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Volume 28, Issue 4
A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations

Susana Serna & Jianliang Qian

DOI: 10.4208/jcm.1003-m0016

J. Comp. Math., 28 (2010), pp. 552-568.

Published online: 2010-08

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  • Abstract

We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted PowerENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion.

  • Keywords

Fast sweeping methods, Gauss-Seidel iteration, High order accuracy, Static Hamilton-Jacobi equations, Eikonal equations.

  • AMS Subject Headings

65N06, 65N12, 35F21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-552, author = {Susana Serna and Jianliang Qian}, title = {A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {4}, pages = {552--568}, abstract = {

We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted PowerENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m0016}, url = {http://global-sci.org/intro/article_detail/jcm/8536.html} }
TY - JOUR T1 - A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations AU - Susana Serna & Jianliang Qian JO - Journal of Computational Mathematics VL - 4 SP - 552 EP - 568 PY - 2010 DA - 2010/08 SN - 28 DO - http://doi.org/10.4208/jcm.1003-m0016 UR - https://global-sci.org/intro/article_detail/jcm/8536.html KW - Fast sweeping methods, Gauss-Seidel iteration, High order accuracy, Static Hamilton-Jacobi equations, Eikonal equations. AB -

We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted PowerENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion.

Susana Serna and Jianliang Qian. (2010). A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations. Journal of Computational Mathematics. 28 (4). 552-568. doi:10.4208/jcm.1003-m0016
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