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. We aim to provide a route to investigate this question, by examining popular high-order mesh generation methods in the context of an efficient 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 efficient multi-threading parallelisation strategy, we demonstrate the effectiveness of the framework, showing how it can be used for both mesh quality optimisation and untangling of invalid meshes.
Turner, M., Peiró, J., & Moxey, D. (2016). A Variational Framework for High-order Mesh Generation. In Procedia Engineering (Vol. 163, pp. 340–352). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2016.11.069