Multiscale-FEM

This repo contains matlab code for multiscale finite element method. We implemented the multiscale finite element method proposed in Xiaohui Wu's paper. Check our final presentation. The implementation detail is in the short paper. This project got the highest score in the class of Math/CS 715 - Computational Mathematics II.

For traditional FEM, in order to capture the small scale information of periodic media with high frequency, very fine grid should be used. The size of the problem could be very large which is computational prohibitive. From the below figure, we can see if 10 X 10 grid is used, the result can not capture the fluctuation of solution. In order to capture the feature, 200 X 200 grid is used which is every expensive and has large memory foot print.

Using multiscale FEM, we can get similar results with much coarser grid. It can be seen from the below figure that multiscale FEM uses much less computing resource than traditional bilinear base FEM.