Abstract
We present a simple and efficient finite difference method for the phase-field crystal (PFC) equation on curved surfaces embedded in R3. 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.
| Original language | English |
|---|---|
| Pages (from-to) | 32-43 |
| Number of pages | 12 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 307 |
| DOIs | |
| Publication status | Published - 2016 Aug 1 |
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Keywords
- Closest point method
- Curved surface
- Finite difference method
- Narrow band domain
- Phase-field crystal equation
ASJC Scopus subject areas
- Computer Science Applications
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
Cite this
A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces. / Lee, Hyun Geun; Kim, Junseok.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 307, 01.08.2016, p. 32-43.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces
AU - Lee, Hyun Geun
AU - Kim, Junseok
PY - 2016/8/1
Y1 - 2016/8/1
N2 - We present a simple and efficient finite difference method for the phase-field crystal (PFC) equation on curved surfaces embedded in R3. 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.
AB - We present a simple and efficient finite difference method for the phase-field crystal (PFC) equation on curved surfaces embedded in R3. 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.
KW - Closest point method
KW - Curved surface
KW - Finite difference method
KW - Narrow band domain
KW - Phase-field crystal equation
UR - http://www.scopus.com/inward/record.url?scp=84965066570&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84965066570&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2016.04.022
DO - 10.1016/j.cma.2016.04.022
M3 - Article
AN - SCOPUS:84965066570
VL - 307
SP - 32
EP - 43
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -