Brief Bio

Frédéric Gibou's research is focused on the design and the applications of new high resolution multiscale computational algorithms for a variety of applications including materials science, multiphase flows at the micro/nanoscale, computer vision with an emphasis on the segmentation of medical images and computer graphics. He 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 Mechanical Engineering, the Department of Computer Science, the Department of Mathematics, and a core faculty member in the Computational Science and Engineering program.

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Awards

• Sloan Research Fellowship in Mathematics

• Regent’s Junior Faculty Fellowship

• NSF Mathematical Sciences Postdoctoral Fellowship

• The Robert Sorgenfrey Distinguished Teaching Award

Present and past support from the following agencies is gratefully acknowledged!

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Teaching

• ME 226, Level Set Methods and their Applications, Winter quarter 2007.
• ME_140A, Numerical Analysis in Engineering, Fall quarter 2006.
• CS_111, Introduction to Computational Science, Fall quarter 2006.
• Math 210C, Partial Differential Equation – Finite Difference Methods, Spring quarter 2006.
• ME 226, Level Set Methods and their Applications, Winter quarter 2006.
• CS 140, Parallel Scientific Computing, Fall quarter 2005.
• ME 140B, Theoretical Analysis in Mechanical Engineering, Spring quarter 2008.
• ME 226, Level Set Methods and their Applications, Winter quarter 2005.

NEW: I am developing an experimental interactive web-based virtual lab in Computational Science and Engineering to demonstrate the impact of Computational Mathematics. You can input your own parameter values and see their effects; a great way to learn more about the field! A demo developed by Christopher Wilson is available here.

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Students

Postdoctoral Trainees

· Dr. Chohong Min (2005-2007). Assistant Professor of Mathematics at Kyung Hee University (Korea).

Graduate Students

· Yen Ting Ng (PhD).

· Asdis Helgardottir (PhD) (co-advised with Bud Homsy).

· Ryan DePuit (PhD) (co-advised with Todd Squires).

· David Boy (PhD) (co-advised with Sumita Penathur).

· Joseph Papac (PhD) (co-advised with Eckart Meiburg).

Former Interns

· Antoine du Chéné (École Polytechnique – Paris), April-July 2006.

· Abdellah chkifa (École Polytechnique – Paris), April-July 2007.

Former Students

· Han Chen, PhD 2007. Assistant Professor of Mechanical Engineering, Huazhong University of Science and Technology.

· Liguo Chen (co-advised with Sanjoy Banerjee), MS 2005. PhD student in Mechanical Engineering.

· Antoine Du Chéné, MS 2007 and Ingénieur Polytechnicien. Analyst, Sophis Inc.

· Claire Chen (undergraduate).

· Christopher Wilson (undergraduate).

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Research

My research is focused on the design of multiscale computational algorithms for a variety of applications including materials science, computer vision with an emphasis on the segmentation of medical images and multiphase flows.

· Simulation of Porous Media Flows:

Stable Viscosity Ratio Unstable Viscosity Ratio

· Simulation on Unrestricted Meshes:

Driven Cavity Problem Interaction of Four Vortices

(With Min – Click to play the movies)

(With Losasso and Fedkiw – Click to play the movies)

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· Sharp Interface Simulation of Boiling Flows:

Thin Film Boiling

(With Chen, Nguyen and Banerjee – Click to play the movies)

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· Materials Science:

Three Dimensional Crystal Growth Four Fold Anisotropy

(With Caflisch, Fedkiw and Osher – Click to play the movies)

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· Image Segmentation for Engineering:

Cross-Section and Three-Dimensional Reconstruction of a Turbulent Flow from Two-Dimensional Images

(With Fedkiw – Data from Koseff)

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· Image Segmentation for Medical Images:

Visualization Tool VolVist

(With Boyer, Cardenas and Koumerian)

Segmentation of the Left Kidney Segmentation of the Rectum Segmentation of the Bladder

(With Boyer Cardenas and Levy)

Three-Dimensional Reconstruction of the Left Hemisphere of a Brain From Two-Dimensional CT-Scans

(With Fedkiw – Data from Boyer)

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· Incompressible Flows (Free Surface Flows):

A Three-Dimensional Splash

(With Enright, Fedkiw and Nguyen – Click to play the movies)

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· Compressible Flows (Detonation):

Density Profile for a Two-Dimensional Expanding Gas

(With Fedkiw and Nguyen)

Capman-Jouguet Detonation Wave – Triple Point

(With Fedkiw and Nguyen)

Capman-Jouguet Detonation Wave – Time Snap Shots of Density Contours

(With Fedkiw and Nguyen)

