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：固态脱湿（SSD）是固-固-气相系统中广泛存在的现象，可用于描述固体薄膜在基底上的聚集过程。本研究考虑具有各向异性表面能的轴对称SSD的尖锐界面模型。通过引入各向异性函数导出的两类表面能矩阵，我们旨在设计两种针对轴对称SSD的结构保持算法。新设计的方案适用于更广泛各向异性函数，并可理论证明其体积守恒性与能量稳定性。此外，基于轴对称SSD的新型弱形式，我们进一步构建了另外两种具有良好网格性质的数值方案。最后，通过大量数值测试验证了数值方法的精确性和高效性。