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

作者：Lee Hyun Geun; Kim Junseok

来源：Computer Methods in Applied Mechanics and Engineering, 2016, 307: 32-43.

DOI：10.1016/j.cma.2016.04.022

• Phase-field crystal equation
• Curved surface
• Finite difference method
• Narrow band domain
• Closest point method

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.

• 出版日期2016-8-1