A variational framework for high-order mesh generation

M. Turner, J. Peiró, D. Moxey

Procedia Engineering, vol. 82, pp. 127-135 (2016)

@inproceedings{turner-2016b,
  title = {A variational framework for high-order mesh generation},
  author = {Turner, M. and Peir\'o, J. and Moxey, D.},
  booktitle = {Procedia Engineering},
  year = {2016},
  volume = {82},
  pages = {127-135},
  doi = {10.1016/j.proeng.2016.11.069},
  url = {http://www.sciencedirect.com/science/article/pii/S1877705816333781},
  abstract = {The generation of sufficiently high quality unstructured high-order meshes remains a significant obstacle in the adoption of high-order methods. However, there is little consensus on which approach is the most robust, fastest and produces the 'best' meshes. In this work we aim to provide a route to investigate this question, by examining popular high-order mesh generation methods in the context of an e cient variational framework for the generation of curvilinear meshes. By considering previous works in a variational form, we are able to compare their characteristics and study their robustness. Alongside a description of the theory and practical implementation details, including an e cient multi-threading parallelisation strategy, we demonstrate the e↵ectiveness of the framework, showing how it can be used for both mesh quality optimisation and untangling of invalid meshes.}
}

There is little agreement over which high-order mesh generation method is the most robust, the fastest, or produces the best meshes. This paper offers a route to answering that, recasting several popular methods in a common variational form so their characteristics can be compared and their robustness studied, with an efficient multi-threaded implementation and examples of both mesh quality optimisation and untangling.