skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A methodology for quadrilateral finite element mesh coarsening

Abstract

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedral meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.

Authors:
 [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Brigham Young University, Provo, UT (United States)
  3. Univ. of Texas, Austin, TX (United States). Institute for Computational Engineering and Sciences (ICES)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1426953
Report Number(s):
SAND-2007-1498J
Journal ID: ISSN 0177-0667; 526842
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Engineering with Computers
Additional Journal Information:
Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 0177-0667
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Adaptivity; Quadrilateral; Coarsening; Refinement; Finite elements

Citation Formats

Staten, Matthew L., Benzley, Steven, and Scott, Michael. A methodology for quadrilateral finite element mesh coarsening. United States: N. p., 2008. Web. doi:10.1007/s00366-008-0097-y.
Staten, Matthew L., Benzley, Steven, & Scott, Michael. A methodology for quadrilateral finite element mesh coarsening. United States. doi:10.1007/s00366-008-0097-y.
Staten, Matthew L., Benzley, Steven, and Scott, Michael. Thu . "A methodology for quadrilateral finite element mesh coarsening". United States. doi:10.1007/s00366-008-0097-y. https://www.osti.gov/servlets/purl/1426953.
@article{osti_1426953,
title = {A methodology for quadrilateral finite element mesh coarsening},
author = {Staten, Matthew L. and Benzley, Steven and Scott, Michael},
abstractNote = {High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedral meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.},
doi = {10.1007/s00366-008-0097-y},
journal = {Engineering with Computers},
number = 3,
volume = 24,
place = {United States},
year = {2008},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Parallel refinement and coarsening of tetrahedral meshes
journal, November 1999


New method for graded mesh generation of all hexahedral finite elements
journal, July 2000


Automated refinement of conformal quadrilateral and hexahedral meshes
journal, March 2004

  • Tchon, Ko-Foa; Dompierre, Julien; sCamarero, Ricardo
  • International Journal for Numerical Methods in Engineering, Vol. 59, Issue 12
  • DOI: 10.1002/nme.926

Octree-Based Hexahedral mesh Generation
journal, August 2000

  • Schneiders, Robert
  • International Journal of Computational Geometry & Applications, Vol. 10, Issue 04
  • DOI: 10.1142/s021819590000022x

Octree-based hexahedral mesh generation for viscous flow simulations
conference, February 2013

  • Tchon, Ko-Foa; Hirsch, Charles; Schneiders, Robert
  • 13th Computational Fluid Dynamics Conference
  • DOI: 10.2514/6.1997-1980

Remeshing for metal forming simulations?Part II: Three-dimensional hexahedral mesh generation
journal, January 2002

  • Kwak, Dae-Young; Im, Yong-Taek
  • International Journal for Numerical Methods in Engineering, Vol. 53, Issue 11
  • DOI: 10.1002/nme.404

Local refinement of three-dimensional finite element meshes
journal, September 1997

  • Staten, M. L.; Jones, N. L.
  • Engineering with Computers, Vol. 13, Issue 3
  • DOI: 10.1007/bf01221213

Conformal Refinement and Coarsening of Unstructured Hexahedral Meshes
journal, June 2005

  • Benzley, Steven E.; Harris, Nathan J.; Scott, Michael
  • Journal of Computing and Information Science in Engineering, Vol. 5, Issue 4
  • DOI: 10.1115/1.2052848

The Whisker Weaving Algorithm: a Connectivity-Based Method for Constructing All-Hexahedral Finite Element Meshes
journal, October 1996


Tetrahedral grid refinement
journal, December 1995


A dynamic adaptation scheme for general 3-D hybrid meshes
journal, November 2005

  • Kallinderis, Yannis; Kavouklis, Christos
  • Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 48-49
  • DOI: 10.1016/j.cma.2004.11.023

The spatial twist continuum: A connectivity based method for representing all-hexahedral finite element meshes
journal, December 1997


Parallel refinement and coarsening of tetrahedral meshes
journal, November 1999


Tetrahedral grid refinement
journal, December 1995


Local refinement of three-dimensional finite element meshes
journal, September 1997

  • Staten, M. L.; Jones, N. L.
  • Engineering with Computers, Vol. 13, Issue 3
  • DOI: 10.1007/BF01221213

Octree-Based Hexahedral mesh Generation
journal, August 2000

  • Schneiders, Robert
  • International Journal of Computational Geometry & Applications, Vol. 10, Issue 04
  • DOI: 10.1142/S021819590000022X

New method for graded mesh generation of all hexahedral finite elements
journal, July 2000


The Whisker Weaving Algorithm: a Connectivity-Based Method for Constructing All-Hexahedral Finite Element Meshes
journal, October 1996


The spatial twist continuum: A connectivity based method for representing all-hexahedral finite element meshes
journal, December 1997


    Works referencing / citing this record:

    Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains
    journal, July 2009