Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	孙亚兵副研究员，国防科技大学
Inviter:	王旭副研究员
Title:	Energy stability of exponential time differencing schemes for the nonlocal Cahn-Hilliard equation
Language:	Chinese
Time & Venue:	2023.02.09 19:00-20:00 腾讯会议：278-667-726
Abstract:	In this talk, we consider a class of exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard equation. We first use the Fourier collocation method to discretize the space domain, and then the ETD-based multistep and Runge-Kutta schemes are adopted for the time integration. In particular, some specific multistep and Runge-Kutta schemes up to fourth order are constructed. We rigorously establish the energy stabilities of the multistep schemes up to fourth order and the second order Runge-Kutta scheme, which show that the first order ETD and the second order Runge-Kutta schemes unconditionally decrease the original energy. We also theoretically prove the mass conservations of the proposed schemes. Several numerical experiments in two and three dimensions are carried out to test the temporal convergence rates of the schemes and to verify their mass conservations and energy stabilities. The long time simulations of coarsening dynamics are also performed to verify the power law for the energy decay.