Finite difference heterogeneous multi-scale method for homogenization problems

Assyr Abdulle, E. Weinan

Research output: Contribution to journalArticle

68 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)18-39
Number of pages22
JournalJournal of Computational Physics
Volume191
Issue number1
DOIs
StatePublished - Oct 10 2003

All Science Journal Classification (ASJC) codes

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

Keywords

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

Fingerprint Dive into the research topics of 'Finite difference heterogeneous multi-scale method for homogenization problems'. Together they form a unique fingerprint.

  • Cite this