A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations
AffiliationDepartment of Mathematics, University of Arizona
KeywordsFast sweeping method
Finite difference methods
Steady-state Hamilton-Jacobi equation
MetadataShow full item record
PublisherSpringer Science and Business Media LLC
CitationParkinson, C. (2021). A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations. Journal of Scientific Computing, 88(1).
JournalJournal of Scientific Computing
Rights© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractWe present a fast sweeping method for a class of Hamilton-Jacobi equations that arise from time-independent problems in optimal control theory. The basic method in two dimensions uses a four point stencil and is extremely simple to implement. We test our basic method against Eikonal equations in different norms, and then suggest a general method for rotating the grid and using additional approximations to the derivatives in different directions in order to more accurately capture characteristic flow. We display the utility of our method by applying it to relevant problems from engineering. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Note12 month embargo; published: 26 May 2021
VersionFinal accepted manuscript