Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport

Houston, Paul; Hubbard, Matthew E.; Radley, Thomas J.; Sutton, Oliver J.; Widdowson, Richard S. J.

Abstract

We introduce an hp–version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost identical form to standard multigroup discrete ordinates methods, meaning that solutions can be computed efficiently with high accuracy and in parallel within existing software. This method provides a unified discretisation of the space, angle, and energy domains of the underlying integro-differential equation and naturally incorporates both local mesh and local polynomial degree variation within each of these computational domains. Moreover, general polytopic elements can be handled by the method, enabling efficient discretisations of problems posed on complicated spatial geometries. We study the stability and hp–version a priori error analysis of the proposed method, by deriving suitable hp–approximation estimates together with a novel inf-sup bound. Numerical experiments highlighting the performance of the method for both polyenergetic and monoenergetic problems are presented.

Citation

Houston, P., Hubbard, M. E., Radley, T. J., Sutton, O. J., & Widdowson, R. S. J. (2024). Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport. Journal of Scientific Computing, 100(2), Article 52. https://doi.org/10.1007/s10915-024-02569-3

• Journal Article Type: Article
• Acceptance Date: May 13, 2024
• Online Publication Date: Jul 2, 2024
• Publication Date: 2024-08
• Deposit Date: May 20, 2024
• Publicly Available Date: May 20, 2024
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 100
• Issue: 2
• Article Number: 52
• DOI: https://doi.org/10.1007/s10915-024-02569-3
• Keywords: hp-finite element methods; Discontinuous Galerkin methods; Linear Boltzmann transport problem; Polytopic meshes; Discrete ordinates methods
• Public URL: https://nottingham-repository.worktribe.com/output/35145397
• Publisher URL: https://link.springer.com/article/10.1007/s10915-024-02569-3