Computing the effective Hamiltonian using a variation AL approach

Diogo A. Gomes; Adam M. Oberman

doi:10.1137/S0363012902417620

Computing the effective Hamiltonian using a variation AL approach

Diogo A. Gomes^*, Adam M. Oberman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

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. One and two dimensional examples are worked in detail, comparing known results with the numerical ones and computing new examples. The cases of nonstrictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution are treated.

Original language	English (US)
Pages (from-to)	792-812
Number of pages	21
Journal	SIAM Journal on Control and Optimization
Volume	43
Issue number	3
DOIs	https://doi.org/10.1137/S0363012902417620
State	Published - 2005
Externally published	Yes

Keywords

Calculus of variations
Hamilton-Jacobi
Homogenization
Numerics

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/S0363012902417620

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abstract = "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. One and two dimensional examples are worked in detail, comparing known results with the numerical ones and computing new examples. The cases of nonstrictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution are treated.",

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AB - 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. One and two dimensional examples are worked in detail, comparing known results with the numerical ones and computing new examples. The cases of nonstrictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution are treated.

KW - Calculus of variations

KW - Hamilton-Jacobi

KW - Homogenization

KW - Numerics

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Computing the effective Hamiltonian using a variation AL approach

Abstract

Keywords

ASJC Scopus subject areas

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