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Mathematical Problems in Engineering
Volume 2014, Article ID 140180, 17 pages
Research Article

Researches on the Generation of Three-Dimensional Manifold Element under FEM Mesh Cover

China Institute of Water Resources and Hydropower Research, Beijing 100038, China

Received 18 October 2013; Revised 12 March 2014; Accepted 15 April 2014; Published 7 August 2014

Academic Editor: Sarp Adali

Copyright © 2014 Li HaiFeng and Zhang Guoxing. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Three-dimensional manifold element generation and contact detection algorithm between blocks are the bottleneck for the development of three-dimensional numerical manifold method (NMM). For building mathematics cover, the technology of three-dimensional finite element mesh generation is utilized in the paper. Aiming at the characteristics of complex formation and difficult identification of three-dimensional manifold block, three-dimensional manifold cutting technology is developed. It is important to achieve the coding of mathematical cover (MC) and physical cover (PC) for NMM, which directly determines the correctness of three-dimensional manifold element generation. Based on the character that the coding of three-dimensional manifold is the same as two-dimensional field essentially, coding algorithm of PC system proposed by Dr. Shi is extended to be three-dimensional. A three-dimensional manifold cutting program 3D MC.f90 is developed in this paper, which can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh cover. Several examples are made, and results show that three-dimensional manifold block shape and the coding of manifold node and element generated by three-dimensional manifold cutting program all agree well with the definition of three-dimensional manifold element.