Integrating angular and domain decomposition with space-angle discontinuous Galerkin methods in 2D radiative transfer

Abstract

A space-angle discontinuous Galerkin (saDG) method is used to solve the steady-state radiative transfer equation (RTE) for 2D problems involving absorption, emission, and scattering for a semitransparent medium. This approach discretizes both spatial and angular domains. Parallel computing is based on angular decomposition (AD), and domain decomposition (DD) techniques. The DD technique directly solves the entire domain using the MUMPS library, whereas the AD technique results in an iterative approach for scattering media. This study proposes a novel hybrid AD-DD method, combining the best aspects of both techniques. Numerical results investigate the scalability, performance, and efficiency of AD and DD techniques. It is shown that a hybrid AD-DD technique is superior to these individual techniques by taking advantage of their strengths. Numerical methods demonstrate the applicability of the method of the best combination of hybrid AD-DD to 2D scattering gray media with complex geometries or enclosures with circular and square obstacles.