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A SIMPLE EXPLICIT OPERATOR-SPLITTING METHOD FOR EFFECTIVE HAMILTONIANS
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DOI：10.1137/17M1137322.png)
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Abstract
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Understanding effective Hamiltonians quantitatively is essential for the homogenization of Hamilton-Jacobi equations. We propose in this article a simple efficient operator-splitting method for computing effective Hamiltonians when the Hamiltonian is either convex or nonconvex in the gradient variable. To speed up our Lie scheme based operator-splitting method, we further propose a cascadic initialization strategy so that the steady state of the underlying time-dependent Hamilton-Jacobi equation can be reached more rapidly. Extensive numerical examples demonstrate the efficiency and accuracy of the new algorithm.
Keywords:
Hamilton-Jacobi
homogenization
effective Hamiltonian
operator-splitting methods
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