A second order discontinuous Galerkin fast sweeping method for Eikonal equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:227

Article

Li, Fengyan¹  Shu, Chi-Wang²  Zhang, Yong-Tao³  Zhao, Hongkai⁴ 

[1] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[4] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

关键词: fast sweeping methods;    discontinuous Galerkin finite element methods;    second order accuracy;    static Hamilton-Jacobi equations;    Eikonal equations;   

DOI  :  10.1016/j.jcp.2008.05.018

来源: Elsevier

【 摘 要 】

in this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method. Published by Elsevier Inc.

【 授权许可】

Free