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Fast Sweeping Fifth Order WENO Scheme for Static Hamilton-Jacobi Equations with Accurate Boundary Treatment

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Abstract

A fifth order weighted essentially non-oscillatory (WENO) fast sweeping method is designed in this paper, extending the result of the third order WENO fast sweeping method in J. Sci. Comput. 29, 25–56 (2006) and utilizing the two approaches of accurate inflow boundary condition treatment in J. Comput. Math. 26, 1–11 (2008), which allows the usage of Cartesian meshes regardless of the domain boundary shape. The resulting method is tested on a variety of problems to demonstrate its good performance and CPU time efficiency when compared with lower order fast sweeping methods.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Tao Xiong & Mengping Zhang

  2. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556-4618, USA

    Yong-Tao Zhang

  3. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

Authors
  1. Tao Xiong
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  2. Mengping Zhang
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  3. Yong-Tao Zhang
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  4. Chi-Wang Shu
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Corresponding author

Correspondence to Chi-Wang Shu.

Additional information

This paper is dedicated to the memory of Professor David Gottlieb.

M. Zhang research supported by NSFC grant 10671190.

Y.-T. Zhang research supported by NSF grant DMS-0810413 and Oak Ridge Associated Universities (ORAU) Ralph E. Powe Junior Faculty Enhancement Award.

C.-W. Shu research supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-0809086.

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Xiong, T., Zhang, M., Zhang, YT. et al. Fast Sweeping Fifth Order WENO Scheme for Static Hamilton-Jacobi Equations with Accurate Boundary Treatment. J Sci Comput 45, 514–536 (2010). https://doi.org/10.1007/s10915-010-9345-6

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  • DOI: https://doi.org/10.1007/s10915-010-9345-6

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