(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.
Stephen A. Vavasis
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
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
(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.
Acting Director: Center for
Editor: Journal Global
Optimization, SIAM Journal
Matrix Analysis Appl., SIAM
Book reviewer: SIAM Review
Referee: Math. Progr.,
Math. Comp., SIAM Journal
Comp., Oper. Res. Letters,
Journal Complexity, Journal
Egyptian Math. Soc., Proc.
Found. Comp. Sci., SIAM
Journal Matrix An. App.
parameters for graphs. Invited
presentation. Conference on
Approximation and Complexity
in Optimization, Univ. of
Florida, March 1, 1999.
- Solving polynomial systems
values. Sixth SIAM
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
Comp. 19 (1998), 1783-1803 (with