Where: Building 110, Room N.103
when: Oct. 31st 2019, Thursday, 16:00--17:15

Speaker: Hyea Hyun Kim, Kyung Hee University

Title: A two-level overlapping Schwarzpreconditioner utilizing multiscale finite element basis as a coarse basis

A two-level overlapping Schwarzpreconditioner is developed for second order elliptic problems with random and high contrast coefficients. The standard coarse problem in the two-level preconditioner often fails for such model problems and the coarse problem can be enriched by eigenvectors selected from well-designed eigenvalue problems  in each subdomain. In my talk, new coarse basis functions are formed by using the idea in a recent work on energy minimizing multiscale finite element methods where the selected eigenvectors are postprocessed to produce the coarse basis functions with a better orthogonality property. The proposed basis is shown to give a more robust two-level preconditioner than those in other previous approaches. Numerical results are included and they show the robustness of the new coarse basis with respect to the contrast in the coefficient  and the overlapping width in the subdomain partition.