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The Effect of Vertex Reordering on 2D LocalMesh Optimization Efficiency

Shontz, Suzanne M., and Patrick Knupp

Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.107-124, October 12-15 2008

IMR
PROCEEDINGS

17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008

Department of Computer Science and Engineering, 343J Information Sciences
and Technology Building, The Pennsylvania State University,
University Park, PA 16802
shontz@cse.psu.edu
Applied Mathematics and Applications, MS 1318, P.O. Box 5800, Sandia
National Laboratories, Albuquerque, NM 87185-1318
pknupp@sandia.gov

First Paragraph
Many applications in computational science such as heat transfer, advectiondiffusion, and fluid dynamics numerically solve partial differential equations. To numerically solve the equations, finite element, finite volume, and other PDEdiscretization methods are commonly used, along with meshes to discretize the physical domain. It is well-known that the mesh and its quality can greatly impact the accuracy of simulations, as well as solver efficiency. Mesh quality can be improved by various methods including adaptivity smoothing and swapping. In mesh smoothing, one employs vertex-movement strategies to change the coordinates of mesh vertices, leaving initial mesh connectivity intact. Mathematically rigorous methods for formulating the smoothing problem entail the use of an objective function that measures quality; included in this category are the variational methods for structured meshes, and the direct optimization methods based on mesh entities such as lengths and angles.

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