1998 - 1999 CS Annual Report                                                                  Faculty
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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.
Ph.D. 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 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 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  

  • Acting Director: Center for Applied Mathematics 
  • Faculty Senate 
Professional Activities  
  • Editor: Journal Global Optimization, SIAM Journal
    Matrix Analysis Appl., SIAM Review  
  • Book reviewer: SIAM Review  
  • Referee: Math. Progr., Math. Comp., SIAM Journal Sci. Comp., Oper. Res. Letters,
    Journal Complexity, Journal Egyptian Math. Soc., Proc. Found. Comp. Sci., SIAM
    Journal Matrix An. App. 
  • Weighted least-squares parameters for graphs. Invited presentation. Conference on
    Approximation and Complexity in Optimization, Univ. of Florida, March 1, 1999. 
  • Solving polynomial systems using eigen values. Sixth SIAM Optimization Conference,
    Atlanta, GA, May 12, 1999. 
  • . Numerical Analysis Colloquium, Stanford Univ., May 18, 1999. 
  • . Numerical Analysis Colloquium, Bell Labs, Murray Hill, NJ, June 3, 1999. 
  • Support trees for structural analysis. Plenary talk. Householder Conference on Numerical Linear Algebra, Whistler, BC, June 16, 1999. 
  • Numerical conformal mapping using cross-ratios and Delaunay triangulation, SIAM Journal Sci. Comp. 19 (1998), 1783-1803 (with T. Driscoll).