10.5281/zenodo.5559211
https://zenodo.org/records/5559211
oai:zenodo.org:5559211
Mohammadi, Fariba
Fariba
Mohammadi
University of Kansas
Shontz, Suzanne M.
Suzanne M.
Shontz
University of Kansas
A Direct Method for Generating Quadratic Curvilinear Tetrahedral Meshes Using an Advancing Front Approach
Zenodo
2021
high-order mesh generation
advancing front
tetrahedral meshes
2021-10-09
eng
10.5281/zenodo.5559210
https://zenodo.org/communities/imr29
Creative Commons Attribution 4.0 International
Computational modeling and simulation of real-world problems, e.g., various applications in the automotive, aerospace, and biomedical industries, often involve geometric objects which are bounded by curved surfaces. The geometric modeling of such objects can be performed via high-order meshes. Such a mesh, when paired with a high-order partial differential equation (PDE) solver, can realize more accurate solution results with a decreased number of mesh elements (in comparison to a low-order mesh). There are several types of high-order mesh generation approaches, such as direct methods, a posteriori methods, and isogeometric analysis (IGA)-based spline modeling approaches. In this paper, we propose a direct, high-order, curvilinear tetrahedral mesh generation method using an advancing front technique. After generating the mesh, we apply mesh optimization to improve the quality and to take advantage of the degrees of freedom available in the initially straight-sided quadratic elements. Our method aims to generate high-quality tetrahedral mesh elements from various types of boundary representations including the cases where no computer-aided design files are available. Such a method is essential, for example, for generating meshes for various biomedical models where the boundary representation is obtained from medical images instead of CAD files. We present several numerical examples of second-order tetrahedral meshes generated using our method based on input triangular surface meshes.