Journal
MULTISCALE MODELING & SIMULATION
Volume 8, Issue 1, Pages 269-295Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080743019
Keywords
partial differential equations; Hamilton-Jacobi; homogenization; geodesic; metric; front propagation
Funding
- ONR [N00014-03-1-0071]
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In this work we provide a novel approach to homogenization for a class of static Hamilton-Jacobi (HJ) equations, which we call metric HJ equations. We relate the solutions of the HJ equations to the distance function in a corresponding Riemannian or Finslerian metric. The metric approach allows us to conclude that the homogenized equation also induces a metric. The advantage of the method is that we can solve just one auxiliary equation to recover the homogenized Hamiltonian H(p). This is a significant improvement over existing methods which require the solution of the cell problem (or a variational problem) for each value of p. Computational results are presented and compared with analytic results when available for piecewise constant periodic and random speed functions.
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