Abstract
We present a refinement algorithm for unstructured tetrahedral grids which generates possibly highly non-uniform but nevertheless consistent (closed) and stable triangulations. Therefore we first define somelocal regular and irregular refinement rules that are applied to single elements. Theglobal refinement algorithm then describes how these local rules can be combined and rearranged in order to ensure consistency as well as stability. It is given in a rather general form and includes also grid coarsening.
Zusammenfassung
Es wird ein Verfeinerungsalgorithmus für unstrukturierte Tetraeder-Gitter vorgestellt, der möglicherweise stark nicht-uniforme aber dennoch konsistente (d.h. geschlossene) und stabile Triangulierungen liefert. Dazu definieren wir zunächst einigelokale reguläre bzw. irreguläre Verfeinerungsregeln für einzelne Elemente. Derglobale Verfeinerungsalgorithmus beschreibt dann, wie diese lokalen Regeln kombiniert und umgeordnet werden können, so daß sowohl Konsistenz als auch Stabilität garantiert sind. Die Formulierung des globalen Algorithmus ist sehr allgemein gehalten und erlaubt auch Gitter-Vergröberungen.
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Bey, J. Tetrahedral grid refinement. Computing 55, 355–378 (1995). https://doi.org/10.1007/BF02238487
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DOI: https://doi.org/10.1007/BF02238487