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 - <p style="text-align: justify;">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.</p>