On Broyden's method for the solution of the multilevel non-LTE radiation transfer problem

TL;DR

This paper introduces a Broyden's method-based iterative scheme for solving multilevel non-LTE radiation transfer problems, demonstrating significant speed improvements over traditional methods like MALI in 1D geometries.

Contribution

The study proposes and evaluates a Broyden's method approach as a faster alternative to MALI for nonlinear radiation transfer equations.

Findings

Broyden's method is 4.5 times faster than MALI.

The method is competitive with Gauss-Seidel and Successive Over-Relaxation.

Broyden's method improves computational efficiency in 1D transfer problems.

Abstract

This study concerns the fast and accurate solution of multilevel non-LTE radiation transfer problems. We propose and evaluate an alternative iterative scheme to the classical MALI method. Our study is indeed based on the application of Broyden's method for the solution of nonlinear systems of equations. Comparative tests, in 1D plane-parallel geometry, between the popular MALI method and our alternative method are discussed. The Broyden method is typically 4.5 times faster than MALI. It makes it also fairly competitive with Gauss-Seidel and Successive Over-Relaxation methods developed after MALI.