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A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Conference:

Abstract

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 (2-dimensional) or polyhedral (3-dimensional) 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. (authors)
Authors:
Bailey, T S; Adams, M L; [1]  Yang, B; Zika, M R [2] 
  1. Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States)
  2. Lawrence Livermore National Lab., Livermore, CA (United States)
Publication Date:
Jul 01, 2005
Product Type:
Conference
Report Number:
INIS-FR-09-1046
Resource Relation:
Conference: M and C 2005: international topical meeting on mathematics and computation, supercomputing, reactor physics and nuclear and biological applications, Avignon (France), 12-15 Sep 2005; Other Information: 6 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FINITE ELEMENT METHOD; MESH GENERATION; NEUTRON DIFFUSION EQUATION; SPACE DEPENDENCE; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS
OSTI ID:
21217626
Research Organizations:
SFEN, 75 - Paris (France)
Country of Origin:
France
Language:
English
Other Identifying Numbers:
TRN: FR0802266086410
Availability:
Available from SFEN, 5 rue des Morillons, 75015 - Paris (France)
Submitting Site:
FRN
Size:
13 pages
Announcement Date:
Oct 17, 2009

Conference:

Citation Formats

Bailey, T S, Adams, M L, Yang, B, and Zika, M R. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids. France: N. p., 2005. Web.
Bailey, T S, Adams, M L, Yang, B, & Zika, M R. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids. France.
Bailey, T S, Adams, M L, Yang, B, and Zika, M R. 2005. "A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids." France.
@misc{etde_21217626,
title = {A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids}
author = {Bailey, T S, Adams, M L, Yang, B, and Zika, M R}
abstractNote = {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 (2-dimensional) or polyhedral (3-dimensional) 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. (authors)}
place = {France}
year = {2005}
month = {Jul}
}