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Friday, March 8, 2019 at 3:30pm
We present in this talk the scalar auxiliary variable (SAV) approach to deal with nonlinear terms in a large class of gradient flows. The technique is not restricted to specific forms of the nonlinear part of the free energy; it leads to linear and unconditionally energy stable second-order (or higher-order with weak stability conditions) schemes which only require solving decoupled linear equations with constant coefficients. Hence, these schemes are extremely efficient as well as accurate.
We apply the SAV approach to deal with several challenging applications which can not be easily handled by existing approaches, and present convincing numerical results to show that the new schemes are not only much more efficient and easy to implement, but also can better capture the physical properties in these models.
We shall also present a convergence and error analysis under mild assumptions on the nonlinear free energy.
Professor Jie Shen received his B.S. in Computational Mathematics from Peking University in 1982, and his Ph.D in Numerical Analysis from Universite de Paris-Sud at Orsay in 1987. Before joining the Purdue faculty in Fall 2002, he served as Professor of Mathematics at Penn State University and University of Central Florida. Since January, 2012, he serves as the Director of Center for Computational and Applied Mathematics at Purdue University.
He received the Fulbright award in 2008, the Inaugural Research Award of the College of Science at Purdue University in 2013, and is an elected Fellow of AMS. He serves on editorial boards for several leading international research journals, and has authored/coauthored over 200 peer-reviewed research articles and two books.
His main research interests are numerical analysis, spectral methods and scientific computing with applications in computational fluid dynamics and materials science.