Volume 4, Issue 5
Sequential Multiscale Modeling Using Sparse Representation

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

DOI:

Commun. Comput. Phys., 4 (2008), pp. 1025-1033.

Published online: 2008-11

Preview Full PDF 126 529
Export citation
  • Abstract

The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich ofteninvolves many independentvariables. 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. 

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

  • BibTex
  • RIS
  • TXT
@Article{CiCP-4-1025, author = {Carlos J. García-Cervera, Weiqing Ren, Jianfeng Lu and Weinan E}, title = {Sequential Multiscale Modeling Using Sparse Representation}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {5}, pages = {1025--1033}, abstract = {

The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich ofteninvolves many independentvariables. 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. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7825.html} }
TY - JOUR T1 - Sequential Multiscale Modeling Using Sparse Representation AU - Carlos J. García-Cervera, Weiqing Ren, Jianfeng Lu & Weinan E JO - Communications in Computational Physics VL - 5 SP - 1025 EP - 1033 PY - 2008 DA - 2008/11 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7825.html KW - AB -

The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich ofteninvolves many independentvariables. 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. 

Carlos J. García-Cervera, Weiqing Ren, Jianfeng Lu & Weinan E. (1970). Sequential Multiscale Modeling Using Sparse Representation. Communications in Computational Physics. 4 (5). 1025-1033. doi:
Copy to clipboard
The citation has been copied to your clipboard