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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:350

Article

Lathouwers, Danny¹  Perko, Zoltan¹ 

[1] Delft Univ Technol, Dept Radiat Sci & Technol, Mekelweg 15, NL-2629 JB Delft, Netherlands

关键词: Discontinuous Galerkin;    Fokker-Planck;    Particle transport;    Radiation transport;    Multigrid;    Interior penalty;   

DOI  :  10.1016/j.cam.2018.10.010

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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