Skip to main content
SpringerLink
Log in

Computation of nonlinear functionals in particle methods

Berechung von nichtlinearen Funktionalen bei Partikelmethoden

  • Published:
Computing Aims and scope Submit manuscript

Abstract

We consider the numerical computation of nonlinear functionals of distribution functions approximated by point measures. Two methods are described and estimates for the speed of convergence as the number of points tends to infinity are given. Moreover, numerical results for the entropy functional are presented.

Zusammenfassung

Wir betrachten die numerische Berechung nichtlinearer Funktionale von Verteilungsfunktionen, die durch Punktmaße angenähert werden. Zwei Methoden werden beschrieben und Abschätzungen für die Konvergenzgeschwindigkeit werden angegeben. Außerdem werden numerische Resultate für das Entropiefunktional vorgestellt.

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

References

  1. Babovsky, H., Illner, R.: A convergence proof for Nanbu's simulation method for the full Boltzmann equation. SIAM J. Numer. Anal.26, 45 (1989).

    Google Scholar 

  2. Bird, G. A.: Molecular gas dynamics. Oxford: Clarendon Press 1976.

    Google Scholar 

  3. Cercignani, C.: The Boltzmann equation and its applications. Berlin, Heidelberg, New York, Tokyo: Springer 1988.

    Google Scholar 

  4. Grad, H.: On the kinetic theory of rarefied gases. CPAM2, 331 (1949).

    Google Scholar 

  5. Illner, R., Neunzert, H.: On simulation methods for the Boltzmann equation. TTSP16, 141 (1987).

    Google Scholar 

  6. Kuipers, L., Niederreiter, H.: Uniform distribution of sequences. New York: Wiley 1974.

    Google Scholar 

  7. Mott Smith, H. M.: The solutions of the Boltzmann equation for a shock wave. Phys. Rev.82, 885 (1951).

    Google Scholar 

  8. Neunzert, H., Struckmeier, J.: Boltzmann simulation by particle methods. Acta Numer. 1995 (1994).

  9. Neunzert, H., Wick, J.: Die Darstellung von Funktionen mehrerer Variabler durch Punktmengen. Berichte der KFA Jülich 996 (1973).

  10. Struckmeier, J., Pfreundt, F. J.: On the efficiency of simulation methods for the Boltzmann equation on parallel computers. Parallel Comput.19, 103 (1993).

    Google Scholar 

  11. Weyl, H.: Über die Gleichverteilung von Zahlen mod 1. Math. Ann.77 (1916).

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, D-67663, Kaiserlautern, Federal Republic of Germany

    A. Klar

Authors
  1. A. Klar
    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

Klar, A. Computation of nonlinear functionals in particle methods. Computing 55, 207–221 (1995). https://doi.org/10.1007/BF02238432

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02238432

AMS Subject Classifications

Key words

Search

Navigation