2019/03/31 by Alexey V. Smirnov, Smirnov, Alexey V., Michael V. Klibanov +3
Engineering · Mathematics · #35R30 #Calibration and Measurement Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Radiative Heat Transfer Studies
paper · pdf · doi:10.48550/arxiv.1904.00547
openalex publication_date 2019/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new numerical method to solve an inverse source problem for the radiative\ntransfer equation involving the absorption and scattering terms, with\nincomplete data, is proposed. No restrictive assumption on those absorption and\nscattering coefficients is imposed. The original inverse source problem is\nreduced to boundary value problem for a system of coupled partial differential\nequations of the first order. The unknown source function is not a part of this\nsystem. Next, we write this system in the fully discrete form of finite\ndifferences. That discrete problem is solved via the quasi-reversibility\nmethod. We prove the existence and uniqueness of the regularized solution.\nEspecially, we prove the convergence of regularized solutions to the exact one\nas the noise level in the data tends to zero via a new discrete Carleman\nestimate. Numerical simulations demonstrate good performance of this method\neven when the data is highly noisy.\n