Journal of Applied Mathematics
Volume 2012 (2012), Article ID 109542, 13 pages
Research Article

A Novel Mesh Quality Improvement Method for Boundary Elements

Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 18 June 2012; Revised 5 September 2012; Accepted 19 September 2012

Academic Editor: Mehmet Sezer

Copyright © 2012 Hou-lin Liu et al. 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.


In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.