Preconditioned Bi-Conjugate Gradient Method for Radiative Transfer in Spherical Media

TL;DR

This paper introduces the Preconditioned Bi-Conjugate Gradient method and its stabilized variant for solving radiative transfer equations in spherical media, demonstrating robustness and versatility in astrophysical applications.

Contribution

The paper presents a new iterative numerical method, Pre-BiCG, and its stabilized version, Pre-BiCG-STAB, specifically designed for radiative transfer in spherical geometries, improving solution robustness.

Findings

Pre-BiCG effectively solves complex radiative transfer problems.

The methods handle challenging astrophysical radiative transfer scenarios.

Pre-BiCG shows versatility in benchmark tests.

Abstract

A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG)method is proposed for the solution of radiative transfer equation in spherical geometry.A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of Pre-BiCG method in some benchmark tests show that the method is quite versatile, and can handle hard problems that may arise in astrophysical radiative transfer theory.