Efficient and accurate structure preserving schemes for a class of complex nonlinear systems

Abstract

We present in this talk the scalar auxiliary variable (SAV) approach to deal with nonlinear terms in a large class of complex dissipative/conservative systems. In particular, for gradient flows driven by a free energy, it leads to linear and unconditionally energy stable second-order (extendable to higher-orders) schemes which only require solving decoupled linear equations with constant coefficients. Hence, these schemes are extremely efficient as well as accurate, which are also validated by ample numerical results.

We shall present a convergence and error analysis under mild assumptions on the nonlinear free energy, and discuss applications of the SAV approach to various complex dissipative/conservative systems.

Biography

Prof. Jie SHEN will present a talk on “Efficient and accurate structure preserving schemes for a class of complex nonlinear systems”. Prof. Shen is currently Professor of Department of Mathematics and Director of Center for Computational and Applied Mathematics in Purdue University. He got his PhD degree from Universite de Paris-Sud. His research areas include numerical analysis, spectral methods, scientific computing, computational fluid dynamics and computational materials science, etc.