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A Fast Sweeping Method for Static Convex Hamilton–Jacobi Equations

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We develop a fast sweeping method for static Hamilton–Jacobi equations with convex Hamiltonians. Local solvers and fast sweeping strategies apply to structured and unstructured meshes. With causality correctly enforced during sweepings numerical evidence indicates that the fast sweeping method converges in a finite number of iterations independent of mesh size. Numerical examples validate both the accuracy and the efficiency of the new method.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wichita State University, Wichita, KS, 67260, USA

    Jianliang Qian

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

    Yong-Tao Zhang

  3. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    Hong-Kai Zhao

Authors
  1. Jianliang Qian
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  2. Yong-Tao Zhang
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  3. Hong-Kai Zhao
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Correspondence to Hong-Kai Zhao.

Additional information

In memory of Xu-Dong Liu.

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Qian, J., Zhang, YT. & Zhao, HK. A Fast Sweeping Method for Static Convex Hamilton–Jacobi Equations. J Sci Comput 31, 237–271 (2007). https://doi.org/10.1007/s10915-006-9124-6

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  • DOI: https://doi.org/10.1007/s10915-006-9124-6

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