A dual element based geometric element transformation method for all-hexahedral mesh smoothing

Due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements. In particular, there is a lack of geometry-based all-hexahedral smoothing methods for mesh quality improvement being easy to implement, practicable, and efficient. The recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency. By giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all-hexahedral meshes. First numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization-based approach while being significantly faster.