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Fast Sweeping Methods for Static Hamilton-Jacobi Equations

Chiu-Yen Kao, Stanley Osher and Yen-Hsi Tsai
SIAM Journal on Numerical Analysis
Vol. 42, No. 6 (2005), pp. 2612-2632
Stable URL: http://www.jstor.org/stable/4101355
Page Count: 21
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Fast Sweeping Methods for Static Hamilton-Jacobi Equations
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Abstract

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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