Professor André Tits (ECE/ISR) is the principal investigator and Professor Dianne O’Leary (CS/UMIACS) is the co-PI for a new Department of Energy grant, “Advanced Optimization Techniques for Entropy-Based Moment Closures.” The University of Maryland portion of the three-year grant is funded at $769,918, and the work is being done in collaboration with Dr. Cory Hauck of the Oak Ridge National Laboratory.
The research team will design and implement advanced convex optimization methods for solving entropy maximization problems. In transport and kinetic theory, solutions to these problems are used to derive closures for moment models that inherit many fundamental features of kinetic transport. Specific applications include gas dynamics, radiative transfer, charged-particle transport, and neutron transport.
The natural approach to solving the entropy maximization problem is via the solution of the dual problem--a finite-dimensional, strictly convex problem, known to have a unique solution. The researchers will investigate novel optimization algorithms for three problem cases: an unconstrained case, a constrained case, and what amounts to an “intermediate case.” Their tools include globally convergent variants of Newton's method, recent interior-point methods which exploit the conic nature of the feasible set, and the extension of new reduced constraint methods from linear to general convex optimization.
Algorithms will be implemented as local computations in parallel PDE solvers and the accuracy, efficiency, and practicality of entropy-based closures in realistic settings will be determined. This analysis includes (i) the use of multi-level preconditioning for increased efficiency and (ii) sensitivity analysis to determine the choice of moments that, based on user-defined criteria, leads to an efficient calculation.
September 16, 2009