In the finite element method, poor quality elements typically increase the condition number of the underlying stiffness matrix, thereby potentially: (1) degrading the computed solution, and (2) slowing the convergence of iterative solvers. Current mesh improvement strategies rely on node movement and edge-flipping to alleviate these problems. However, these methods cannot guarantee a lower-bound on mesh quality, especially in 3-D. In this paper we propose the concept, and use, of inverted elements to improve mesh quality and condition number. Inverted elements are standard finite elements, but with negative Jacobian. After establishing the mathematical properties of these elements we show how they can be used to dramatically improve the quality of a mesh through the use of an ‘element cover’. Further, we show that a lower-bound on the mesh quality can be easily achieved, as supported by numerical experiments and case-studies.
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ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 28–31, 2011
Washington, DC, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
978-0-7918-5479-2
PROCEEDINGS PAPER
Improving the Condition Number of Finite Element Stiffness Matrices via Inverted Elements
Josh Danczyk,
Josh Danczyk
University of Wisconsin - Madison, Madison, WI
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Krishnan Suresh
Krishnan Suresh
University of Wisconsin - Madison, Madison, WI
Search for other works by this author on:
Josh Danczyk
University of Wisconsin - Madison, Madison, WI
Krishnan Suresh
University of Wisconsin - Madison, Madison, WI
Paper No:
DETC2011-47328, pp. 31-38; 8 pages
Published Online:
June 12, 2012
Citation
Danczyk, J, & Suresh, K. "Improving the Condition Number of Finite Element Stiffness Matrices via Inverted Elements." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2: 31st Computers and Information in Engineering Conference, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 31-38. ASME. https://doi.org/10.1115/DETC2011-47328
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