Abstract
A new mesh smoothing algorithm that can improve quadrilateral mesh quality is presented. Poor quality meshes can produce inaccurate finite element analysis; their improvement is important. The algorithm improves mesh quality by adjusting the position of the mesh’s internal nodes based on optimization of a torsion spring system using a Gauss-Newton-based approach. The approach obtains a reasonably optimal location of each internal node by optimizing the spring system’s objective function. The improvement offered by applying the algorithm to real meshes is also exhibited and objectively evaluated using suitable metrics.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Freitag, L.: On Combining Laplacian and Optimization-Based Mesh Smoothing Techniques. In: Proc., 6th Int’l Mesh. Roundtable, London, AMD-vol. 220, pp. 375–390 (1997)
Zhou, T., Shimada, K.: An Angle-Based Approach to Two-Dimensional Mesh Smoothing. In: Proc., 9th Int’l Mesh, Roundtable, New Orleans, pp. 373–384 (2000)
Canann, S., Stephenson, M., Blacker, T.: Optismoothing: An optimization-driven approach to mesh smoothing. Finite Elements in Analysis and Design 13, 185–190 (1993)
Li, T., Wong, S., Hon, Y., Armstrong, C., McKeag, R.: Smoothing by optimisation for a quadrilateral mesh with invalid element. Finite Elements in Analysis and Design 34, 37–60 (2000)
Amenta, N., Bern, M., Eppstein, D.: Optimal point placement for mesh smoothing. In: Proc., 8th ACM-SIAM Symp. on Disc. Alg., New Orleans, pp. 528–537 (1997)
Canann, S., Tristano, J., Staten, M.: An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes. In: Proc., 7th Int’l Mesh, Roundtable, Dearborn, Mich., pp. 479–494 (1998)
Freitag, J., Jones, M., Plassmann, P.: A Parallel Algorithm for Mesh Smoothing. SIAM J. on Scientific Computing 20, 2023–2040 (1999)
Hansbo, P.: Generalized Laplacian Smoothing of Unstructured Grids. Communications in Numerical Methods in Engineering 11, 455–464 (1995)
Field, D.: Laplacian Smoothing and Delaunay Triangulations. Comm. in Applied Numerical Methods 4, 709–712 (1988)
Xu, H.: An Optimization Approach for 2D Finite Element Mesh Smoothing, M. S. Thesis, Dept. of Comp. Sci., Univ. of Ala. in Huntsville, Huntsville (2003)
Nocedal, J., Wright, S.: Numerical Optimization. Springer, New York (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, H., Newman, T.S. (2005). 2D FE Quad Mesh Smoothing via Angle-Based Optimization. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428831_2
Download citation
DOI: https://doi.org/10.1007/11428831_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26032-5
Online ISBN: 978-3-540-32111-8
eBook Packages: Computer ScienceComputer Science (R0)