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Received May 11, 2022; Accepted December 22, 2022; Published February 21, 2023
Abstract. In origami theory, the problem of rigid maps consists in finding a paper folding from the two-dimensional space onto the three-dimensional space. This problem is an example of a first-order fully nonlinear equation. In this article, we present a general variational framework to solve the problem of rigid maps with Dirichlet boundary conditions. The numerical framework relies on the introduction of a regularized objective function and the penalization of the constraints.A splitting algorithm is advocated for the corresponding flow problem. The iterations sequence consists of local nonlinear problems and a global linear variational problem at each step. Numerical experiments validate the efficiency of the method for piecewise smooth exact solutions.
How to Cite this Article:
A. Caboussat, D. Gourzoulidis, Numerical approximation of rigid maps in origami theory, Commun. Optim. Theory 2023 (2023) 8.