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.


Keywords:
Article Type:
scientifique
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Economie/gestion
Date:
2018-10
Pagination:
26 p.
Published in:
Journal of scientific computing
Numeration (vol. no.):
2018, vol. 77, no. 1, pp. 53-78
DOI:
ISSN:
0885-7474
Appears in Collection:



 Record created 2018-05-28, last modified 2019-04-11

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