Mesh smoothing using the Geometric Element Transformation Method

The quasi-uniformity condition for reproducing kernel element method meshes

“…Removing this limitation may allow meshes that fail the current algorithm to, in fact, pass a less restrictive test. Nevertheless, it was shown that 16 Second refinement which now passes quasi-uniformity the current algorithm is sufficiently lenient to allow dense and highly graded meshes to meet the current RKEM quasiuniformity criteria. The definitions given are general and can be applied to any support shape, element shape or dimension.…”

“…Laplacian smoothing [4] is a popular technique, which relocates a node to the centroid of its neighboring nodes. Recent work [16] presents a method for smoothing the mesh by linearly transforming the element from its initial state to an equilateral triangle. This affects multiple nodes simultaneously and is iteratively applied while aspect ratios and/or minimum angle criteria are maintained.…”

DARSS: a hybrid mesh smoother for all hexahedral meshes

“…Application of a variational functional formulated using a local cell quality metric for mesh improvement has been demonstrated on 2D and 3D meshes in [28] while use of gradient-based smoothing has been demonstrated in [29]. A sequential geometric element transformation method (GETMe) for smoothing of triangular surface meshes has been reported in [30]. Geometric transformations are used to iteratively improve the worst element of the mesh to regular shape element and hence achieve mesh improvement.…”

Regularization of heptahedra using geometric element transformation method

“…In [11], Geometric Element Transformation Method (GETMe) is represented as a simple geometric operation. The effect of this transformation, if applied iteratively, gives asymptotical but rapid regularization of the initial element.…”

“…The effect of this transformation, if applied iteratively, gives asymptotical but rapid regularization of the initial element. The authors of [11] have also introduced the concepts of global smoothing control and gave an algorithmic description of this method. The potential of the GETMe based smoothing is also illustrated there.…”