Numerical approximation of orthogonal maps

Alexandre Caboussat, Roland GLOWINSKI, Dimitrios Gourzoulidis, Marco Picasso

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)B1341-B1367
JournalSIAM Journal of Scientific Computing
Volume41
Issue number6
DOIs
Publication statusPublished - 2019

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Dynamical flow
  • Eikonal equation
  • Finite element methods
  • Operator splitting
  • Origami
  • Orthogonal maps

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