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A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces

Title
A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces
Authors
Lee, Hyun GeunKim, Junseok
Ewha Authors
이현근
SCOPUS Author ID
이현근scopus
Issue Date
2016
Journal Title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN
0045-7825JCR Link1879-2138JCR Link
Citation
vol. 307, pp. 32 - 43
Keywords
Phase-field crystal equationCurved surfaceFinite difference methodNarrow band domainClosest point method
Publisher
ELSEVIER SCIENCE SA
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We present a simple and efficient finite difference method for the phase-field crystal (PFC) equation on curved surfaces embedded in R-3. We employ a narrow band neighborhood of a curved surface that is defined as a zero level set of a signed distance function. The PFC equation on the surface is extended to the three-dimensional narrow band domain. By using the closest point method and applying a pseudo-Neumann boundary condition, we can use the standard seven-point discrete Laplacian operator instead of the discrete Laplace-Beltrami operator on the surface. The PFC equation on the narrow band domain is discretized using an unconditionally stable scheme and the resulting implicit discrete system of equations is solved by using the Jacobi iterative method. Computational results are presented to demonstrate the efficiency and usefulness of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.
DOI
10.1016/j.cma.2016.04.022
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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