It is of great interests to solve inverse stationary radiative transport equation (RTE) with very large data sets. The standard way is to formulate the inverse problem into an optimization problem, but the bottle-neck is that one has to solve the forward problem over and over again which is time consuming. In this talk, we propose an online/offline solver for RTE based on the Tailored Finite Point Method (TFPM). TFPM for RTE is uniformly convergent with respect to the mean free path and valid up to the boundary and interface layers. The solver can be decomposed into offline/online stages. The cost at offline stage is comparable to classical methods, while the cost at online stage is much lower. Two cases are considered, one is to solve the RTE with fixed scattering and absorption cross sections, while the boundary conditions vary; the other is when cross sections vary only in a small domain and the boundary conditions change for a lot of times. In these two cases, one only needs to calculate the offline stage once and update the online stage when varying the parameters. Our proposed solver is much cheaper when one needs to solve RTE with multiple right hand sides and accelerate the speed of inverse RTE problems.
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。