Sequential multiscale modeling using sparse representation

Carlos J. García-Cervera, Weiqing Ren, Jianfeng Lu, E. Weinan

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relation which often involves many independent variables. The constitutive relation of a polymeric fluid is a function of six variables, even after making the simplifying assumption that stress depends only on the rate of strain. Precomputing such a function is usually considered too expensive. Consequently the value of sequential multiscale modeling is often limited to "parameter passing". Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables. This strategy dramatically increases the efficiency of sequential multiscale modeling, making it very competitive in many situations.

Original languageEnglish (US)
Pages (from-to)1025-1033
Number of pages9
JournalCommunications in Computational Physics
Issue number5
StatePublished - Nov 2008

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


  • Multiscale modeling
  • Sparse grids


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