ABSTRACT
In the previous chapter, regularizing element transformations for polygonal and polyhedral elements have been considered. If applied iteratively, these transformations convert arbitrary single elements into their regular counterparts. Such transformations will now be used for defining a framework of smoothing method variants, providing a purely geometric approach to high-quality mesh smoothing. The resulting methods, called geometric element transformation methods, abbreviated as GETMe, are highly effective and efficient, although conceptually simple. GETMe variants are introduced in the following sections, starting with a basic scheme not involving any quality aspects, thus being entirely based on geometric operations. After that, refined versions are described, which incorporate a quality criterion for improved smoothing and termination control. Such methods are of particular interest in the context of finite element mesh smoothing that requires the resulting mesh to be valid.
