A general strategy for designing seamless multiscale methods

Weinan E, Weiqing Ren, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

69 Scopus citations

Abstract

We present a new general framework for designing multiscale methods. Compared with previous work such as Brandt's systematic up-scaling, the heterogeneous multiscale method (HMM) and the "equation-free" approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macro- and micro-models evolve simultaneously using different time steps (and therefore different clocks), and they exchange data at every step. The micro-model uses its own appropriate time step. The macro-model runs at a slower pace than required by accuracy and stability considerations for the macroscale dynamics, in order for the micro-model to relax. Examples are discussed and application to modeling complex fluids is presented.

Original languageEnglish (US)
Pages (from-to)5437-5453
Number of pages17
JournalJournal of Computational Physics
Volume228
Issue number15
DOIs
StatePublished - Aug 20 2009

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

  • Complex fluids
  • Error estimates
  • Multiscale method
  • Seamless

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