Curvilinear mesh generation using a variational framework

M. Turner, J. Peiró, D. Moxey

Comput. Aided Design, vol. 103, pp. 73-91 (2018)

@article{turner-2018,
  title = {Curvilinear mesh generation using a variational framework},
  author = {Turner, M. and Peir\'o, J. and Moxey, D.},
  journal = cad,
  volume = {103},
  pages = {73-91},
  year = {2018},
  doi = {10.1016/j.cad.2017.10.004},
  url = {http://www.sciencedirect.com/science/article/pii/S0010448517301744},
  abstract = {We aim to tackle the challenge of generating unstructured high-order meshes of complex three-dimensional bodies, which remains a significant bottleneck in the wider adoption of high-order methods. In particular we show that by adopting a variational approach to the generation process, many of the current popular high-order generation methods can be encompassed under a single unifying framework. This allows us to compare the effectiveness of these methods and to assess the quality of the meshes they produce in a systematic fashion. We present a detailed overview of the theory and numerical implementation of the framework, and in particular we highlight how this can be effectively exploited to yield a highly-efficient parallel implementation. The effectiveness of this approach is examined by considering a number of two- and three-dimensional examples, where we show how it can be used for both mesh quality optimisation and untangling of invalid meshes.}
}

Generating unstructured high-order meshes of complex three-dimensional bodies remains one of the main obstacles to wider use of high-order methods. This paper shows that many of the popular generation methods can be written as variational problems within one framework, which allows them to be compared on the same footing, and gives the theory, an efficient parallel implementation, and examples of both mesh quality optimisation and untangling of invalid meshes.