Volume 1, Issue 4
An Efficient Online-Offline Method for Elliptic Homogenization Problems

Yufang Huang, Pingbing Ming & Siqi Song

CSIAM Trans. Appl. Math., 1 (2020), pp. 664-692.

Published online: 2020-12

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  • Abstract

We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method is analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of the accuracy.

  • Keywords

Numerical homogenization, heterogeneous multiscale method, online-offline computing, least-squares reconstruction, stability

  • AMS Subject Headings

35B27, 65N30, 74S05, 74Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-664, author = {Yufang and Huang and and 10034 and and Yufang Huang and Pingbing and Ming and and 10035 and and Pingbing Ming and Siqi and Song and and 10036 and and Siqi Song}, title = {An Efficient Online-Offline Method for Elliptic Homogenization Problems}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {4}, pages = {664--692}, abstract = {

We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method is analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of the accuracy.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0035}, url = {http://global-sci.org/intro/article_detail/csiam-am/18541.html} }
TY - JOUR T1 - An Efficient Online-Offline Method for Elliptic Homogenization Problems AU - Huang , Yufang AU - Ming , Pingbing AU - Song , Siqi JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 664 EP - 692 PY - 2020 DA - 2020/12 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0035 UR - https://global-sci.org/intro/article_detail/csiam-am/18541.html KW - Numerical homogenization, heterogeneous multiscale method, online-offline computing, least-squares reconstruction, stability AB -

We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method is analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of the accuracy.

Yufang Huang, Pingbing Ming & Siqi Song. (2020). An Efficient Online-Offline Method for Elliptic Homogenization Problems. CSIAM Transactions on Applied Mathematics. 1 (4). 664-692. doi:10.4208/csiam-am.2020-0035
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