On accelerated iterative schemes for anisotropic radiative transfer using residual minimization

TL;DR

This paper develops and analyzes residual minimization iterative schemes for solving anisotropic radiative transfer problems, demonstrating convergence and robustness, especially with discontinuous Galerkin discretizations, through numerical experiments.

Contribution

It introduces a residual minimization framework for anisotropic radiative transfer, proving convergence and robustness in finite-dimensional Galerkin discretizations.

Findings

Convergence of the iterative scheme is established using Hilbert space norms.

The schemes are robust with respect to finite-dimensional Galerkin projections.

Numerical experiments show effectiveness for highly anisotropic scattering problems.

Abstract

We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain algorithms that are robust with respect to finite-dimensional realizations via Galerkin projections. We investigate in particular the behavior of the iterative scheme for discontinuous Galerkin discretizations in the angular variable in combination with subspaces that are derived from related diffusion problems. The performance of the resulting schemes is investigated in numerical examples for highly anisotropic scattering problems with heterogeneous parameters.