An Operator-Splitting Finite Element Method for the Numerical Solution of Radiative Transfer Equation

TL;DR

This paper introduces an operator-splitting finite element method combining streamline upwind Petrov-Galerkin and discontinuous Galerkin techniques with backward Euler time discretization for solving high-dimensional radiative transfer equations, including error analysis and numerical validation.

Contribution

It presents a novel operator-splitting finite element scheme with stability and convergence analysis for high-dimensional radiative transfer equations.

Findings

Error estimates for the fully discrete scheme

Demonstrated stability and convergence through numerical experiments

Validated the effectiveness of the operator-splitting approach

Abstract

An operator-splitting finite element scheme for the time-dependent, high-dimensional 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 implicit 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 numerical simulation of high-dimensional equations is also presented. The validation of the derived estimates and implementation is demonstrated with appropriate numerical experiments.