A Comparison of Gradient- and Hessian-BasedOptimization Methods for Tetrahedral MeshQuality Improvement
Sastry, Shankar Prasad and Suzanne M. Shontz
Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.631-648, October 25-28 2009
18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009
Department of Computer Science and Engineering,
The Pennsylvania State University
University Park, PA 16802
Discretization methods, such as the finite element method, are commonly
used in the solution of partial differential equations (PDEs). The accuracy
of the computed solution to the PDE depends on the degree of the approximation
scheme, the number of elements in the mesh , and the quality of
the mesh [2, 3]. More specifically, it is known that as the element dihedral
angles become too large, the discretization error in the finite element solution
increases . In addition, the stability and convergence of the finite element
method is affected by poor quality elements. It is known that as the angles
become too small, the condition number of the element matrix increases .
Recent research has shown the importance of performing mesh quality improvement
before solving PDEs in order to: (1) improve the condition number
of the linear systems being solved , (2) reduce the time to solution ,
and (3) increase the solution accuracy. Therefore, mesh quality improvement
methods are often used as a post-processing step in automatic mesh generation.
In this paper, we focus on mesh smoothing methods which relocate mesh
vertices, while preserving mesh topology, in order to improve mesh quality.
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