Published

Mesh smoothing schemes based on optimal Delaunay triangulations

Long Chen

13th International Meshing Roundtable, pages 109-120, Williamsburg, VA, 2004.

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Abstract:

  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.