High frequency wave propagation has been a longstanding challenge in scientific computing. For the time-harmonic problems, integral formulations and/or efficient numerical discretization often lead to dense linear systems. Such linear systems are extremely difficult to solve for standard iterative methods since they are highly indefinite. In this talk, we consider several such examples with important applications. For each one, we construct a sparsifying preconditioner that reduces the dense linear system to a sparse one and solves the problem within a small number of iterations.

Lexing Ying received his BS at Shanghai Jiao Tong University and earned a PhD degree (2004) from New York University. In 2004-2006, he was a Postdoctoral Scholar at California Institute of Technology.  From 2006 to 2012, he was a professor at Department of Mathematics of The University of Texas at Austin. Since Dec 2012, he has been a Professor of Mathematics at Stanford University. His research focuses on developing efficient and accurate algorithms for numerical solution of partial differential equations and integral equations. He was awarded a Sloan Fellowship in 2007, an NSF CAREER ward in 2009, the Feng Kang prize of Scientific Computing from Chinese Academy of Sciences in 2011, and the SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing in 2013.