Sequential Multiscale Modeling Using Sparse Representation (Communications in Computational Physics, 2008)
The main obstacle in sequential multiscale modeling is the pre-computationof the constitutive relation which often involves many independent variables. The constitutive relation of a polymeric fluid is a function of six variables, even after makingthe simplifying assumption that stress depends only on the rate of strain. Precomputing such a function is usually considered too expensive. Consequently the valueof sequential multiscale modeling is often limited to "parameter passing". Here wedemonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables. This strategy dramaticallyincreases the efficiency of sequential multiscale modeling, making it very competitivein many situations.