Computing the Effective Hamiltonian using a Variational Approach

Computing the Effective Hamiltonian using a Variational Approach
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使用变分方法计算有效哈密顿量

DOI：
10.1137/s0363012902417620
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发表时间：
2004
期刊：
Proceedings of the 44th IEEE Conference on Decision and Control
影响因子：
--
通讯作者：
Adam M. Oberman
Adam M. Oberman
中科院分区：
--
文献类型：
--
作者：
D. Gomes;Adam M. Oberman

文献摘要

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通过求解非线性凸优化问题，可以发现汉密尔顿 - 雅各布方程的均质化方法详细工作，包括非刻板印象的哈密顿人和哈密顿人的案例，这些案例没有解决方案。
A numerical method for homogenization of Hamilton-Jacobi equations is presented and implemented as an L∞calculus of variations problem. Solutions are found by solving a nonlinear convex optimization problem. The numerical method is shown to be convergent and error estimates are provided. Several examples are worked in detail, including the cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution.