An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions

H. Z. Tang, Tao TANG*, Pingwen Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)

Abstract

This paper presents an adaptive mesh redistribution (AMR) method for solving the nonlinear Hamilton-Jacobi equations and level-set equations in two- and three-dimensions. Our approach includes two key ingredients: a non-conservative second-order interpolation on the updated adaptive grids, and a class of monitor functions (or indicators) suitable for the Hamilton-Jacobi problems. The proposed adaptive mesh methods transform a uniform mesh in the logical domain to cluster grid points at the regions of the physical domain where the solution or its derivative is singular or nearly singular. Moreover, the formal second-order rate of convergence is preserved for the proposed AMR methods. Extensive numerical experiments are performed to demonstrate the efficiency and robustness of the proposed adaptive mesh algorithm.

Original languageEnglish
Pages (from-to)543-572
Number of pages30
JournalJournal of Computational Physics
Volume188
Issue number2
DOIs
Publication statusPublished - 1 Jul 2003

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Finite difference method
  • Hamilton-Jacobi equations
  • Level set equations
  • Moving adaptive grid method

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