A penalty-regularization-operator splitting method for the numerical solution of a scalar Eikonal equation

Caboussat, Alexandre ( Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale) ; Glowinski, Roland ( University of Houston, Texas, USA)

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.


Keywords:
Article Type:
scientifique
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Economie/gestion
Date:
2015
Pagination:
30 p.
Published in:
Chinese Annals of Mathematics, Series B
Numeration (vol. no.):
2015, vol. 36, no. 5, pp. 659-688
DOI:
ISSN:
1860-6261
Appears in Collection:

Note: The status of this file is: restricted


 Record created 2015-08-20, last modified 2019-04-11

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