A conjugate gradient method for the solution of the non-LTE line radiation transfer problem

TL;DR

This paper introduces a preconditioned bi-conjugate gradient method for solving non-LTE line radiation transfer problems, demonstrating faster convergence and effective smoothing compared to classical iterative schemes.

Contribution

It presents a novel application of the BiCG-P method for non-LTE line transfer, outperforming traditional ALI-Jacobi and GS/SOR schemes in convergence speed and smoothing ability.

Findings

BiCG-P converges faster than classical methods.

BiCG-P demonstrates effective smoothing capabilities.

Timing tests show improved efficiency of BiCG-P.

Abstract

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model, with monochromatic scattering, are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as well as their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.