Skip to main content
SpringerLink
Log in

An algorithm for adaptive mesh refinement inn dimensions

  • Published:
Computing Aims and scope Submit manuscript

Abstract

The author describes a fast algorithm for local adaptive mesh refinement inn dimensions based on simplex bisection. A ready-to-use implementation of the algorithm in C++ pseudocode is given. It is proven that the scheme satisfies all conditions one usually places on grid refinement in the context of finite-element calculations. Bisection refinement also offers an interesting additional feature over the usual, regular, refinement scheme: all linear finite-element basis functions of one generation are of disjoint support. In the way the scheme is presented here, all generated simplex meshes satisfy a ‘structural condition’ which is exploited to simplify bookkeeping of the neighbour graph. However, bisection refinement places certain restrictions on the initial, coarsest grid. For a simply connected domain, a precise and useful criterion for the applicability of the described refinement scheme is formulated and proven.

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.

Similar content being viewed by others

References

  1. Yserentant, H.: On the multi-level splitting of finite element spaces. Num. Math.49, 379–412 (1986).

    Article  MATH  Google Scholar 

  2. Bank, R. E., Dupont, T. F., Yserentant, H.: The hierarchical basis multigrid method. Num. Math.52, 427–458 (1988).

    Article  MATH  Google Scholar 

  3. Bramble, J. H., Pasciak, J. E., Xu, J.: Parallel multilevel preconditioners. Math. Comp.55, 1–22 (1990).

    Article  MATH  Google Scholar 

  4. Freudenthal, H.: Simplizialzerlegungen von beschränkter Flachheit. Ann. Math.43, 580–582 (1942).

    Article  Google Scholar 

  5. Bank, R. E., Sherman, A. H., Weiser, H.: Refinement algorithms and data structures for regular local mesh refinement. In: Scientific computing (Stepleman, R., et al., eds.), p. 3. Amsterdam: IMACS North-Holland (1983).

    Google Scholar 

  6. Rivara, M. C.: Design and data structures of fully adaptive, multigrid, finite-element software. ACM Trans. Math. Soft.10, 242–264 (1984).

    Article  MATH  Google Scholar 

  7. Bank, R. E.: PLTMG User’s Guide 6.0. Philadelphia: SIAM, 1990.

    Google Scholar 

  8. Bänsch, E.: Local mesh refinement in 2 and 3 dimensions. IMPACT Comput. Sci. Eng.3, 181–191 (1991).

    Article  MATH  Google Scholar 

  9. Mitchell, W.: Optimal multilevel iterative methods for adaptive grids. SIAM J. Sci. Stat. Comp.13, 146–167 (1992).

    Article  MATH  Google Scholar 

  10. Moore, D.: Subdividing simplices. In: Graphics gems III. (D. Kirk, ed.), pp. 250–255. Boston: Academic Press 1992.

    Google Scholar 

  11. Bornemann, F., Erdmann, B., Kornhuber, R.: Adaptive multilevel methods in three space dimensions. Int. J. Num. Meth. Eng.36, 3187–3202 (1993).

    Article  MATH  Google Scholar 

  12. Bey, J.: Tetrahedral grid refinement. Computing55, 355–378 (1995).

    Article  MATH  Google Scholar 

  13. Maubach, J. M.: Local bisection refinement forN-simplical grids generated by reflections. SIAM J. Sci. Comput.16, 210–227 (1995).

    Article  MATH  Google Scholar 

  14. Traxler, C.: MUESLEA (program written in C++) (in preparation).

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Gießen, Heinrich-Buff-Ring 16, D-35392, Gießen, Federal Republic of Germany

    C. T. Traxler

Authors
  1. C. T. Traxler
    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

Traxler, C.T. An algorithm for adaptive mesh refinement inn dimensions. Computing 59, 115–137 (1997). https://doi.org/10.1007/BF02684475

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684475

AMS Subject Classification

Key words

Search

Navigation