An angular multigrid preconditioner for the radiation transport equation with Fokker–Planck scattering

Journal article (2019)

Authors

D. Lathouwers RST/Reactor Physics and Nuclear Materials - AS
Z. Perko RST/Reactor Physics and Nuclear Materials - AS
Research Group
RST/Reactor Physics and Nuclear Materials (AS) (TU Delft)
Copyright: © 2019 D. Lathouwers, Z. Perko
DOI: https://doi.org/10.1016/j.cam.2018.10.010
Particle transport Multigrid Discontinuous Galerkin Fokker–Planck Interior penalty Radiation transport
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Published Date

2019

Language

English

Faculty

Applied Sciences

Department

RST/Radiation, Science and Technology

Research Group

RST/Reactor Physics and Nuclear Materials

Abstract

In a previous paper (Hennink and Lathouwers, 2017) we developed a finite element discretization for the Boltzmann transport equation with forward peaked scatter modeled by the Fokker–Planck approximation. The discretization was based on the discontinuous Galerkin method in both space and angle. It was expected and found that the regular source iteration algorithm for the Boltzmann equation is not effective in solving the discretized system and becomes excessively expensive for problems with many angular degrees of freedom. The purpose of this paper is to develop a multigrid scheme as preconditioner for the above mentioned discretization. The method exploits the nested nature of the meshes and the natural prolongation/restriction between meshes by Galerkin projection. A set of test problems ranging from pure spherical diffusion to the complete Boltzmann transport problem in 3D are presented to illustrate that the method is very effective, resulting in iteration counts nearly independent of problem size even for highly non-isotropically refined angular meshes.