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Journal of Scientific Computing

, Volume 29, Issue 1, pp 25–56 | Cite as

High Order Fast Sweeping Methods for Static Hamilton–Jacobi Equations

  • Yong-Tao ZhangEmail author
  • Hong-Kai ZhaoEmail author
  • Jianliang Qian
Article

Abstract

We construct high order fast sweeping numerical methods for computing viscosity solutions of static Hamilton–Jacobi equations on rectangular grids. These methods combine high order weighted essentially non-oscillatory (WENO) approximations to derivatives, monotone numerical Hamiltonians and Gauss–Seidel iterations with alternating-direction sweepings. Based on well-developed first order sweeping methods, we design a novel approach to incorporate high order approximations to derivatives into numerical Hamiltonians such that the resulting numerical schemes are formally high order accurate and inherit the fast convergence from the alternating sweeping strategy. Extensive numerical examples verify efficiency, convergence and high order accuracy of the new methods.

Keywords

fast sweeping methods WENO approximation high order accuracy static Hamilton–Jacobi equations Eikonal equations 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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