 
Summary: Sequential multiscale modeling using sparse representation
Carlos J. Garc´iaCervera,1,
Weiqing Ren,2,
Jianfeng Lu,3,
and Weinan E4, §
1
Mathematics Department, University of California, Santa Barbara, CA 93106.
2
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.
3
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544.
4
Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544.
(Dated: June 8, 2007)
The main obstacle in sequential multiscale modeling is the precomputation 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 considered too expensive. Hence the
value of sequential multiscale modeling is limited to "parameter passing". Here we demonstrate
that sparse representations can be used to drastically reduce the computational cost for precom
