Abstract

In scientific and engineering computing, one major computational bottleneck is the solution of large scale linear algebraic systems resulted from the discretization of various partial differential equations (PDEs). These systems are still often solved by traditional methods such as Gaussian elimination (and variants) in many practical applications.  Mathematically optimal methods, such as multigrid methods, have been developed for decades but they are still not that much used in practice.  In this talk, the speaker will report some recent advances in the development of optimal iterative methods that can be applied to various practical problems in a user-friendly fashion. Starting from some basic ideas and theories on multiscale methods such as multigrid and domain decomposition methods, the speaker will give a description of a general framework known as the Fast Auxiliary Space Preconditioning (FASP) Methods and report some applications in various problems including Newtonian and non-Newtonian models, Maxwell equations, Magnetohydrodynamics and reservoir (porous media) simulations.

About the Speaker

Jinchao Xu is currently the Francis R. and Helen M. Pentz Professor of Science, Director of the Center for Computational Mathematics and Applications at Pennsylvania State University and also the Changjiang Professor in Peking University. He studies numerical methods for partial-differential equations. He is known for his basic theories (for multigrid methods and the method of subspace corrections) and algorithms (such as Bramble-Pasiack-Xu and Hiptmair-Xu preconditioners) that he developed for solving large-scale systems of equations that arise from simulating scientific and engineering problems. He is one of the most highly cited mathematicians in the world and his algorithms have been widely used in practice (one of them was ranked in 2008 by the US Department of Energy as one of the 10 breakthroughs in computational science in recent years).

Prof Xu was a plenary speaker at the International Congress for Industrial and Applied Mathematics in 2007 and also a 45-minute invited speaker at the International Congress for Mathematicians in 2010. His works were also recognized with awards such as the first Feng Kang Prize for Scientific Computing in 1995 from the Chinese Academy of Sciences, the Humboldt Award for Senior US Scientists in 2005 in Germany and the Research Award for National Outstanding Youth (Class B) in 2006 in China.

Prof Xu earned his bachelor’s degree at Xiangtan University in 1982, master’s degree at Peking University in 1984 and doctoral degree at Cornell University in 1989. He joined Pennsylvania State University in 1989 as assistant professor of mathematics, and then was promoted to associate professor in 1991, to professor in 1995, and to Distinguished Professor in 2007.

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