题目：Stabilized Compact Exponential Time Differencing Methods for Gradient Flow Problems and Scalable Implementation
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.
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