Volume 4, Issue 5
Sequential Multiscale Modeling Using Sparse Representation

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

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

Published online: 2008-11

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  • Abstract

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.

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@Article{CiCP-4-1025, author = {}, 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 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.

}, 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 JO - Communications in Computational Physics VL - 5 SP - 1025 EP - 1033 PY - 2008 DA - 2008/11 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7825.html KW - AB -

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.

Carlos J. García-Cervera, Weiqing Ren, Jianfeng Lu & Weinan E. (2020). Sequential Multiscale Modeling Using Sparse Representation. Communications in Computational Physics. 4 (5). 1025-1033. doi:
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