On the numerical solution of some Eikonal equations : an elliptic solver approach

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

The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential operators. Numerical experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.


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:
14 p.
Published in:
Chinese Annals of Mathematics, Series B
Numeration (vol. no.):
2015, vol. 36, no. 5, pp. 689-702
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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