An Efficient Online-Offline Method for Elliptic Homogenization Problems (CSIAM Transactions on Applied Mathematics, 2020)
We present a new numerical method for solving the elliptic homogenizationproblem. The main idea is that the missing effective matrix is reconstructed by solvingthe local least-squares in an offline stage, which shall be served as the input data forthe online computation. The accuracy of the proposed method is analyzed with theaid of the refined estimates of the reconstruction operator. Two dimensional and threedimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss ofthe accuracy.