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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 54

Studying the Quality Measures for Finite Element Meshes with Triangular Elements

J. Radó1, F. Hartung2 and P. Iványi1

1Department of Information Technology, University of Pécs, Hungary
2Department of Mathematics and Computing, University of Pannonia, Hungary

Full Bibliographic Reference for this paper
J. Radó, F. Hartung, P. Iványi, "Studying the Quality Measures for Finite Element Meshes with Triangular Elements", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 54, 2008. doi:10.4203/ccp.89.54
Keywords: mesh smoothing, quality measures, gradient based optimization.

The smoothing of the finite element meshes can be accomplished by many algorithms [1]. The application of different algorithm may have different results. The quality of the meshes can be compared with the different quality measures. One type of the smoothing is the topological operation, when the numbers of the elements can change, for example by node insertion or removal. Other topological operations can change the edges of the elements for example when using the edge flip algorithm.

Other possibilities of the smoothing are the algorithms, which are not based on topological operations. In these cases the position of the interior node can be changed, but the number of nodes or edges is not changed. The subject of this paper is one of these non-topological methods.

To study the quality measures [1] initially an internal mesh point is considered with all attached triangles. This shape can be called a "wheel". Combining the quality measure of the triangles around the internal mesh point a mathematical surface is derived. There are several ways to derive the surface with different mathematical "combinations", for example: sum, quadratic-sum or multiplication. According to the characteristics of the surface the interior mesh node can be replaced with the maximum or minimum of the surface performing an optimization. This extremum will provide the optimum position of the internal mesh node.

The paper presents a parametric study which compares the different quality measures when they are used for the optimization of the location of the internal point of a wheel.

One of the key findings of the paper that the statistically the best results for a wheel can be obtained by the algorithm using the min/max quality measure and the production surface construction method. The second best is the method using the max/inscribed with product surface method. The Laplacian algorithm is not ranked among the best algorithms.

The algorithm has been applied to a full mesh and it can be stated that depending on the target to achieve, it is possible to improve the quality of the worst element or increase the number of ideal elements.

B.H.V. Topping, J. Muylle, P. Iványi, R. Putanowicz, B. Cheng, "Finite Element Mesh Generation", Saxe-Coburg Publications, Stirling, Scotland, 2004.

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