  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.
