A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations

Authors:
Jianliang Qian;Yong-Tao Zhang;Hong-Kai Zhao
Affiliations:
Department of Mathematics and Statistics, Wichita State University, Wichita, USA 67260;Department of Mathematics, University of Notre Dame, Notre Dame, USA 46556-4618;Department of Mathematics, University of California, Irvine, USA 92697-3875
Venue:
Journal of Scientific Computing
Year:
2007

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Abstract

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.