A stopping criterion for higher-order sweeping schemes for static Hamilton-Jacobi equations

Susana Serna, Jianliang Qian

Research output: Contribution to journalArticleResearchpeer-review

23 Citations (Scopus)

Abstract

We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted Power ENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion. © 2010 by AMSS, Chinese Academy of Sciences.
Original languageEnglish
Pages (from-to)552-568
JournalJournal of Computational Mathematics
Volume28
Issue number4
DOIs
Publication statusPublished - 1 Jul 2010

Keywords

  • Eikonal equations
  • Fast sweeping methods
  • Gauss-Seidel iteration
  • High order accuracy
  • Static Hamilton-Jacobi equations

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