Combined Laplacian and optimization-based smoothing for quadratic mixed surface meshes
Chen, Zhijian, Joseph R. Tristano and Wa Kwok
Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.201-213, Sept. 2003
12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.
Ansys, inc., 275 Technology Drive, Canonsburg, PA 15317, U.S.A.
Quadratic elements place stringent requirements on a surface mesh smoother. One of the
biggest challenges is that a good linear element may become invalid when mid-side nodes
are introduced. To help alleviate this problem, a new objective function for
optimization-based smoothing is proposed for triangular and quadrilateral elements,
linear or quadratic. Unlike the current popular approaches, this objective function
makes it possible for a smoothing algorithm to untangle and smooth in a single process.
This objective function has higher order continuous derivatives and only one minimum,
if any, that make it suitable for optimization techniques. Even though optimization-based
smoothing obtains much higher quality results compared to other algorithms, such as
constrained Laplacian smoothing, it is also slower than these algorithms. That said,
we also present an effective way to limit the number of calls to optimization-based
smoothing such that the highest quality mesh is obtained in the least amount of time.
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