Abstract: High-order methods for the numerical solution of PDEs offer many advantages including higher accuracy and lower computational cost. In order to realize the full potential of these high-order PDE solvers, they must be paired with a high-order discretization of the domain. Generation of high-order curvilinear meshes presents several challenges including: validity, numerical stability, and efficiency. In this talk, I will first survey some existing techniques for high-order curvilinear mesh generation. Then I will present our optimization-based methods for generation of second- and third-order Lagrange curvilinear triangular and tetrahedral meshes. Our methods consist of the following steps. First, for each interior mesh node, an optimization problem is solved to calculate an affine or convex combination of nodal positions that relate each interior node to its neighbors. Second, a deformation is applied to the high-order boundary nodes to move them to the true boundary. Third, the new positions of the interior nodes are calculated by solving a linear system of equations using the weights and the new boundary node positions from steps one and two, respectively. We will investigate the numerical properties of our methods and will demonstrate the performance of our methods on several examples of aerospace engineering geometries for use in CFD simulations. Finally, we will give some future directions for research in high-order mesh generation for aerospace engineering geometries. This talk represents joint work with Mike Stees, University of Kansas.
Biosketch: Suzanne Shontz is an Associate Professor of Electrical Engineering and Computer Science at the University of Kansas. She is also the Director of the Computational Bioengineering Track for the Bioengineering Graduate Program and is affiliated with the Information and Telecommunication Technology Center. Prior to joining the University of Kansas in 2014, Suzanne was on the faculty at Mississippi State and Pennsylvania State Universities. Previously, she was also a postdoc at the University of Minnesota and earned her Ph.D. from Cornell University in 2005. Suzanne’s research focuses centrally on parallel scientific computing, more specifically on the development of unstructured mesh and numerical optimization algorithms and their applications to computational medicine and aerospace engineering, among others. She has received numerous awards for her research including the prestigious NSF Presidential Early CAREER Award (i.e., NSF PECASE Award) from President Obama for her research in computational- and data-enabled science and engineering and an NSF CAREER Award for her research on parallel dynamic meshing algorithms, theory, and software for simulation-assisted medical interventions. She has chaired or co-chaired several top conferences in computational science and engineering including the 2019 SIAM Computational Science and Engineering Conference and the 2019 International Meshing Roundtable.