Description

Scopus ID: 8871330400 – Google Scholar Nancy Hitschfeld -- dblp Nancy Hitschfeld

This project centers on the study and design of algorithms and data structures for two and half
dimensional (2 1/2 D) mesh generation and three dimensional (3D) mixed element meshes that can
be useful in several engineering applications. In particular, we are interested in two problems:
(1) 2 1/2 D triangulations for face modeling and three growth simulation, and (2) 3D mixed element
meshes appropriated for the finite volume method (cvm) useful, for example, for the simulation of
semiconductor devices.

We already count with a tool for the generation of 2 1/2 D triangulations and for 3D mixed element
meshes but the implemented algorithms still have several drawbacks in modeling complex domains,
in the moving boundary strategies, in generating elements of good quality, in fulfilling the density
requirements with as few points as possible and in performance. In particular, (a) for face modeling
we need to improve the quality of the mesh and the interpolation strategy to model large mouth
movements, (b) for tree stem deformation, we need to improve the collision detection algorithms
and to add smoothing algorithms, and (c) for the mixed element meshes useful for the cvm, we
need to generate 3D Delaunay meshes where no Voronoi point is outside the domain and to model
more complex domains than before.

We propose to improve, extend and adapt our previous tools in order to fit the requirements of the
applications mentioned above. This work involves (a) the design of more general strategies to fit
domain geometries (b) the design of more efficient and robust strategies to move boundaries (c) the
design of more efficient strategies to refine, derefine and improve elements. We plan to improve
the performance of the algorithms by designing and implementing parallel solutions on the gpgpu
(General-Purpose computation on Graphics Processing Unit) using CUDA, a non-graphics API
for NVIDIA gpus that support the development of parallel applications.

As result of this research, we expect to count with more efficient and robust tools for the generation
of both surface triangulations and mixed element meshes and to leave them as open source code
through the web. Moreover, we expect to design new parallel gpu-based algorithms for different
aspects involved in the mesh generation process. We also want to explore the application of Delaunay
tessellations for the modeling of atmospherical phenomena in cities and for analyzing the
distribution of galaxies.