Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations

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Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations (2003)

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by Yen-hsi Richard Tsai , Li-tien Cheng , Stanley Osher , Hong-kai Zhao

Venue:	SIAM Journal on Numerical Analysis
Citations:	135 - 20 self

BibTeX

@ARTICLE{Tsai03fastsweeping,
    author = {Yen-hsi Richard Tsai and Li-tien Cheng and Stanley Osher and Hong-kai Zhao},
    title = {Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations},
    journal = {SIAM Journal on Numerical Analysis},
    year = {2003},
    volume = {41},
    pages = {673--694}
}

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Abstract

We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = � ap 2 + bq 2 − 2cpq, c 2 < ab. We combine our Godunov numerical fluxes with simple Gauss-Seidel type iterations for solving the corresponding Hamilton-Jacobi Equations. The resulting algorithm is fast since it does not require a sorting strategy as found, e.g., in the fast marching method. In addition, it provides a way to compute solutions to a class of HJ equations for which the conventional fast marching method is not applicable. Our experiments indicate convergence after a few iterations, even in rather difficult cases. 1

Keyphrases

hamilton-jacobi equation fast sweeping algorithm difficult case simple gauss-seidel type iteration fast marching method godunov-type numerical flux corresponding hamilton-jacobi equation conventional fast marching method godunov numerical flux sorting strategy homogeneous hamiltonians hj equation

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