Nonlinear Krylov Acceleration Applied to a Discrete Ordinates Formulation of the k-Eigenvalue Problem

TL;DR

This paper compares different iterative methods for solving the k-eigenvalue problem in linear Boltzmann transport, highlighting Anderson Mixing's efficiency and providing theoretical insights.

Contribution

It demonstrates that a variant of Anderson Mixing converges faster than other methods and extends theoretical understanding of Anderson Mixing for linear problems.

Findings

Anderson Mixing variant requires fewer iterations

Theoretical results for Anderson Mixing are strengthened

Empirical comparison shows Anderson Mixing's superior performance

Abstract

We compare variants of Anderson Mixing with the Jacobian-Free Newton-Krylov and Broyden methods applied to an instance of the k-eigenvalue formulation of the linear Boltzmann transport equation. We present evidence that one variant of Anderson Mixing finds solutions in the fewest number of iterations. We examine and strengthen theoretical results of Anderson Mixing applied to linear problems.