Numerical approximation of orthogonal maps

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 (Ecole Polytechnique Fédérale de Lausanne, Switzerland) ; Picasso, Marco (Ecole Polytechnique Fédérale de Lausanne, Switzerland)

Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal maps is considered here. A variational approach is advocated for the numerical approximation of the maps. The introduction of a suitable objective function allows us to enforce the uniqueness of the solution. A strategy based on a splitting algorithm for the corresponding flow problem is presented and leads to decoupling the time-dependent problem into a sequence of local nonlinear problems and a global linear variational problem at each time step. Numerical experiments validate the accuracy and the efficiency of the method for various domains and meshes.


Keywords:
Article Type:
scientifique
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Economie/gestion
Date:
2019-12
Pagination:
27 p.
Published in:
SIAM Journal on scientific computing
Numeration (vol. no.):
2019, vol. 41, no 6, pp. B1341--B1367
DOI:
ISSN:
1064-8275
Appears in Collection:



 Record created 2020-01-16, last modified 2020-10-27

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