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Title: Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures
Authors: Ruiz-Girones, Eloi
Oliver, Albert 
Socorro Marrero, Guillermo Valentín 
Manuel Cascón, José
Escobar, José María 
Montenegro, Rafael 
Sarrate, Josep
UNESCO Clasification: 1206 Análisis numérico
Keywords: Meccano method
Mesh untangling and smoothing
Surface insertion
Surface parameterization
Tetrahedral mesh generation, et al
Issue Date: 2018
Journal: International Journal for Numerical Methods in Engineering 
Abstract: In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.
ISSN: 0029-5981
DOI: 10.1002/nme.5706
Source: International Journal for Numerical Methods in Engineering[ISSN 0029-5981],v. 113, p. 1488-1506
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