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It is well known that mesh qualities affect both the accuracy and efficiency of partial differential equation (PDE) solutions [1, 2].
Elements with poor mesh qualities (also, inverted elements) often occur during mesh generation , mesh deformation [4, 5], and mesh optimization .
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To the greatest extent possible, the meshes should have similar element shape; however, topological changes are performed as necessary in order to improve mesh quality. The first step is to perform anisotropic finite element-based mesh warping to estimate the interior vertex positions based upon an appropriate choice of the PDE coefficients.
Mesh smoothing algorithms improve mesh qualities simply by moving vertex positions, while fixing element connectivities.
We conclude that the semi-torsional technique presented here is an improvement over existing spring-based mesh updating schemes.
A method for updating meshes in response to domain deformation is formulated within the target-matrix mesh optimization paradigm.
We propose a framework for performing anisotropic mesh deformations.
Our goal is to produce high quality meshes with no inverted elements on domains which undergo large deformations. 94(1):20–42, 2013; Kim et al., Computer and Mathematics with Applications, Submitted, November 2014) and consists of four steps.