HETEROGENEOUS MULTISCALE METHOD FOR LOCALLY SELF-SIMILAR PROBLEMS*

E. Weinan, Xing Y. Yue

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We present a multiscale method for a class of problems that are locally self-similar in scales and hence do not have scale separation. Our method is based on the framework of the heterogeneous multiscale method (HMM). At each point where macroscale data is needed, we perform several small scale simulations using the microscale model, then using the results and local selfsimilarity to predict the needed data at the scale of interest. We illustrate this idea by computing the effective macroscale transport of a percolation network at the percolation threshold.

Original languageEnglish (US)
Pages (from-to)137-144
Number of pages8
JournalCommunications in Mathematical Sciences
Volume2
Issue number1
DOIs
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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