A second order energy stable numerical scheme is presented for the two and three dimensional Cahn-Hilliard equation, with Fourier pseudo-spectral approximation in space. The convex splitting nature assures its unique solvability and unconditional energy stability. Meanwhile, the implicit treatment of the nonlinear term makes a direct nonlinear solver not available, due to the global nature of the pseudo-spectral spatial discretization. In turn, a linear iteration algorithm is proposed to overcome this difficulty, in which a Douglas-Dupont-type regularization term is introduced. As a consequence, the numerical efficiency has been greatly improved, since the highly nonlinear system can be decomposed as an iteration of purely linear solvers. Moreover, a careful nonlinear analysis shows a contraction mapping property of this linear iteration. In addition, a maximum norm bound of numerical solution is also derived at a theoretical level. A few numerical examples are also presented in this talk.

Cheng Wang received his Ph.D (under Jian-Guo Liu) at Temple University, USA, in 2000. Afterward, he spent 3 years at Indiana University as a postdoc, with Roger Temam and Shouhong Wang as his postdoc mentors. In 2003-2008, he was a tenure-track assistant professor at University of Tennessee. In 2008, he moved to University of Massachusetts dartmouth; right now he is an associate professor there. His research area is applied mathematics, including numerical analysis, partial differential equations, fluid mechanics, computational electro-magnetics, material sciences, etc; he has had over 40 peer-reviewed articles at different scientific journals.