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Higher Order Energy Stable ETD Based Methods for Gradient Flows

Speaker

Xiaoming Wang, Southern University of Science and Technology

Time

2020.08.11 14:00-15:00

Venue

Online—ZOOM APP

Zoom Info

ZOOM Link

Meeting ID: 970-577-37564

Password: 971666

Abstract

Many natural and engineering problems follow gradient flow structures in the sense that systems evolve to decrease certain energy. The dynamics of most of these gradient systems are complicated and hence numerical methods are called for. There are at least two desirable features for numerical algorithms for gradient flows with long evolution process: efficient higher order in time, and long-time stability. We present a class of efficient higher-order energy stable methods for a class of gradient flows based on the exponential time differencing (ETD) method combined with multi-step methods and interpolation. As a specific example, we present a third order ETD based scheme for thin film epitaxial growth model together with numerical results establishing the convergence and stability of the scheme, and the ability of the scheme to capture long-time scaling properties of the system.