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Publications

• Bertelli, L., Sumengen, B., Manjunath, B. S., and Gibou, F., “A Variational Framework for Multi-Region Pairwise Similarity-Based Image Segmentation”, Pattern Analysis and Machine Intelligence, In press (2007)
• Min, C.-H., and Gibou, F., “A Second Order Accurate Level Set Method on Non-Graded Adaptive Grids”, J. Comput. Phys., 225, 300-321 (2007).
• Min, C.-H., and Gibou, F., “Geometric Integration over Irregular Domains with Application to Level Set Methods”, J. Comput. Phys., 226, 1432-1443 (2007).
• Gibou, F., Min, C.-H, and Ceniceros, H., “Finite Difference Schemes for Incompressible Flows on Non-Graded Adaptive Cartesian Grids”, Fluid Dynamics and Materials Processing, 3, 37-48 (2007).
• Min, C.-H., and Gibou, F., “A Second Order Accurate Projection Method for the Incompressible Navier-Stokes Equations on Fully Adaptive Grids”, J. Comput. Phys., 219, 912-929 (2006).
• Chen, H., Min, C.-H and Gibou, F., “A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids”, J. Sci. Comput., 31, 19-60 (2007).
• Min, C.-H, Gibou, F., and Ceniceros, H., “A Supra-Convergent Finite Difference Scheme for the Variable Coefficient Poisson Equation on Fully Adaptive Grids”, J. Comput. Phys., 202, 577-601 (2006).
• Gibou, F., Chen, L., Nguyen, D., and Banerjee, S., “A Level Set Based Sharp Interface Method for the Multiphase Incompressible Navier-Stokes Equations with Phase Change”, J. Comput. Phys., 222, 536-555 (2007).
• Gibou, F. and Fedkiw, R., "A Fourth Order Accurate Discretization for the Laplace and Heat Equations on Arbitrary Domains, with Applications to the Stefan Problem", J. Comput. Phys., 202, 577-601 (2005).
• Losasso, F., Gibou, F. and Fedkiw, R., "Simulating Water and Smoke with an Octree Data Structure", SIGGRAPH 2004, ACM TOG 23, 457-462 (2004).
• Gibou, F. and Fedkiw, "Fast Hybrid k-Means Level Set Algorithm For Segmentation”, Stanford Technical Report, November 2002. Also in the proceeding of the 4^th Annual Hawaii International Conference on Statistics and Mathematics.
• Gibou, F., Levy, D., Cardenas, C., Liu, P. and Boyer, A., "Partial Differential Equation based Segmentation for Radiotherapy Treatment Planning", Mathematical Biosciences and Engineering, 2, 209-226 (2005).
• Gibou, F., Ratsch, C., and Caflisch, R., "Capture Numbers in Rate Equations and Scaling Laws for Epitaxial Growth", Phys. Rev. B, 67, 155403 (2003).
• Gibou, F., Fedkiw, R. Caflisch, R. and Osher S., "A Level Set Approach for the Numerical Simulation of Dendritic Growth", J. Sci. Comput. 19, 183-199 (2003).
• Vvdensky, D. Ratsch, C., Gibou, F. and Vardavas, R., "Singularities and Spatial Fluctuations in Submonolayer Epitaxy", Phys Rev. Lett. 90, 189601 (2003).
• Enright, D., Nguyen, D., Gibou, F. and Fedkiw, R., "Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows", Proc. of the 4th ASME-JSME Joint Fluids Eng. Conf., FEDSM2003-45144, edited by M. Kawahashi and A. Ogut and Y. Tsuji, pp. 1-6, Honolulu, HI 2003.
• Gibou, F., Fedkiw, R., Cheng, L.-T. and Kang, M., "A Second Order Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains", J. Comput. Phys. 176, 205-227 (2002).
• Ratsch, C., Gyure, M., Caflisch, R., Gibou, F., Petersen, M., Kang, M., Garcia, J. and Vvedensky, D,
  "Level-Set Method for Island Dynamics in Epitaxial Growth", Phys. Rev. B, 65, 195403 (2002).
• Nguyen, D., Gibou, F. and Fedkiw, R., "A Fully Conservative Ghost Fluid Method & Stiff Detonation Waves", 12th Int. Detonation Symposium, San Diego, CA, 2002.
• Gibou, F., Ratsch, C., Chen, S., Gyure, M. and Caflisch, R., "Rate Equations and Capture Numbers with Implicit Island Correlations", Phys. Rev. B, 63, 115401 (2001).