Mesh Smoothing Schemes Based on Optimal Delaunay Triangulations
Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.109-120, September 19-22 2004
13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004
Math Department, The Pennsylvania State University, State College, PA, U.S.A.
We present several mesh smoothing schemes based on the concept of optimal Delaunay triangulations. We define the optimal
Delaunay triangulation (ODT) as the triangulation that minimizes the interpolation error among all triangulations with the same
number of vertices. ODTs aim to equidistribute the edge length under a new metric related to the Hessian matrix of the approximated
function. Therefore we define the interpolation error as the mesh quality and move each node to a new location, in its local patch,
that reduces the interpolation error. With several formulas for the interpolation error, we derive a suitable set of mesh smoothers
among which Laplacian smoothing is a special case. The computational cost of proposed new mesh smoothing schemes in the
isotropic case is as low as Laplacian smoothing while the error-based mesh quality is provably improved. Our mesh smoothing
schemes also work well in the anisotropic case.
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