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

Matthew T. Calef; Erin D. Fichtl; James S. Warsa; Markus Berndt; Neil N. Carlson

doi:10.1016/j.jcp.2012.12.024

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arXiv · 1112.3568

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

Matthew T. Calef·Erin D. Fichtl·James S. Warsa·Markus Berndt·Neil N. Carlson

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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.

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Matthew T. Calef, Erin D. Fichtl, James S. Warsa, Markus Berndt, Neil N. Carlson. 2011-12-15. Nonlinear Krylov Acceleration Applied to a Discrete Ordinates Formulation of the k-Eigenvalue Problem. https://doi.org/10.1016/j.jcp.2012.12.024

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