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A domain splitting algorithm for parabolic problems

Ein Gebietszerlegungsalgorithmus für parabolische Probleme

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Abstract

In the parallel implementation of solution methods for parabolic problems one has to find a proper balance between the parallel efficiency of a fully explicit scheme and the need for stability and accuracy which requires some degree of implicitness. As a compromise a domain splitting scheme is proposed which is locally implicit on slightly overlapping subdomains but propagates the corresponding boundary data by a simple explicit process. The analysis of this algorithm shows that it has satisfactory stability and approximation properties and can be effectively parallelized. These theoretical results are confirmed by numerical tests on a transputer system.

Zusammenfassung

Die Implementierung von Lösungs-methoden für parabolische Probleme erfordert eine ausreichende Balance zwischen der parallelen Effizienz voll-expliziter Schemata und der Notwendigkeit von Stabilität und Genauigkeit, welche einen gewissen Grad an Implizitheit bedingt. Als ein Kompromiß wird ein Gebietszerlegungsverfahren vorgeschlagen, welches lokal implizit ist auf leicht überlappenden Teilgebieten, die lokalen Randdaten aber durch einen einfachen expliziten Prozeß fortpflanzt. Die Analyse dieses Algorithmus zeigt, daß er zufriedenstellende Stabilitäts- und Approximationseigenschaften besitzt und effektiv parallelisiert werden kann. Diese theoretischen Resultate werden bestätigt durch numerische Tests auf einem Transputer-System.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Dortmund, Vogelpothsweg 87, D-W-4600, Dortmund, Federal Republic of Germany

    H. Blum

  2. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-W-6900, Heidelberg, Federal Republic of Germany

    S. Lisky & R. Rannacher

Authors
  1. H. Blum
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  2. S. Lisky
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  3. R. Rannacher
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Blum, H., Lisky, S. & Rannacher, R. A domain splitting algorithm for parabolic problems. Computing 49, 11–23 (1992). https://doi.org/10.1007/BF02238647

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  • DOI: https://doi.org/10.1007/BF02238647

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