Finite difference heterogeneous multi-scale method for homogenization problems

Assyr Abdulle, E. Weinan

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


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, non-conservative form and implementation issues. Finally, the new method is illustrated with several test examples.

Original languageAmerican English
Pages (from-to)18-39
Number of pages22
JournalJournal of Computational Physics
Issue number1
StatePublished - Oct 10 2003

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Finite difference
  • Heterogeneous multi-scale method
  • Homogenization
  • Multi-scale problem


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