Joseph E. Flaherty

Dean, School of Science
Professor, Computer Science
Amos Eaton Professor

Education:

B.S., Aeronautical Engineering, Polytechnic Institute of Brooklyn, 1964
M.S., Applied Mechanics, Polytechnic Institute of Brooklyn, 1966
Ph.D., Applied Mechanics, Polytechnic Institute of Brooklyn, 1969

Career Highlights:

Flaherty has held visiting teaching and research appointments at such institutions as Stanford University, the University of Minnesota, the University of Arizona, and New York University. He joined Rensselaer in 1973 and became the founding chair of the university's Department of Computer Science in 1984. Flaherty has been co-author of over a dozen books and more than 130 articles in refereed journals. He is a fellow and secretary of the U.S. Association for Computational Mechanics, and the recipient of an IBM Director's Award and an Army Service Recognition Award. He is an editor of SIAM Review for the Society for Industrial and Applied Mechanics, SIAM Monographs in Modeling and Simulation, and Applied Numerical Mathematics, and member of the editorial boards of the International Journal of Computational Engineering Science, SIAM Journal on Scientific Computing, and IACM Journal of Computational Mechanics for the Institute of Applied and Computational Mathematics.

Research Interests:

Flaherty conducts research on the adaptive and parallel solution of large-scale problems involving partial differential equations and the application of these techniques to problems in mechanics and materials. Flaherty has worked on each adaptive approach as well as their combination and has focused on time-dependent problems and space-time adaptivity. He has also conducted research on solution reliability through the use of computable discretization error estimation techniques. Flaherty's error estimation procedures utilize superconvergence properties of the solution that greatly simplify the computational costs of obtaining such estimates.

The solution of large-scale problems must typically be done on parallel computers to achieve acceptable accuracy. His research includes researching a variety of load balancing techniques, such as tiling of overlapping neighborhoods, iterative tree balancing, and octree balancing. Some of these procedures have been incorporated into the ZOLTAN dynamic load-balancing library of Sandia National Laboratories.

Flaherty has also worked on the discontinuous Galerkin method for solving hyperbolic partial differential equations. He's investigated several aspects of the method including numerical flux evaluation, basis construction, solution limiting, error estimation, parallel computation, and local time stepping.

Flaherty has applied the adaptive and parallel software and methods to multiscale problems arising in several disciplines. Recent applications include compressible flow, bulk crystal growth, thin film coatings, soft tissue analysis, stellar flashes, and composite media. He has also worked on singular perturbation theory and computational methods for singularly perturbed problems.

Selected Publications:

R. Biswas, K. Devine, and J. E. Flaherty, "Parallel Adaptive Finite Element Methods for Conservation Laws,'' Applied Numerical Mathematics, 14, Nos. 1-3, pp. 255-284, 1994.

S. Adjerid, J. E. Flaherty, W. Hillig, J. Hudson, and M. S. Shephard, "Modeling and the Adaptive Solution of Reactive Vapor Infiltration Problems," Modeling and Simulation in Materials Science Engineering, 3, pp. 737-752, 1995.

D. Givoli, J. E. Flaherty, and M. S. Shephard, "Parallel Adaptive Finite Element Analysis of Viscous Flows Based on a Combined Compressible-Incompressible Formulation," International Journal of Numerical Methods in Heat and Fluid Flow, 7, pp. 880-906, 1997. Awarded best paper of the year 1997 by the journal.

D. Givoli, J. E. Flaherty, and M. S. Shephard, "Simulation of Czochralski Melt Flows Using Parallel Adaptive Finite Element Procedures," Modeling and Simulation in Materials Science and Engineering, 4, pp. 623-639, 1996.

S. Dey, M. S. Shephard, and J. E. Flaherty, "Geometry-based Issues Associated with p-version Finite Element Computations,'' Computer Methods in Applied Mechanics and Engineering, 150, pp. 39-50, 1997.

S. Adjerid, J. E. Flaherty, and I. Babuska, "A Posteriori Error Estimation for the Finite Element Method-of-Lines Solution of Parabolic Problems," Mathematical Models and Methods in Applied Science, 9, No. 2, pp. 261-286, 1999.

J. D. Teresco, M. W. Beall, J. E. Flaherty, and M. S. Shephard, "A Hierarchical Partition Model for Adaptive Finite Element Computation," Computer Methods in Applied Mechanics and Engineering, 184, pp. 269-285, 2000.

S. Adjerid, K. D. Devine, J. E. Flaherty, and L. Krivodonova, "A Posteriori Error Estimation for Discontinuous Galerkin Solutions of Hyperbolic Problems," Computer Methods in Applied Mechanics and Engineering, 191, pp. 1097-1112, 2002.

J.-F. Remacle, J. E. Flaherty, and M. S. Shephard, "An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Rayleigh-Taylor Flow Instabilities," SIAM Review, 2002, to appear.

L. Krivodonova and J. E. Flaherty, "Error Estimation for Discontinuous Galerkin Solutions of Multidimensional Hyperbolic Problems," submitted to Advances in Computational Mathematics, November 2001.

Contact Information:

Joseph E. Flaherty
1C05 Jonsson-Rowland Science Center
(518) 276-6305
flahej@rpi.edu
www.cs.rpi.edu/~flaherje