Abstract
In this talk the speaker will present some recent works on discretization and preconditioning techniques for coupled partial differential equations (PDE) systems such as complex fluids, fluid-structure interaction and magnetohydrodynamics that involve Stokes and/or Maxwell equations. Both conforming and discontinuous Galerkin methods will be discussed. One particular issue to be addressed is the role played by the divergence-free condition in the design of both discretization and preconditioning methods.
About the speaker
Prof Jinchao Xu received his PhD in Mathematics from Cornell University in 1989. He joined the Pennsylvania State University in 1989. He was named a Distinguished Professor of Mathematics in 2007, and is currently Francis R. and Helen M. Pentz Professor of Science. He is concurrently the Changjiang Professor at Peking University.
Prof Xu’s research specialty is numerical methods for partial differential equations that arise from modeling scientific and engineering problems. One of his major research interests is in multigrid methods for their theoretical analysis, algorithmic developments, and practical application, especially developing, designing, and analyzing fast methods for solving large-scale systems of equations. His work ranges from studying fundamental theoretical questions in numerical analysis to developing and applying numerical algorithms for practical applications. He is best known for the Bramble-Pasciak-Xu preconditioner — an algorithm that is one of the two most fundamental multigrid approaches to solve large-scale discretized partial differential equations. He is also noted for the Hiptmair-Xu preconditioner, which was featured in 2008 by the US Department of Energy as one of the top 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 an invited speaker at the International Congress for Mathematicians in 2010. He is a Fellow of the Society for Industrial and Applied Mathematics and also the inaugural class of the American Mathematical Society. He is one of the most cited mathematicians in the world identified by Thomson Reuters.
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Free and open to the public. Seating is on a first-come first-served basis.
Institute for Advanced Study
Enquiries ias@ust.hk / 2358 5912
http://ias.ust.hk
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