Stephen A. Vavasis
As computer hardware becomes more powerful, there is a corresponding growth in the demand for more efficient algorithms to solve large-scale scientific problems. My research is on the design and analysis of such algorithms. Ph.D. student V. Howle and I developed algorithms for modeling and simulation of AC electric power networks.
Utility companies are interested in modeling the behavior of the network in the presence of a fault (closed circuit breaker). The governing equations, called the “swing equations,” are differential algebraic equations for the rotor angles of the generators in the system. We are developing new, more accurate algorithms for the swing equations and for linear subproblems.
Work on geometry in scientific computing continues. Ph.D. student G. Jonsson and I have studied the problem of robust intersection of parametric patches with rays and planes. This problem arises in geometric modeling and mesh generation. We are building on recent previous work that transforms the problem to an eigenvalue computation to improve accuracy. Accuracy is paramount in this setting because a single failure of a point-in-model computation could cause an entire numerical simulation to fail. Another ongoing project is the development of new preconditioners (based on support-tree ideas) for rapid analysis of large-scale three-dimensional finite-element structures. That project is joint with colleagues in the Department of Civil Engineering.
Member: Graduate admissions committee, Center for Applied Mathematics; Undergraduate admissions committee, College of Arts & Sciences.
Member: Faculty Senate.
Editor: Journal Global Optimization; SIAM Journal Matrix Analysis Applications.; SIAM Review; Math. Program.
Book Reviewer: SIAM Review.
Referee: Journal of Complexity; Numerical Linear Algebra and Applications; ACM Transactions on Mathematical Software; International Journal of Computational Geometry and Applications; Mathematical Programming; SIAM Journal on Numerical Analysis; Journal of Optimization Theory Applications.
Stable algorithms for systems of polynomial equations. Conference on Foundations of Computational Mathematics, Oxford, England, July 1999.
—. US National Conference on Computational Mechanics, Boulder, CO, August 1999. Support tree preconditioners for finite element structures. CEE Department, University of Delaware, March 2000.
“A norm bound for projections with complex weights.” Linear Algebra and its Applications 307 (2000), 69–75 (with E.Y. Bobrovnikova).