A Piecewise Linear Finite Element Discretization of the Diffusion Equation for Arbitrary Polyhedral Grids

Conference · Fri Jul 15 00:00:00 EDT 2005

DOI:https://doi.org/10.1016/j.jcp.2007.11.026· OSTI ID:881630

Bailey, T S; Adams, M L; Yang, B; Zika, M R

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 881630
• Report Number(s): UCRL-PROC-213665; TRN: US0602977
• Resource Relation: Journal Volume: 227; Journal Issue: 8; Conference: Presented at: Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications Conference (ANS), Avignon, France, Sep 12 - Sep 15, 2005
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
DIFFUSION EQUATIONS
RADIATIONS
REACTOR PHYSICS