Skip to main content
SpringerLink
Log in

Data structures and mesh modification tools for unstructured multigrid adaptive techniques

  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

A complete set of data structures and mesh modification tools for effectively defining unstructured threedimensional multigrids on general curved domains is presented. The mesh adaptive procedures can be used for generating hierarchies of unstructured grids by means of uniform or local refinement and coarsening, while a local retriangulation algorithm is used for controlling the degradation of the quality of the mesh during adaptation. Intergrid transfer operators are efficiently realized ‘on the fly’ during adaptation. The data structure allows the efficient storage and handling of multiple grids, where mesh entities belonging to multiple levels can be stored just once. The capabilities and performance of the proposed procedures are exemplified by means of examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

g :

Geometric model

m r :

Mesh model at levelr

Ωv :

Domain associated with modelv (v=g,m)

∂(Ωv):

Boundary of modelv

\(\overline \Omega _\nu \) :

Closure of domain of modelv (Ωv∪∂(Ωv))

G d i j :

Topological entityi of dimensiond j in the geometric model

M d i j (p,q) :

Topological entityi of dimensiond j in the mesh model, appearing at mesh levelsp throughq

M d i j (r) :

Topological entityi in the mesh model of dimensiond j , considered at mesh levelr

ϱ(M d i j):

Boundary of topological entity

[·]:

Ordered list of entities

{·}:

Unordered list of entities

M d i j (r) {M d j}:

Unordered group of topological entities of dimensiond j that are adjacent toM d i j (r) at mesh levelr

⊂:

Classification, i.e. association of a topological entity with a model entity

References

  1. Brandt, A. (1988) Multilevel computations: review and recent developments In S.F. McCormick, editor, Multigrid Methods, Lecture Notes in Pure and Applied Mathematics 110 Marcel Dekker, New York

    Google Scholar 

  2. Mavriplis, D.J.: Jameson, A. (1987) Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes. AIAA Paper 87-0353

  3. Mavriplis, D.J. (1991) Three dimensional unstructured multigrid for the Euler equations. AIAA Paper 91-1549

  4. Parthasarathy, V.; Kallinderis, Y. (1994) New multigrid approach for three-dimensional unstructured, adaptive grids. AIAA Journal, 32, 956–963

    Google Scholar 

  5. Parthasarathy, V.; Kallinderis, Y. (1995) Directional viscous multigrid using adaptive prismatic meshes. AIAA Journal, 33, 69–78

    Google Scholar 

  6. Schroeder, W.J.; Shephard, M.S., (1991) On rigorous conditions for automatically generated finite element meshes. In J. Turner, J. Pegna and M. Wozny, editors, Product Modeling for Computer Aided Design and Manufacturing, pp. 267–281, North-Holland

  7. Beall, M.W.; Shephard, M.S. (1977) A general topology-based mesh data structure. International Journal of Numerical Methods Engineering, 40, 1573–1596

    Google Scholar 

  8. Shephard, M.S. (1988) The specification of physical attribute information for engineering analysis. Engineering with Computers. 4, 145–155

    Google Scholar 

  9. Mäntylä, M. (1988) Introduction to Solid Modeling. Computer Science Press. Rockville, MD

    Google Scholar 

  10. Shephard, M.S.; Georges, M.K. (1991) Automatic three-dimensional mesh generation by the Finite Octree Technique. International Journal of Numerical Methods in Engineering, 32, 709–749

    Google Scholar 

  11. Brandt, A. (1988) Multilevel adaptive solutions to boundary value problems. Math. Comp., 31, 333–390

    Google Scholar 

  12. De Cougny, H.L.: Shephard, M.S. (1995) Parallel mesh adaptation by local mesh modification. Scientific Report 21-95, Scientific Computation Research Center, RPI, Troy, NY

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via Lambruschini 15, 20138, Milano, Italy

    Carlo L. Bottasso

  2. Scientific Computation Research Center, Rensselaer Polytechnic Institute, NY, Troy, USA

    Ottmar Klaas & Mark S. Shephard

Authors
  1. Carlo L. Bottasso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ottmar Klaas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark S. Shephard
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bottasso, C.L., Klaas, O. & Shephard, M.S. Data structures and mesh modification tools for unstructured multigrid adaptive techniques. Engineering with Computers 14, 235–247 (1998). https://doi.org/10.1007/BF01215977

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01215977

Keywords

Search

Navigation