Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 42, Issue 6, Pages 2612-2632Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036142902419600
Keywords
fast sweeping method; Godunov Hamiltonian; static Hamilton-Jacobi equation
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We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimization that is related to the Legendre transform in our sweeping scheme can either be solved analytically or numerically. We illustrate the efficiency and accuracy approach with several numerical examples in two and three dimensions.
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