# Meeting Details

Title: Algebraic Multigrid Methods Based on Subgraph Matching with Applications to Anisotropic Problems Computational and Applied Mathematics Colloquium Yao Chen, Department of Mathematics, Penn State http:// We consider a linear system $Ax=b$ where $A$ is the Laplacian of a weighted graph derived from an elliptic PDE with anisotropic coefficients. We introduce a local measure $\pi_{k}$ on a set of subgraphs which is a partition of the graph corresponding to $A$. We prove that the convergence rate of a two grid method is bounded by a function of $\pi_{k}$. We then suggest a matching algorithm that optimizes the choice of subgraphs by minimizing $\pi_{k}$ locally. The algorithm has low complexity and is designed to use only the algebraic information of the matrix $A$. This algorithm is used to detect the direction of anisotropy and to setup algebraic multigrid schemes. We also present numerical results that show the effectiveness of this subgraph matching method for generic anisotropic problems.