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 assistantships.
• 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.

The successful candidate will have a good first degree in mathematics, computer science, or a related field with a substantial mathematical and computational component. The student will be affiliated with the Center for Computational and Applied Mathematics in the Department of Mathematics at Purdue University, as well as Computational Science and Engineering graduate program.

Interested students who are currently enrolled at Purdue University should schedule an appointment with Prof. Melvin Leok to discuss their research interests.

Prospective students should apply directly to the Mathematics graduate program through the following online application:
Graduate Admissions Online Application

The admission deadline, for admission to the graduate program in Fall 2008, is February 1 (for fellowship consideration), and March 1 (for assistantship consideration).

If you are responding to this announcement, you should also send a copy of your application materials to Prof. Melvin Leok.

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