Mitigate the ray effect in RTE simulations

：唐敏（上海交通大学）
：2025-05-16 13:30
：海韵园实验楼S204

报告人：唐敏（上海交通大学）

时  间：2025年5月16日13:30

地  点：海韵园实验楼S204

内容摘要:

The commonly used velocity discretization for simulating the radiative transport equation (RTE) is the discrete ordinates method (DOM). One of the long-standing drawbacks of DOM is the phenomenon known as the ray effect. Due to the high dimensionality of the RTE, DOM results in a large algebraic system to solve. The Source Iteration (SI) method is the most standard iterative method for solving this system. In this talk, by introducing randomness into the SI method, we propose a novel random source iteration (RSI) method that offers a new way to mitigate the ray effect without increasing the computational cost. We have rigorously proved that RSI is unbiased with respect to the SI method and that its variance is uniformly bounded across iteration steps; thus, the convergence order with respect to the number of samples is 1/2. Furthermore, we prove that the RSI iteration process, as a Markov chain, is ergodic under mild assumptions. Numerical examples are presented to demonstrate the convergence of RSI and its effectiveness in mitigating the ray effect.

个人简介：

唐敏，上海交通大学自然科学研究院教授，教育部青年长江学者，主要研究兴趣包括生物数学中的数学建模和数值模拟，多尺度辐射输运方程，各向异性扩散方程等方程的数值算法设计和分析等，是国际期刊《Communications in Mathematical Sciences》和《Journal of Mathematical Biology》编委，已在SISC、PRL和JCP等期刊发表论文50余篇。

 

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