Jacobian-Free Newton-Krylov method for multilevel NLTE radiative transfer problems

TL;DR

This paper introduces a Jacobian-Free Newton-Krylov method for multilevel NLTE radiative transfer problems, achieving faster convergence and lower residual errors compared to traditional methods, with potential applications in spectral modeling and data inversion.

Contribution

The paper develops a novel JFNK solver for multilevel NLTE radiative transfer, improving speed and accuracy over existing methods like Rybicki & Hummer (1992).

Findings

Achieves up to twice the speed of traditional methods.

Reduces residual errors in statistical equilibrium equations.

Eases incorporation of charge conservation and partial redistribution effects.

Abstract

The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependency of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the Non-Local Thermodynamical Equilibrium (NLTE) problem. In this study we have developed a Jacobian-Free Newton-Krylov method (JFNK) to solve multi-level NLTE radiative transfer problems. Using the Rybicki & Hummer (1992) method as a reference (Rybicki, G. B. & Hummer, D. G. 1992, A&A, 262, 209), our results show that our JFNK solver can achieve up to a factor two speed up when using local approximate operators / preconditioners, while also achieving a lower residual error in the statistical equilibrium equations. Another advantage of this method is that the addition of charge conservation and partial redistribution effects should be straight forward. Our method can help accelerating the calculation of the emerging spectra from numerical models and also the reconstruction of chromospheric datasets through NLTE inversions.