Curvilinear mesh generation using a variational framework. (October 2018)

• Record Type: Journal Article
• Authors: Turner, Michael; Peiró, Joaquim; Moxey, David
• Is Part Of: Computer aided design. Volume 103(2018)
• Page Start: 73
• Page End: 91
• Publication Date: 2018-10
• Subjects: High-order mesh generation -- Variational mesh generation -- Energy functional -- Numerical optimisation; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2017.10.004
• Languages: English
• ISSNs: 0010-4485

Abstract

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 formulation of the variational framework, and we highlight how such formulation 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 the proposed approach can be used for both mesh quality optimisation and untangling of invalid high-order meshes. Highlights: We present a method to generate curved meshes using a variational framework. The framework encompasses many existing high-order mesh generation techniques. We outline the mathematical and numerical techniques used in the framework. An efficient parallelisation strategy is presented to increase performance. The framework is applied to a number of two-and three-dimensional examples.