Most modern problems in science and engineering are described on irregular geometries or free boundaries that are notoriously difficult to handle numerically. In addition, the differences in length scale and the limitation of computational resources necessitate the use of adaptive grids for their numerical approximations. I will discuss a numerical strategies based on the level-set method, sharp treatment of boundary conditions and Quad/Oc-tree cartesian grids on massively parallel architecture. I will also consider some applications from materials, fluid dynamics and biology.
Professor Gibou is a faculty member in the Department of Mechanical Engineering, in the Department of Computer Science and in the Department of Mathematics at the University of California, Santa Barbara. He currently is the Chair of the Department of Mechanical Engineering. He received his PhD from the Applied Mathematics Department at UCLA, working with Stan Osher and Russ Caflisch, and did his post-doctoral research in the Departments of Mathematics and Computer Science at Stanford University working with Ron Fedkiw. He was awarded an Alfred P. Sloan Fellowship in Mathematics, the Regent’s Junior Faculty Fellowship, and the Robert Sorgenfrey Distinguished Teaching award. Professor Gibou is on the Editorial Board of the Journal of Computational Physics. His research is at the interface between Applied Mathematics, Computer Science and Engineering Sciences. It is focused on the design of a novel paradigm for high resolution computational methods for large scale computations and their use for a variety of applications including Computational Materials Science, Computational Fluid Dynamics and Computational Biology