Summary
Summary. The vast majority of visualization algorithms for finite element (FE) simulations assume that linear constitutive relationships are used to interpolate values over an element, because the polynomial order of the FE basis functions used in practice has traditionally been low – linear or quadratic. However, higher order FE solvers, which become increasingly popular, pose a significant challenge to visualization systems as the assumptions of the visualization algorithms are violated by higher order solutions. This paper presents a method for adapting linear visualization algorithms to higher order data through a careful examination of a linear algorithm’s properties and the assumptions it makes. This method subdivides higher order finite elements into regions where these assumptions hold (κ-compatibility). Because it is arguably one of the most useful visualization tools, isosurfacing is used as an example to illustrate our methodology.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Michael Brasher and Robert Haimes. Rendering planar cuts through quadratic and cubic finite elements. In Proceedings of IEEE Visualization, pages 409–416, October 2004.
Barry Joe. Three dimensional triangulations from local transformations. SIAM Journal on Scientific and Statistical Computing, 10:718–741, 1989.
Rahul Khardekar and David Thompson. Rendering higher order finite element surfaces in hardware. In Proceedings of the first international conference on computer graphics and interactive techniques in Australasia and South East Asia, pages 211–ff, February 2003.
Gregorio Malajovich. PSS 3.0.5: Polynomial system solver, 2003. URL http://www.labma.ufrj.br:80/ gregorio
Gregorio Malajovich and Maurice Rojas. Polynomial systems and the momentum map. In Proceedings of FoCM 2000, special meeting in honor of Steve Smale’s 70th birthday, pages 251–266. World Scientific, July 2002.
M. Meyer, B. Nelson, R.M. Kirby, and R. Whitaker. Particle systems for efficient and accurate finite element subdivision. IEEE Trans. Visualization and Computer Graphics, 13, 2007.
J.-F Remacle, N. Chevaugeon, E. Marchandise, and C. Geuzaine. Efficient visualization of high-order finite elements. Intl. J. Numerical Methods in Engineering, 69:750–771, 2006.
W. J. Schroeder, F. Bertel, M. Malaterre, D. C. Thompson, P. P. Pébay, R. O’Bara, and S. Tendulkar. Framework and methods for visualizing higher-order finite elements. IEEE Trans. on Visualization and Computer Graphics, Special Issue Visualization 2005, 12(4):446–460, 2006.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pébay, P.P., Thompson, D. (2008). k-Compatible Tessellations*. In: Brewer, M.L., Marcum, D. (eds) Proceedings of the 16th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75103-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-75103-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75102-1
Online ISBN: 978-3-540-75103-8
eBook Packages: EngineeringEngineering (R0)