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Keywords: mesh smoothing, quality measures, gradient based optimization.

Summary

A mathematically formulated, gradient based mesh smoothing technique has been investigated in this paper. For the smoothing of the mesh different quality measures have been used. Earlier studies tried to determine which quality measure may provide the best result overall [1]. However when the method is applied to the smoothing of a mesh similar problems occur as in the case of Laplacian smoothing. The paper investigates this problem in a new way.

In this study it can be concluded that even though the method presented is mathematically formulated it has similar problems as in the case of Laplacian smoothing. It seems that the optimization of a wheel shape may require a new formulation which must be robust for all kind of distorted shapes. Further investigation is also required to determine how to formulate the problem in such a way that the contradictory requirements for equilateral triangles on the sides can be handled using the optimization algorithms. For example further constraints may be applied to "drive" the optimization to keep the point inside the wheel.

As a result of this problem when the smoothing method was applied to not only an interior point but to a whole mesh it became clear, that it is not practical to use the gradient based mesh smoothing with all mesh generation algorithms. For example the Delaunay triangulation is susceptible to generate shapes which have the above problems and where the algorithm may not work.

References

1: 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

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 91 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros Paper 282 An Investigation of the Convergence of Mesh Smoothing J. Radó^1,2, F. Hartung² and P. Iványi¹ ¹Department of System and Software Technology, Pollack Mihály Faculty of Engineering, University of Pécs, Hungary ²Department of Mathematics and Computing, University of Pannonia, Veszprém, Hungary doi:10.4203/ccp.91.282 purchase the full-text of this paper Full Bibliographic Reference for this paper , "An Investigation of the Convergence of Mesh Smoothing", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 282, 2009. doi:10.4203/ccp.91.282 Keywords: mesh smoothing, quality measures, gradient based optimization. Summary A mathematically formulated, gradient based mesh smoothing technique has been investigated in this paper. For the smoothing of the mesh different quality measures have been used. Earlier studies tried to determine which quality measure may provide the best result overall [1]. However when the method is applied to the smoothing of a mesh similar problems occur as in the case of Laplacian smoothing. The paper investigates this problem in a new way. In this study it can be concluded that even though the method presented is mathematically formulated it has similar problems as in the case of Laplacian smoothing. It seems that the optimization of a wheel shape may require a new formulation which must be robust for all kind of distorted shapes. Further investigation is also required to determine how to formulate the problem in such a way that the contradictory requirements for equilateral triangles on the sides can be handled using the optimization algorithms. For example further constraints may be applied to "drive" the optimization to keep the point inside the wheel. As a result of this problem when the smoothing method was applied to not only an interior point but to a whole mesh it became clear, that it is not practical to use the gradient based mesh smoothing with all mesh generation algorithms. For example the Delaunay triangulation is susceptible to generate shapes which have the above problems and where the algorithm may not work. References 1 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 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £140 +P&P)
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