Operator-splitting finite element method for solving the radiative transfer equation
File(s)
Published online version
Author(s)
Ganesan, Sashikumaar
Singh, Maneesh Kumar
Type
Journal Article
Abstract
An operator-splitting finite element scheme for the time-dependent radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite element method are used for the spatial-angular discretization of the radiative transfer equation, whereas the backward Euler scheme is used for temporal discretization. Error analysis of the proposed numerical scheme for the fully discrete radiative transfer equation is presented. The stability and convergence estimates for the fully discrete problem are derived. Moreover, an operator-splitting algorithm for the numerical simulation of high-dimensional equations is also presented. The validity of the derived estimates and implementation is illustrated with suitable numerical experiments.
Date Issued
2025-04-01
Date Acceptance
2024-05-22
Citation
Numerical Algorithms, 2025, 98 (4), pp.1725-1753
ISSN
1017-1398
Publisher
Springer
Start Page
1725
End Page
1753
Journal / Book Title
Numerical Algorithms
Volume
98
Issue
4
Copyright Statement
© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007/s11075-024-01850-8
Publication Status
Published
Date Publish Online
2024-05-29