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.

翻译：固态去湿（SSD）作为固-固-气系统中的普遍现象，可用于描述固体薄膜在基底上的聚集过程。本文研究具有各向异性表面能的轴对称固态去湿问题的尖锐界面模型。通过从各向异性函数引入两类表面能矩阵，我们旨在为轴对称固态去湿问题设计两种保持结构特性的算法。新设计的方案适用于更广泛的各向异性函数类别，并能从理论上证明其体积守恒性与能量稳定性。此外，基于轴对称固态去湿问题的新型弱形式表述，我们进一步构建了另外两种具有良好网格特性的数值格式。最后，通过大量数值实验验证了所提数值方法的精确性与计算效率。