The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.