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. 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
|angles of the generators in the system. We
are developing new, more accurate algorithms for the swing equations and for linear
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.
Director: Graduate Studies, Applied Mathematics
Editor: J. Global Optimization, SIAM J.
Matrix Analysis Appl., SIAM Review
Program Committee: ACM Symp. Computational
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.
Preconditioning complex-symmetric layered systems
arising in electric power modeling. Proc. 1998 Copper Mountain Conf. Iterative Methods
(with V. Howle).