Sequential Multiscale Modeling Using Sparse Representation  

作　　者：Carlos J.Garcıa-Cervera Weiqing Ren Jianfeng Lu Weinan E 

机构地区：[1]Mathematics Department,University of California,Santa Barbara,CA 93106,USA [2]Courant Institute of Mathematical Sciences,New York University,New York,NY 10012,USA [3]Program in Applied and ComputationalMathematics,Princeton University,Princeton,NJ 08544,USA [4]Department of Mathematics and PACM,Princeton University,Princeton,NJ 08544,USA

出　　处：《Communications in Computational Physics》2008年第10期1025-1033,共9页计算物理通讯（英文）

基　　金：The work of Carlos J.Garcıa-Cervera is supported in part by NSF grants DMS-0411504 and DMS-0505738;The work of Weiqing Ren is supported in part by NSF grant DMS-0604382;The work of Jianfeng Lu and Weinan E is supported in part by ONR grant N00014-01-0674,DOE grant DE-FG02-03ER25587 and NSF grant DMS-0407866.

摘　　要：The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany 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.

关 键 词：Multiscale modeling sparse grids 

分 类 号：O17[理学—数学]