Many simulation algorithms depend on an underlying spatial discretization---a mesh that decomposes the domain into a finite set of elements that can be analyzed by a computer. The quality of the simulation is, in part, determined by the quality of the mesh. However, in the past, mesh generation and simulation were done as separate processes. Better results can be achieved by tightly integrating simulation with mesh generation and recent advices in computational topology provide the key to doing so. Computational topology allows for the analysis of the structure of data---in this case simulation variables. By understanding the structure of the simulation the mesh generation algorithms can adapt to it, providing meshes that are closely linked to the actual simulation.
Because simulation is a powerful tool for discovery throughout computational science, this research has the potential to have broad impact across all fields of science and enable new scientific breakthroughs that could have tremendous societal impact. This research will also produce open-source software, short courses, and workshops around the topic of coupling simulation and meshing. The interdisciplinary nature of this project will lead to a rich educational and research environment for graduate and undergraduate students. The project web site provides access to research results, software and educational materials (http://sealab.cs.utah.edu/SimulationMeshingTopology).