Skip to main content
Log in

Capturing expert knowledge of mesh refinement in numerical methods of impact analysis by means of genetic programming

Soft Computing Aims and scope Submit manuscript

Abstract

The mesh refinement decisions of an experienced user of high-velocity impact numerical approximation finite differences computations are discovered as a set of comprehensible rules by means of Genetic Programming. These rules that could automatically trigger adaptive mesh refinement to mimic the expert user, detect mesh cells that require refinement by evolving a formula involving cell quantities such as material densities. Various cell variable combinations are investigated in order to identify the optimal ones for indicating mesh refinement. A high-velocity impact phenomena example of a tungsten ball that strikes a steel plate illustrates this methodology.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Axelsson O, Barker VA (1984) Finite element solution of boundary value problems. Academic Press, New York

  • Brooks AN, Hughes TJR (1982) SUPG formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comp Methods Appl Mech Eng 32:199–259

    Article  MATH  MathSciNet  Google Scholar 

  • Fletcher CAJ (1988) Computational techniques for fluid dynamics. Springer Series in Computational Physics, Springer, Heidelberg

  • Gresho PM, Lee R, Sani R (1979) Don’t suppress the wiggles—they’re telling you something. In: Hughes TJR (ed) Finite elements for convection dominated flows, AMD vol 34, ASME, New York

  • Kelmanson MA, Maunder SB (1999) Modelling high-velocity impact phenomena using unstructured dynamically-adaptive Eulerian meshes. J Mech Phys Solids 47:731–762

    Article  MATH  MathSciNet  Google Scholar 

  • Koza JR (1992) Genetic Programming: on the programming of computers by means of natural selection. The MIT Press, Cambridge

  • Leonard BP (1979) Quick scheme. Comp Methods Appl Mech Eng 19:59–98

    Article  MATH  Google Scholar 

  • Mitchell AR, Fairweather G (1980) The finite difference method in partial differential equation. Wiley-Interscience, New York

    Google Scholar 

  • Morton KW (1983) Finite element methods for non-self-adjoint elliptic and hyperbolic problems: optimal approximations and recovery techniques. Numerical Analysis Report 7/83, Department of Mathematics, Reading University, UK

  • Nakazawa S (1982) Finite element analysis applied to polymer processing. PhD thesis, University of Wales, Swansea

  • Zienkiewicz OC (1977) The finite element method in engineering science, 2nd edn. McGraw-Hill, New York

  • Zienkiewicz OC, Zhu JZ (1992a) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33:1331–1363

    Article  MATH  MathSciNet  Google Scholar 

  • Zienkiewicz OC, Zhu JZ (1992b) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33:1365–1382

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge assistance from I. Cullis for acting as our expert and the assistance from S.C. Roberts and R.W. Brankin with aspects of the computations, Fortran programming, and engineering data manipulation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Howard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Howard, D., Brezulianu, A. Capturing expert knowledge of mesh refinement in numerical methods of impact analysis by means of genetic programming. Soft Comput 15, 103–110 (2011). https://doi.org/10.1007/s00500-010-0684-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-010-0684-x

Keywords

Navigation