**Speaker:** Dr. Yousef Saad, College of Science & Engineering Distinguished Professor in the Department of Computer Science & Engineering at the University of Minnesota

**Title: **

Multilevel Algebraic Preconditioning Techniques with Applications

**Abstract: **

Solving linear systems of equations with iterative methods is becoming more difficult due to a number of new challenges. Matrices of these systems are becoming larger, more ill-conditioned, and are often poorly structured, and indefinite. Multilevel methods have been advocated for handling some of these challenges. This talk will introduce a variety of multilevel preconditioners for solving linear systems of equations, with an emphasis on indefinite systems. We begin with the Algebraic Recursive Multilevel Solver (ARMS) and see how a class of "coarsening" schemes can be adapted to this framework.

ILU-type preconditioners have difficulties for some types of indefinite problems. We will show how they can be adapted for problems arising from Helmholtz equations. Then a new class of methods based on low-rank approximations which has some appealing features will be introduced. The methods handle indefiniteness quite well and are more amenable to SIMD computations, which makes them attractive for GPUs. We will then present an application in dynamic mean field theory (DMFT) where the problem is to compute the diagonal of the inverse of a matrix.

**Bio:**

Yousef Saad is a College of Science & Engineering Distinguished Professor in the Department of Computer Science & Engineering at the University of Minnesota. He holds the William Norris Chair for Large-Scale Computing and is a fellow of SIAM and AAAS. He is known for his contributions to matrix computations, including iterative methods for solving large sparse linear algebraic systems, eigenvalue problems, and parallel computing. Dr. Saad is an ISI highly cited researcher in mathematics and is the author of the highly cited book, Iterative Methods for Sparse Linear Systems. For more information, please visit http://www-users.cs.umn.edu/~saad

Host: Edmond Chow; echow [at] cc [dot] gatech [dot] edu