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Unconditionally stable methods for gradient flow using Convex Splitting Runge–Kutta scheme

Title
Unconditionally stable methods for gradient flow using Convex Splitting Runge–Kutta scheme
Authors
Shin J.Lee H.G.Lee J.-Y.
Ewha Authors
이준엽
SCOPUS Author ID
이준엽scopus
Issue Date
2017
Journal Title
Journal of Computational Physics
ISSN
0021-9991JCR Link
Citation
vol. 347, pp. 367 - 381
Keywords
Cahn–Hilliard equationConvex splittingEnergy stabilityGradient flowGradient stabilityPhase-field model
Publisher
Academic Press Inc.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We propose a Convex Splitting Runge–Kutta (CSRK) scheme which provides a simple unified framework to solve a gradient flow in an unconditionally gradient stable manner. The key feature of the scheme is a combination of a convex splitting method and a specially designed multi-stage two-additive Runge–Kutta method. Our methods are high order accurate in time and assure the gradient (energy) stability for any time step size. We provide detailed proof of the unconditional energy stability and present issues on the practical implementations. We demonstrate the accuracy and stability of the proposed methods using numerical experiments of the Cahn–Hilliard equation. © 2017 Elsevier Inc.
DOI
10.1016/j.jcp.2017.07.006
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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