# Meeting Details

Title: An Algebraic Multilevel Preconditioner for Anisotropic Elliptic Equations based on Subgraph Matching CCMA Luncheon Seminar Yao Chen, Penn State We present a multilevel method for the solution of algebraic systems arising from discretizations of anisotropic (not necessarily grid aligned) diffusion equation. The overall solution procedure is the Algebraic MultiLevel Iteration (AMLI) method. The coarsening phase in the proposed algorithm is based on matching along strong connections in the graph associated with the underlying stiffness matrix. To identify the strong connections, we introduce a measure based on localized estimate of the stability of the $\ell_2$-orthogonal projection on the coarse spaces. The algorithm is algebraic and does not use the underlying geometry of the finite element of finite difference mesh. In case of anisotropic diffusion, the proposed strength of connection measures correctly indicate the direction of the underlying anisotropy. We present several numerical tests to illustrate the performance of this algorithm.