Scientific Computing
Numerical simulation of real-world phenomena provides fertile ground for building interdisciplinary relationships. The SCI Institute has a long tradition of building these relationships in a win-win fashion – a win for the theoretical and algorithmic development of numerical modeling and simulation techniques and a win for the discipline-specific science of interest. High-order and adaptive methods, uncertainty quantification, complexity analysis, and parallelization are just some of the topics being investigated by SCI faculty. These areas of computing are being applied to a wide variety of engineering applications ranging from fluid mechanics and solid mechanics to bioelectricity.
| Dynamic Particle Systems for Adaptive Sampling of Implicit Surfaces |
The generation of a set of point samples is a ubiquitous requirement in many mathematical and computational problems -- from shape statistics, to mesh generation, to visualization. Dynamic particle systems are an intuitive and controllable mechanism for producing very even distributions of points across complex implicit surfaces. Controlled by only a few constraints, these systems can robustly provide nearly-regular packings that smoothly adapt to surface features. The constraints cause particles to first stick to the zero set of an implicit function, and then to move across the surface until particles are arranged in minimal energy configurations. Adaptivity is added into the system by scaling the distance between particles, causing higher densities of particles around surface features. The end result is an adaptive, yet very regular, set of surface points. |
