# Acceleration of the Sn Equations with Highly Anisotropic Scattering using the Fokker-Planck Equation

## TL;DR

This paper proposes using the Fokker-Planck equation as a preconditioner to accelerate the convergence of discrete ordinates methods in highly anisotropic scattering transport problems, where traditional acceleration techniques fail.

## Contribution

It introduces a novel approach of employing the Fokker-Planck equation as a preconditioner to improve convergence in forward-peaked transport simulations.

## Key findings

- Fokker-Planck preconditioning significantly speeds up convergence.
- Standard acceleration methods are ineffective for highly anisotropic scattering.
- The approach enhances computational efficiency in forward-peaked transport modeling.

## Abstract

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration and GMRES. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. We explore the idea of using Fokker-Planck as a preconditioner to accelerate forward-peaked transport problems in this paper.