faculty.gif (20410 bytes)
choices.gif (4488 bytes)

Stephen A. Vavasis

Associate Professor

PhD Stanford, 1989

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. PhD student V. Howle and I are developing 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

steve.tif (273858 bytes)
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. PhD student G. Jonsson and I are studying 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. We are also continuing work on QMG mesh generation software (based on an algorithm developed jointly with S. Mitchell of Sandia). The forthcoming version of QMG will robustly handle very general domains with boundaries defined by curved Bezier patches. The QMG project is part of a grand-challenge project on computational fracture mechanics involving colleagues in CS, Civil Engineering, and other schools.

University Activities

Director: Graduate Studies, Applied Mathematics

Professional Activities

  • Editor: J. Global Optimization, SIAM J. Matrix Analysis Appl., SIAM Review

  • Program Committee: ACM Symp. Computational Geometry

  • Review Panel: Dept. Energy DOE2000 program

  • Referee: SIAM Review; SIAM J. Matrix Analysis Appl.; J. Complexity, Numerical Linear Algebra; J. Optimization Theory and Appl.; Comm. Numerical Methods in Engineering; NSF; SIAM Book Publications; Advances in Computational Mathematics; J. Algorithms; IEEE Trans. Parallel and Distributed Systems; Handbook of Algorithms


Invited Panelist, ACM Symp. Computational Geometry, Minneapolis, MN, June 9, 1998.


  • Geometric separators for finite-element meshes. SIAM J. Scientific Computation 19 (1998), 364-386 (with G. Miller, S. Teng and W. Thurston).

  • Preconditioning complex-symmetric layered systems arising in electric power modeling. Proc. 1998 Copper Mountain Conf. Iterative Methods (with V. Howle).