A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

TL;DR

This paper introduces a parametric finite element method for accurately simulating solid-state dewetting of thin films with anisotropic surface energies, addressing high-order geometric PDEs with improved stability and efficiency.

Contribution

The paper presents a novel PFEM that effectively solves high-order geometric PDEs for anisotropic dewetting, outperforming traditional methods in accuracy and stability.

Findings

High accuracy in simulating anisotropic dewetting

Enhanced numerical stability for open curve evolution

Efficient computation demonstrated through extensive results

Abstract

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.