Towards accurate artificial boundary conditions for nonlinear PDEs through examples

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Abstract

The aim of this paper is to give a comprehensive review of current developments related to the derivation of artificial boundary conditions for nonlinear partial differential equations. The essential tools to build such boundary conditions are based on pseudodifferential and paradifferential calculus. We present various derivations and compare them. Some numerical results illustrate their respective accuracy and analyze the potential of each technique.

Keywords

Nonlinear PDEs , wave equation , Schrödinger equation , artificial boundary conditions for nonlinear PDEs , numerical schemes
  • Xavier Antoine Institut Elie Cartan Nancy, Nancy-Université, CNRS, INRIA Corida Team, Boulevard des Aiguillettes B.P. 239 F-54506 Vandoeuvre-lès-Nancy, France.
  • Christophe Besse Projet Simpaf-Inria Futurs, Laboratoire Paul Painlevé, Unité Mixte de Recherche CNRS (UMR 8524), UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655 Villeneuve d‘Ascq Cedex, France.
  • Jérémie Szeftel Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000, USA. and CNRS, Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France.
  • Pages: 29–48
  • Date Published: 2009-09-01
  • Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

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Published

2009-09-01

How to Cite

[1]
X. Antoine, C. Besse, and J. Szeftel, “Towards accurate artificial boundary conditions for nonlinear PDEs through examples”, CUBO, vol. 11, no. 4, pp. 29–48, Sep. 2009.

Issue

Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

Section

Articles