Smoothing and local refinement techniques for improving tetrahedral mesh quality

The improvement in the mesh quality without changing its connectivity is bounded. This bound is associated with the topology of the mesh and with the constraints imposed by the boundary of the domain. To solve this problem, we propose in this work to combine the tetrahedral mesh optimisation technique introduced in [Montenegro R, Montero G, Escobar JM, Rodríguez E, González-Yuste JM. Tetrahedral mesh generation for environmental problems over complex terrains. Lect Notes Comput Sci 2002;2329:335–44; Escobar JM, Rodríguez E, Montenegro R, Montero G, González-Yuste JM. Simultaneous untangling and smoothing of tetrahedral meshes. Comput Methods Appl Mech Eng 2003;192:2775–87] with the local mesh refinement algorithm presented in [González-Yuste JM, Montenegro R, Escobar JM, Montero G, Rodríguez E. An object oriented method for tetrahedral mesh refinement. In: Proceedings of the 3rd international conference on engineering computational technology, Praga 2002;1–18]. The main idea consists in increasing the node number, and thus, the degrees of freedom, in the neighbourhood of the regions where the elements have poor quality. Then, we refine all the elements whose quality are below to a certain threshold. Once it is done, we initiate another stage of optimisation until the quality of the mesh reaches a limit.