题目🏄🏽‍♀️：Stabilized Compact Exponential Time Differencing Methods for Gradient Flow Problems and Scalable Implementation

报告人🎂：鞠立力 教授（南卡罗莱纳大学）

时间：2018年1月21日14：00-15🕯：00

地点：致远楼101室

摘要:In this talk, we will present stabilized compact exponential time differencing methods (ETD) for numerical

solutions of a family of gradient flow problems, which have wide applications in materials science, fluid

dynamics and biological researches. These problems often form a special class of parabolic equations of

different orders with high nonlinearity and stiffness, thus are often very hard to solve efficiently and robustly

over large space and time scales. The proposed methods achieve efficiency, accuracy and provable energy

stability under large time stepping by combining linear operator splittings, compact discretizations of spatial

operators, exponential time integrators, multistep or Runge-Kutta approximations and fast Fourier transform.

We will also discuss the corresponding localized ETD methods based on domain decomposition, which are

highly scalable and therefore very suitable for parallel computing. Various numerical experiments are carried

out to demonstrate superior performance of the proposed methods, including extreme scale phase field

simulations of coarsening dynamics on the Sunway TaihuLight supercomputer.