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The Computational Geometric Mechanics group at the University
of California, San Diego
Research Objectives
The computational geometric mechanics group is focused on developing a self-consistent discretization of geometry and mechanics to enable the systematic construction of geometric structure-preserving numerical schemes based on the approach of geometric mechanics, with a view towards obtaining more robust and accurate numerical implementations of feedback and optimal control laws arising from geometric control theory.
Affiliations and Rankings
The group is housed in the Department
of Mathematics within the Division of Physical Sciences
at the University of California, San Diego, and
will be affiliated with the Center
for Computational Mathematics, the Program
in Computational Science, Mathematics, and Engineering, and the Cymer Center for Control Systems and
Dynamics.
The graduate program is ranked 24th
in the nation in mathematics by
U.S. News and World
Report. Furthermore, we are ranked 2nd
in mathematics by The
Chronicle of Higher
Education's 2007 Faculty
Scholarly Productivity
Index.
Funding
The activities
of the group are partially funded by research grants from the National Science Foundation in applied and computational mathematics:
Group Members
- Prof. Melvin Leok, associate professor of mathematics. [ Thesis | Collected works ]
- Dr. Tatiana Shingel,
postdoctoral scholar/teaching visitor, University of California, San
Diego, 2009-2011.
- Dr. Wencheng Li, an assistant professor of computational mathematics
at Northwestern Polytechnical University in Xian, China, will be visiting
our group on a one year fellowship from the Chinese Scholarship Council,
starting April 2010.
- Tomoki Ohsawa, visiting mathematics graduate student from the
University of Michigan. (Ph.D. advisor: Prof. Anthony M. Bloch)
- Giulia Ortolan, a
Ph.D. student in Information Engineering at the University of Padova,
Italy, will be visiting our group for a period of four months on a
scholarship from the University of Padova, starting the end of February
2010.
- Leilani Gilpin, undergraduate research assistant, double major in
mathematics and computer science at UCSD.
Affiliated and Alumni Members
- Dr.
Diana Sosa Martín, visiting assistant professor, Purdue
University, 2008-2009.
Currently an assistant professor of mathematics,
University of La Laguna, Spain.
- Dr. Taeyoung Lee,
Ph.D. in Aerospace Engineering, University of Michigan. (co-advised with
Prof. N. Harris McClamroch)
Currently an assistant professor of mechanical and aerospace engineering, Florida Institute of
Technology. [ Thesis ]
- Jingjing Zhang, was a visiting graduate student from the Institute of
Computational Mathematics, Chinese Academy of Sciences. Her one year visit to our group
was funded by a fellowship from the
Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
(co-advised with Prof. Jialin Hong)
- Masako Kishida,
M.S. in Applied and Interdisciplinary Mathematics
(Michigan),
currently a Ph.D. student in Mechanical Engineering at UIUC.
- Nathan Orlow, NSF REU student.
- Charles Roldan, NSF REU student.
- Wooi-Chen Ng, summer undergraduate research assistant.
Research Opportunities
-
Graduate Positions Available in the Computational Geometric
Mechanics group
Research positions for graduate students are available in the broad
area of geometric numerical methods in geometric mechanics and control.
- Academic
and Industrial, Science and Engineering Collaborations
Welcomed
We are constantly on the lookout for interesting and challenging
collaborations with scientists and engineers from academia or industry.
If you have an interesting application for which geometric
numerical methods might be relevant, please feel free to contact us.
Much of our theoretical work is motivated by specific applications.
To paraphrase William Morris, "Have nothing in your [mathematics] that
you do not know to be useful, or believe to be beautiful."
Related Research Groups
- GeNuIn (Geometric
Numerical Integration) group, Norwegian University of Science and
Technology.
Relevant Courses
Additional Resources
