Computing the effective Hamiltonian using a variation AL approach

Diogo Gomes*, Adam M. Oberman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 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 languageEnglish (US)
Pages (from-to)792-812
Number of pages21
JournalSIAM Journal on Control and Optimization
Volume43
Issue number3
DOIs
StatePublished - Jun 13 2005

Keywords

  • Calculus of variations
  • Hamilton-Jacobi
  • Homogenization
  • Numerics

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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