Finite difference heterogeneous multi-scale method for homogenization problems
نویسنده
چکیده
In this paper, we propose a numerical method, the finite difference heterogeneous multi-scale method (FD-HMM), for solving multi-scale parabolic problems. Based on the framework introduced in [Commun. Math. Sci. 1 (1) 87], the numerical method relies on the use of two different schemes for the original equation, at different grid level which allows to give numerical results at a much lower cost than solving the original equations. We describe the strategy for constructing such a method, discuss generalization for cases with time dependency, random correlated coefficients, nonconservative form and implementation issues. Finally, the new method is illustrated with several test examples. 2003 Elsevier Science B.V. All rights reserved.
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