Efficient numerical approximation of the effective hamiltonian
Martin Nolte · FreiDok plus (Universitätsbibliothek Freiburg) · 2011
The so-called effective Hamiltonian plays an important role in the homogenization of nonlinear partial differential equations. It turns out that analytical expressions for the effective Hamiltonian are only available in rare cases and its evaluations needs to be done numerically. Over the last decade, very different numerical schemes for the approximation of the effective Hamiltonian have been proposed and the objective of this thesis is a direct comparison of these schemes on a fixed set of test problems. Our main focus will be the computational cost of the schemes as well as their robustness.