Speaker: Fei Liu
 Beijing Computational Science Research Center    

Abstract: We present some PDEs models with spectral methods and high-order time discretization methods, including Burgers equation, Korteweg–de Vries equation, Kuramoto–Sivashinsky equation, Allen-Cahn equation and Cahn-Hilliard equation. We usually adopt the method of lines for numerically solving semilinear parabolic PDEs, apply spectral methods to discretize the spatial variables and generate a large coupled system of ordinary differential equations (ODEs) in time. Some high-order time discretization schemes are introduced, including exponential time differencing (ETD) method, semi-implicit spectral deferred correction (SISDC) method and Krylov deferred correction (KDC) method. For Allen-Cahn equation and Cahn-Hilliard equation, it is still a challenge to construct efficient high-order, unconditionally energy stable schemes which are robust with small $\varepsilon$. Stabilized semi-implicit spectral defect correction (SSISDC) methods are constructed for the time discretization of Allen-Cahn and Cahn-Hilliard equations in \cite{Liu.S12}. These methods are unconditionally stable, lead to simple linear system to solve at each iteration and can achieve high-order time accuracy with a few iterations in each time step. Ample numerical results are presented to demonstrate the effectiveness of the SSISDC methods for solving the Allen-Cahn and Cahn-Hilliard equations.

About the Speaker: Dr. Liu Fei received his Ph.D in Mathematics, Zhejiang University in 2012, and his B.S. in Mathematics from Zhejiang University in 2007. He was a joint PhD student at Purdue University from August, 2010 to February, 2012. He is a Lecturer in School of Mathematics and Statistics at Huazhong University of Science and Technology.

DateTime: August 3, 2012 (Friday), 15:30 – 16:30
Location: 606 Conference Room