A least-squares/relaxation method for the numerical solution of the three-dimensional elliptic Monge–Ampère equation

Caboussat, Alexandre (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale) ; Glowinski, Roland (University of Houston, USA ; Hong-Kong Baptist University, Kowloon Tong, Hong Kong) ; Gourzoulidis, Dimitrios (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale ; Ecole Polytechnique Fédérale de Lausanne, Switzerland)

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearities. Dedicated numerical solvers are derived for the efficient solution of the local optimization problems with cubicly nonlinear equality constraints. The approximation relies on mixed low order finite element methods with regularization techniques. The results of numerical experiments show the convergence of our relaxation method to a convex classical solution if such a solution exists; otherwise they show convergence to a generalized solution in a least-squares sense. These results show also the robustness of our methodology and its ability at handling curved boundaries and non-convex domains.


Mots-clés:
Type d'article:
scientifique
Faculté:
Economie et Services
Ecole:
HEG GE Haute école de gestion de Genève
Institut:
CRAG - Centre de Recherche Appliquée en Gestion
Classification:
Economie/gestion
Date:
2018
Pagination:
26 p.
Publié dans
Journal of scientific computing
Numérotation (vol. no.):
2018, pp. 1-26
DOI:
ISSN:
0885-7474
Le document apparaît dans:



 Notice créée le 2018-05-28, modifiée le 2018-08-19

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