FASP Solvers for Large Scale Systems: From Basic Theories to Practical Applications

Abstract

[evdate 2011-04-19] IAS Distinguished Lecture.

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, Prof Xu reports 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, Prof Xu gives 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.

Prof Xu 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).

Duration: 91 min.