<p>We present a simple numerical algorithm for generating circular porous patterns on curved surfaces. The proposed numerical algorithm solves the nonlocal Cahn–Hilliard equation on a narrow band domain using the explicit Saul’yev finite difference method (FDM) and generates the circular porous pattern formation on curved surfaces using the solved numerical solution. Surfaces are represented by the zero-level set of signed distance functions, and the narrow band domain, which includes the surface, is defined as the area within a certain distance from the surface. The proposed algorithm uses the Saul’yev FDM to overcome the severe restriction on the time step size of the fully explicit scheme, maintain the simplicity of the explicit scheme, and solve the problem. Therefore, the computational solution is stable even with relatively large time steps compared to the fully explicit scheme. Furthermore, the proposed algorithm has a simple implementation. We perform numerical experiments on simple and complex surfaces. Numerical experimental results demonstrate that circular porous pattern formation is produced appropriate and efficiently on various curved surfaces.</p>

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A simple numerical algorithm for generating circular porous pattern formation on curved surfaces

  • Youngjin Hwang,
  • Seungyoon Kang,
  • Jyoti,
  • Junseok Kim

摘要

We present a simple numerical algorithm for generating circular porous patterns on curved surfaces. The proposed numerical algorithm solves the nonlocal Cahn–Hilliard equation on a narrow band domain using the explicit Saul’yev finite difference method (FDM) and generates the circular porous pattern formation on curved surfaces using the solved numerical solution. Surfaces are represented by the zero-level set of signed distance functions, and the narrow band domain, which includes the surface, is defined as the area within a certain distance from the surface. The proposed algorithm uses the Saul’yev FDM to overcome the severe restriction on the time step size of the fully explicit scheme, maintain the simplicity of the explicit scheme, and solve the problem. Therefore, the computational solution is stable even with relatively large time steps compared to the fully explicit scheme. Furthermore, the proposed algorithm has a simple implementation. We perform numerical experiments on simple and complex surfaces. Numerical experimental results demonstrate that circular porous pattern formation is produced appropriate and efficiently on various curved surfaces.