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COMPUTING THE EFFECTIVE HAMILTONIAN: A VARIATIONAL APPROACH TO HOMOGENIZATION

A numerical method to homogenization of HamiltonJacobi equations, or effective Hamiltonians, is presented and implemented as an L calculus of variations problem. Finding solutions involves solving a nonlinear 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, as well as computing new examples. The cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution are treated.