Computational Methods for Free Boundary Problems and their Applications

Wednesday, October 31, 2007 - 9:20am

TIME: 3:30 – 4:30 p.m.
PLACE: Computer Science Conference Room, Harold Frank Hall Room 1132


Free boundary problems are ubiquitous in science and engineering: They have important applications not only in the field of semi-conductor processing and in the energy industry, but in disciplines as diverse as bio-nanotechnology, tissue engineering, combustion, the modeling of tumor growth, microfluidics, computer vision, computer graphics, etc. Free boundary problems resist analytical methods and are extremely challenging for direct numerical simulations: the interface (free boundary) motion must be accurately computed as part of the solution; the interface may undergo complex changes in topology such as the merging or pinching of two fronts; partial differential equations must be solved on each side of the interface; one must account for the discontinuities in the solution or its gradients; and one must impose the correct jump conditions /at /the interface. Moreover, the multiscale nature of the problem and the limitations of computer resources demand that efficient numerical schemes on adaptive mesh refinement or/and on massively parallel machines be developed.

In this talk I will present a new paradigm for constructing general numerical methods for adaptive mesh refinement. This approach allows the design of second-order accurate numerical methods on fully adaptive grids as if the grid was uniform, hence combines efficiency and simplicity. I will also present recent advances on numerical methods for the simulation of two-phase flows with phase-change and porous media flows.


Frederic Gibou received his PhD from the Applied Mathematics Department at UCLA, and did his post-doctoral research in the Departments of Mathematics and Computer Science at Stanford University. He was awarded a NSF Mathematical Sciences Postdoctoral Fellowship and a Alfred P. Sloan Fellowship in Mathematics. Frédéric is a faculty member in the Department of Computer Science and the Department of Mechanical Engineering. He also has a courtesy appointment in the Department of Mathematics, and is a core faculty member in the Computational Science and Engineering program.