A Simple Explicit Operator-Splitting Method for Effective Hamiltonians

Roland Glowinski, Shingyu Leung, Jianliang Qian

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
1 Downloads (Pure)

Abstract

Understanding effective Hamiltonians quantitatively is essential for the homogenization of Hamilton--Jacobi equations. We propose in this article a simple efficient operator-splitting method for computing effective Hamiltonians when the Hamiltonian is either convex or nonconvex in the gradient variable. To speed up our Lie scheme--based operator-splitting method, we further propose a cascadic initialization strategy so that the steady state of the underlying time-dependent Hamilton--Jacobi equation can be reached more rapidly. Extensive numerical examples demonstrate the efficiency and accuracy of the new algorithm.

Original languageEnglish
Pages (from-to)A484-A503
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume40
Issue number1
DOIs
Publication statusPublished - 20 Feb 2018

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Hamilton--Jacobi
  • homogenization
  • effective Hamiltonian
  • operator-splitting methods

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