Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies

TL;DR

This paper develops structure-preserving finite element methods for simulating axisymmetric solid-state dewetting with anisotropic surface energies, ensuring volume conservation and energy stability.

Contribution

It introduces four novel algorithms for axisymmetric SSD that handle a wider range of anisotropy functions with proven stability and good mesh properties.

Findings

Algorithms are volume-preserving and energy-stable.

Numerical tests demonstrate high accuracy and efficiency.

Methods are applicable to various anisotropic surface energies.

Abstract

Solid-state dewetting (SSD), a widespread phenomenon in solid-solid-vapor system, could be used to describe the accumulation of solid thin films on the substrate. In this work, we consider the sharp interface model for axisymmetric SSD with anisotropic surface energy. By introducing two types of surface energy matrices from the anisotropy functions,we aim to design two structure-preserving algorithms for the axisymmetric SSD. The newly designed schemes are applicable to a broader range of anisotropy functions, and we can theoretically prove their volume conservation and energy stability. In addition, based on a novel weak formulation for the axisymmetric SSD, we further build another two numerical schemes that have good mesh properties. Finally, numerous numerical tests are reported to showcase the accuracy and efficiency of the numerical methods.