Date: Thu, 21 Nov 1996 19:43:23 GMT Server: Apache/1.1.1 Content-type: text/html Content-length: 2481 Last-modified: Fri, 28 Oct 1994 14:23:17 GMT Joseph E. Flaherty

Joseph E. Flaherty

flaherje@cs.rpi.edu
Amos Eaton Professor
Ph.D. Polytechnic Institute of Brooklyn
Numerical Analysis, Scientific Computation and Adaptive Methods

Flaherty came to Rensselaer from New York University in 1973. Since his arrival, he has been studying scientific computation and is currently investigating adaptive methods for differential equations. He has recently become interested in developing versions of these methods that will run on a variety of parallel computers.

His goal is developing automatic systems for solving partial differential equations. These systems will allow scientists and engineers to describe problems in a natural way, automatically select appropriate numerical techniques, solve the equations to a prescribed level of accuracy, and display the results.

His software is adaptive. It can automatically change numerical methods and can move, create or destroy finite difference or finite element meshes while the system is solving the equations and learning more about their properties. Flaherty's techniques are general, and thus capable of helping engineers confront and describe phenomena such as stresses in metals, aerodynamics, pollution dispersion in lakes, and temperatures in nuclear reactor vessels.

These problems are typical of many practical situations where small scale structures form, evolve, propagate, and decay during the course of calculating the solution. Reliable, robust and efficient software that automatically captures and resolves the phenomena as they appear would be very useful to scientists and engineers who may not know the nature or location of the situation beforehand.

His major successes have been in one- and two-dimensional transient systems. His work relies heavily on the use of computer graphics so that scientists and engineers can easily specify their problems and visualize their results. He and fellow researchers are starting to investigate adaptive methods for three-dimensional problems and procedures that are suitable for parallel computers. Embedded data structures within the adaptive procedures can be exploited to develop efficient parallel strategies.

Faculty and Their Research