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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 20th
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:
- CMMI-1029445, Computational
Geometric Uncertainty Propagation for Hamiltonian Systems
on a Lie
Group, 2010-2013.
- DMS-1010687, CAREER:
Computational Geometric Mechanics: Foundations, Computation,
and Applications, 2008-2013 (transferred from DMS-0747659).
- DMS-1001521, LTB:
Generalized Variational Integrators for Large-Scale Scientific
Computation, 2007-2010 (transferred from DMS-0714223).
- DMS-0726263, Computational Geometric Mechanics and its Applications to Geometric
Control Theory, 2005-2009 (transferred from DMS-0504747).
Group Members
- Prof. Melvin Leok, associate professor of mathematics. [ Thesis | Collected works ]
- Dr. Tatiana Shingel,
Ph.D. in Mathematics, Cambridge University, 2009.
Postdoctoral scholar/teaching visitor, University of California, San
Diego, 2009-2011.
- Dr. Tomoki Ohsawa, Ph.D. in Applied and Interdisciplinary Mathematics,
University of Michigan, 2010. Postdoctoral scholar/teaching
visitor,
University
of California, San Diego, 2010-2011.
- Dr. Joris
Vankerschaver, Ph.D. in Mathematics, Ghent University, 2007.
Postdoctoral scholar/teaching visitor, University of California, San
Diego, 2010-2011.
- James Hall, 3rd year
Ph.D. student in Mathematics (CSME), University of California, San Diego,
and is currently working on variational integrators using spectral
techniques, and GPU based computing.
- Henry Jacobs, a
Ph.D. student in Control and Dynamical Systems at the California Institute
of Technology, is a visiting graduate student working on interconnected
Lagrange-Dirac systems.
- Cuicui Liao, a Ph.D. student in Mathematics at the Harbin Institute of
Technology, is visiting our group for a period of one year on a
postgraduate scholarship from the Chinese Scholarship Council, starting
September 2010.
- Leilani Gilpin,
undergraduate research assistant,
double major in mathematics and computer science at UCSD.
Visitors
- Prof. Hiroaki
Yoshimura, Waseda University, Jan 24-27, 2011.
- Prof. Ping Xu, Penn State
University, Feb 7-10, 2011.
- Leonardo
Colombo, Instituto de Ciencias Matematicas, Madrid, Spain,
Jul 10-Sep 30, 2011.
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.
She defended her thesis in May 2010, and is currently an assistant
professor in Henan Polytechnic University, Jiaozuo, China. (co-advised
with Prof. Jialin Hong)
- Giulia Ortolan, a
Ph.D. student in Information Engineering at the University of Padova,
Italy, visited our group for a period of four months on a
scholarship from the University of Padova.
- 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
Relevant Courses
Additional Resources
