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 strategy based on the level-set method, sharp treatment of boundary conditions, and Quad/Oc-tree cartesian grids on massively parallel architectures. I will also consider some applications from materials and fluid dynamics.
Frederic Gibou is a faculty member in the Departments of Mechanical Engineering, Computer Science, and Mathematics at the University of California, Santa Barbara. His research is at the interface between Applied Mathematics, Computer Science and Engineering Sciences. It focuses 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.
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