The goal of this proposal is to study the development of new and efficient class of parallel guaranteed quality and three-dimensional (3D) mesh generation methods for real-time finite element computations on current and emerging parallel architectures. Specifically, we will: (1) generalize the point insertion theory for 3D guaranteed quality Delaunay mesh generation, (2) develop a parallel theoretical framework that can deploy this method with limited additional effort from sequential to multicore/multithreaded processors and eventually on clusters of multiprocessor nodes with multicore/multithreaded processors, (3) perform complexity analysis using the practical LogP model and (4) finally implement the first ever 3D parallel guaranteed quality mesh generation method using existing state-of-the-art fully functional sequential software and the parallel framework we will develop.
The intellectual merit of this proposal is to derive an entire 3D region inside the circumscribed sphere, for the selection of Steiner point insertion. The novelty of the approach is that we have the flexibility to use many new positions for point insertion of Delaunay methods rather than one or two choices were used in the past; the additional choices create more opportunities to improve size optimality along with other application-centric criteria (multiple tissues/materials). In addition, for the first time ever, we can achieve code re-use for 3D geometries. The project will have broader impact on several scientific computing and engineering communities like mesh generation and bioengineering.
