Efficient and accurate structure preserving schemes for a class of complex nonlinear systems
Efficient and accurate structure preserving schemes for a class of complex nonlinear systems
Instructors/Speakers Prof. Jie SHEN Professor of Department of Mathematics and Director of Center for Computational and Applied Mathematics Purdue University U.S.A. 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 ...