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

PDF Version Also Available for Download.

Description

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 ... continued below

Physical Description

PDF-file: 16 pages; size: 1.7 Mbytes

Creation Information

Bailey, T S; Adams, M L; Yang, B & Zika, M R July 15, 2005.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

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.

Physical Description

PDF-file: 16 pages; size: 1.7 Mbytes

Source

  • Presented at: Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications Conference (ANS), Avignon, France, Sep 12 - Sep 15, 2005

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: UCRL-PROC-213665
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 881630
  • Archival Resource Key: ark:/67531/metadc885830

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • July 15, 2005

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

Description Last Updated

  • Nov. 30, 2016, 4:46 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 2
Total Uses: 6

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

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, article, July 15, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc885830/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.