Parallel energy stable solver for phase field system——some applications for PFC equation and AC/CH coupled equations
北京师范大学数学科学学院计算数学学术报告
报告题目(Title)：Parallel energy stable solver for phase field system——some applications for PFC equation and AC/CH coupled equations
报告人(Speaker)：黄记祖 （中国科学院数学与系统科学研究院）
地点(Place)：电子楼 103
时间(Time)：2020年9月28日13:30
邀请人(Inviter)：陈华杰
报告摘要
In this talk, we present numerical methods for solving phase field system, such as phase field crystal equation and the coupled Allen–Cahn/Cahn– Hilliard equations. Based on the discrete variational derivative method, a semi-implicit finite difference scheme is derived, which is proved to be unconditionally energy stable and can achieve second-order accuracy in both space and time. An adaptive time step strategy is adopted such that the time step size can be flexibly controlled based on the dynamical evolution of the problem. At each time step, a nonlinear algebraic system is constructed from the discretization of the phase field system and solved by a domain decomposition based, parallel Newton–Krylov– Schwarz method with improved boundary conditions for subdomain problems. Numerical experiments with several two and three dimensional test cases show that the proposed algorithm is second-order accurate in both space and time, energy stable with large time steps, and highly scalable to over ten thousands processor cores on the Sunway TaihuLight supercomputer.
