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

Authors:
Tao Xiong;Mengping Zhang;Yong-Tao Zhang;Chi-Wang Shu
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, P.R. China 230026;Department of Mathematics, University of Science and Technology of China, Hefei, P.R. China 230026;Department of Mathematics, University of Notre Dame, Notre Dame, USA 46556-4618;Division of Applied Mathematics, Brown University, Providence, USA 02912
Venue:
Journal of Scientific Computing
Year:
2010

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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.