Formal Solutions for Polarized Radiative Transfer. I. The DELO Family

TL;DR

This paper reviews and characterizes various numerical schemes for polarized radiative transfer, focusing on the DELO family, by analyzing their accuracy, stability, and computational efficiency to clarify their advantages and limitations.

Contribution

It provides a comprehensive framework for evaluating formal solvers of polarized radiative transfer, especially the DELO family, based on key numerical properties.

Findings

DELO methods exhibit specific stability and accuracy characteristics.

A reference paradigm for formal solver comparison is established.

Insights into the computational efficiency of different schemes are provided.

Abstract

The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at facilitating the comprehension of the advantages and drawbacks of the different formal solvers, this work presents a reference paradigm for their characterization based on the concepts of order of accuracy, stability, and computational cost. Special attention is paid to understand the numerical methods belonging to the Diagonal Element Lambda Operator family, in an attempt to highlight their specificities.