The geometric element transformation method for mixed mesh smoothing

The Fractal Nature of an Approximate Prime Counting Function

“…Such transformations leading to regular polygons can for example be used in finite element mesh smoothing [13]. Furthermore, similar smoothing schemes can also be applied to volumetric meshes.…”

DARSS: a hybrid mesh smoother for all hexahedral meshes

“…Geometric transformations are used to iteratively improve the worst element of the mesh to regular shape element and hence achieve mesh improvement. In [31], this approach has been generalized to a simultaneous approach for triangular/quadrilateral mixed surface meshes in which all mesh elements are transformed simultaneously and node updates are obtained by transformed node averaging. Such regularizing transformations have been shown to exist for polygons with an arbitrary number of nodes [32,33].…”

“…Methods like Winslow smoothing [18] and geometric transformation-based smoothing [19] are limited to two-dimensional unstructured meshes. Adaption of such methods for three-dimensional meshes is not obvious.…”

“…Most often, these smoothing methods are used as a final step during mesh generation, to regulate elemental shape variations from an ideal shape. Despite flurry of activity in the field of mesh modification [9][10][11][12][13][14][15][16][17][18][19], this remains a difficult and computationally expensive problem.…”

Regularization of heptahedra using geometric element transformation method

“…The potential of the GETMe based smoothing is also illustrated there. In [13], the generalized transformation was presented and also described the enhanced GETMe-based smoothing by introducing the concepts and quality metric used for smoothing and termination control. Numerical results and a comparison to other smoothing methods, both geometrical and optimization-based were also given.…”