Fast smoothing of mixed volume meshes based on the effective geometric element transformation method

The geometric element transformation method (GETMe) is an efficient geometry driven approach to mesh smoothing. It is based on regularizing element transformations which, if applied iteratively to a single element, improve its regularity and with this its quality. The smoothing method has already successfully been applied in the case of mixed surface meshes as well as all-tetrahedral and all-hexahedral meshes. In this paper, a GETMe-based approach for smoothing mixed volume meshes is presented. For this purpose, dual element-based regularizing transformations for tetrahedral, hexahedral, pyramidal, and prismatic elements are introduced and analyzed. Furthermore, it is shown that the general concept of GETMe smoothing also applies to mixed volume meshes requiring only minor modifications. Numerical results demonstrate that high quality meshes comparable to those obtained by a state of the art global optimization-based approach can be achieved within significantly shorter runtimes.