Updating meshes on deforming domains

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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 [3], mesh deformation [4, 5], and mesh optimization [5].

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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.

updating meshes on deforming domains-63

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.

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