PhD Research Assistantships, Geometric Integration, Mechanics, and
Department of Mathematics, University of California, San Diego, USA.
Partial research assistantships are available for students interested
in pursuing a PhD under the direction of Prof. Melvin Leok. These
positions are open to both prospective graduate students, and currently
enrolled graduate students at UCSD.
Message to Prospective Students
Due to the volume of email inquiries that I receive from
prospective students, I will only endorse graduate applicants who have
familiarized themselves with the research that is conducted in my group,
and can clearly demonstrate the relationship between their academic
background and the broad research directions listed below.
Please take the time to carefully read the entire announcement
describing the position, and I will extend the same courtesy to your
Generic email inquiries, and requests for funded internships will
not be entertained.
Broad Areas of Research Interest
Geometric numerical integration in large-scale scientific computing
Computational geometric mechanics and discrete differential geometry
Computational geometric control theory
Potential Thesis Topics
discrete theory of Dirac mechanics and Dirac structures based on the Hamilton-Pontryagin principle;
multisymplectic variational integrators for Hamiltonian PDEs on Lie groups and homogenenous spaces using techniques from noncommutative harmonic analysis;
propagation of uncertainty in deterministic and stochastic Hamiltonian systems using generalized polynomial chaos techniques, and stochastic Lie group variational integrators;
extending computational geometric control and discrete controlled Lagrangians to systems with uncertainty, Lie groups and homogeneous spaces, and Dirac mechanics;
multi-resolution hierarchical Lie group variational integrators that are well suited to simulating complex biomolecules;
spectral variational integrators with spatial-frequency dependent timesteps that incorporate knowledge about scaling relations between spatial and temporal scales;
partition of unity variational integrators that allow domain decomposition based parallel implementations of intrinsic algorithms on manifolds;
spatio-temporally adaptive variational integrators based on nonlinear approximation spaces to more efficiently capture localized structure in solutions.
Description of Support
Full support (tuition, fee remissions, and stipend) for up to six years though a combination of fellowships,
teaching assistantships, and research assistantships.
Initially, students pursuing coursework in preparation for the qualifying examinations will be funded by a teaching assistantship, or possibly a departmental fellowship.
As their research progresses, students will be transitioned to research
A total of 9.5 student-academic years of research assistantship funding (with no teaching responsibilities) is available, which roughly translates into support for 4 graduate students.