Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision
Mathematics of Computation
Several aspects of three-dimensional Delaunay triangulation
Advances in Engineering Software
Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
Efficient strategies for adaptive 3-D mesh generation over complex orography
Neural, Parallel & Scientific Computations
Algebraic Mesh Quality Metrics
SIAM Journal on Scientific Computing
Tetrahedral Mesh Generation for Environmental Problems over Complex Terrains
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
An object oriented method for tetrahedral mesh refinement
ICECT'03 Proceedings of the third international conference on Engineering computational technology
A priori mesh quality estimation via direct relation between truncation error and mesh distortion
Journal of Computational Physics
Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure
Computers and Structures
Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation
Computer Aided Geometric Design
Finite Elements in Analysis and Design
New software developments for quality mesh generation and optimization from biomedical imaging data
Computer Methods and Programs in Biomedicine
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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, Rodriguez E, Gonzalez-Yuste JM. Tetrahedral mesh generation for environmental problems over complex terrains. Lect Notes Comput Sci 2002;2329:335-44; Escobar JM, Rodriguez E, Montenegro R, Montero G, Gonzalez-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 [Gonzalez-Yuste JM, Montenegro R, Escobar JM, Montero G, Rodriguez 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.