A penalty-regularization-operator splitting method for the numerical solution of a scalar Eikonal equation

Alexandre Caboussat*, Roland GLOWINSKI

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

Original languageEnglish
Pages (from-to)659-688
Number of pages30
JournalChinese Annals of Mathematics. Series B
Volume36
Issue number5
DOIs
Publication statusPublished - 8 Sep 2015

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Dynamical flow
  • Eikonal equation
  • Finite element methods
  • Minimal and maximal solutions
  • Operator splitting
  • Penalization of equality constraints
  • Regularization methods

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