E. Weinan, Bjorn Engquist

Research output: Contribution to journalArticlepeer-review

874 Scopus citations


The heterogeneous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids. Both variational and dynamic problems are considered. The method relies on an efficient coupling between the macroscopic and microscopic models. In cases when the macroscopic model is not explicitly available or invalid, the microscopic solver is used to supply the necessary data for the macroscopic model. Scale separation can be exploited to considerably reduce the complexity of the microscopic solver. Besides unifying several existing multiscale methods such as the ab initio molecular dynamics [13], quasicontinuum methods [73, 69, 68] and projective methods for systems with multiscales [34, 35], HMM also provides a methodology for designing new methods for a large variety of multiscale problems. A framework is presented for the analysis of the stability and accuracy of HMM.

Original languageEnglish (US)
Pages (from-to)87-132
Number of pages46
JournalCommunications in Mathematical Sciences
Issue number1
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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