A team of faculty, staff and students in the College of Science and the College of Engineering at the Pennsylvania State University propose to acquire a multi-processor computer facility to enable the solution of mathematical field equations. The faculty are drawn from the Department of Mathematics, Astronomy and Astrophysics, Aerospace Engineering, and Mechanical Engineering. The goals of the program are: to develop numerical simulations on parallel computer architectures of unsteady, three-dimensional, non-linear phenomena in science and engineering; to compare and share numerical methods applied to similar mathematical problems; and to integrate numerical solutions on parallel computers into the gradua te curriculum. These goals will be achieved by (1) the establishment of a multi-processor computer facility accessible to a team of faculty, staff, and students, (2) the conduct of research on mathematical problems with common themes and challenges, (3) the development of model problems and solutions for use in graduate coursework and, ( 4) the dissemination of the results of the research and instructional activities through the World Wide Web. Research will be conducted in the areas of : black hole collisions; unsteady flow and acoustics; electromagnetics; magneto-thermocapillary convection; and geophysical fluid flows. Different numerical methods will be used to solve problems in these areas including: adaptive finite-elements; high-order finite-differences; and spectral techniques. Though the research topics cover many different phenomena, they all have common mathematical and computational challenges. They all involve the solution of three-dimensional, unsteady, non-linear, partial differential equations. They are all problems that involve a wide range of length and time scales. Also, they all require the analysis of large time-dependent solution data sets. Finally, numerical approaches that run efficiently on multiple processors and take maximum advantage of the hardware architecture are of vital importance to all the simulations. The facility proposed here has not only advanced architecture but also development tools for debugging, profiling, and tuning the programs. The computer also allows all three forms of parallel processing: shared memory; message-passing (MPI and PVM); and data parallel (Fortran 90 and High Performance Fortran). The activities in this proposal have the support of and cooperation with both Silicon Graphics Inc. and IBM. To promote additional cooperation and dissemination the research team will establish a regular workshop/seminar series. This activity will have the goals, to share knowledge on techniques of parallel computation, to keep abreast of new developments in software and algorithms and, to keep facility users informed in detail of the activities of the other team members. In addition to the common threads in the research activities, the proposed research will have extensive links to our graduate education activities. Penn State is establishing a Center for High Performance Computation. This is partially supported by a grant from the National Science Foundation under its Combined Research-Curriculum Development (CRCD) Program. The Center will combine our research activities and our graduate education program, including a minor in High Performance Computation. Five new graduate and undergraduate courses in applied parallel processing are already being offered. Access by students to the proposed research facility, as well as exposure to the research activities will provide an invaluable enhancement to the instructional program
