Formal Solutions for Polarized Radiative Transfer. II. High-order Methods

TL;DR

This paper compares various high-order numerical methods for solving the polarized radiative transfer equation, highlighting their accuracy, stability, and computational efficiency to improve modeling of polarized light.

Contribution

It systematically analyzes and compares different high-order formal solvers for polarized radiative transfer, providing insights into their advantages and limitations.

Findings

High-order methods improve accuracy and allow coarser grids.

Trade-offs exist between stability, accuracy, and computational cost.

Systematic comparison guides method selection for polarized radiative transfer.

Abstract

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al. (2017), emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.