Computing and Mathematics Department at the Karlsruhe Institute of Technology.  His research focuses on model order reduction techniques and uncertainty quantification methods, with an emphasis on developing cost-effective computational approaches based on DLRA.  These methods aim to reduce the computational cost of simulating kinetic equations and addressing high-dimensional problems.  His additional research interests include scientific machine learning and the development of simulation frameworks.  Chinmay’s work lies at the intersection of applied mathematics and computational science, with the goal of advancing efficient numerical methods for complex systems.