Dr. Lili Ju

October 24, 2016

Title: Stabilized Compact Exponential Time Differencing Methods for Gradient Flows and Scalable Implementation

Speaker: Prof. Lili Ju, Department of Mathematics, University of South Carolina.

Abstract:
In this talk, we present stabilized compact exponential time differencing (cETD) methods for numerical solutions of a family of gradient flow problems, which have wide applications in materials, fluids and biology researches. These problems 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 combine linear operator splittings, compact discretizations of spatial operators, exponential time integrators, multistep or Runge-Kutta approximations and fast Fourier transform, to produce efficient, accurate and energy stable numerical algorithms. We also develop a scalable implementation of the cETD methods based on domain decomposition and operator localization with appropriate subdomain boundary conditions, which is highly suitable for parallel computing. Various numerical experiments are carried out to demonstrate superior performance of the methods, including extreme scale phase field simulations of coarsening dynamics on the Sunway TaihuLight supercomputer.