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Projects on the Delta

With 570 nodes and a peak performance of 32 GFLOPS, the Intel Delta at the CRPC's Caltech site has been highly effective for several different research projects. The following projects described below are a few examples of how researchers have used this resource.

Aviation Gridded Forecast System
Leslie Hart, Young Chun, Tom Henderson, Bernando Rodriguez, Frank Tower, Science and Technology Corporation, Boulder, CO

Advancements in real-time forecasting have immediate benefits to both the domestic economy and the national defense. Due to the National Weather Service's new radar and satellite-based sensing systems, the unprecedented quantity of data provided for these models has resulted in the need for increased computing capability. As a parallel machine, the Delta has provided this capability at an order of magnitude that is more cost-effective than traditional vector supercomputers.

Using CRPC-allocated time, researchers in this project used the Delta to test their conversion of sequentially oriented weather models to parallel forms. Their objective is to develop a parallel weather analysis and forecasting system with a 15 km resolution and a three-hour turnaround time on a 24-hour forecast. Researchers hope to improve the resolution to four km while maintaining or improving the three-hour turnaround time.

Other challenges to developing an efficient parallel weather analysis and forecast system include achieving portability on several parallel machines and specifying the memory architecture and algorithms to dictate data movement requirements. Research in operating systems and compilers has also been pursued to supplement these developments.

Concurrent Solver for the Euler Equations
Dan Meiron, Eric Van de Velde, John Hofhaus, Paul Hardy, California Institute of Technology

This project involves the development and use of a numerical scheme to integrate two-dimensional Euler equations in an annulus. The numerical scheme will be used as a basis for high resolution simulations of inviscid and viscid fluid flows. From this simulation, researchers can examine the late-time dynamics of vortex structures that emerge due to the special nature of energy transfer in two-dimensional fluid flows.

With sufficient spatial resolution provided by the use of the Delta, several issues can be investigated in the examination of these vortex structures. These issues include the mechanisms of an irreversible approach to negative temperature states in the two-dimensional flows and the nature of energy distribution at equilibrium. Several theories that have been advanced regarding these issues can now be tested with the help of the simulations being developed through this project. The algorithms being used are well suited for use on parallel machines.

In addition, axisymmetrical three-dimensional flows can be simulated by modifying these algorithms slightly. These three-dimensional flows have been of use lately to study the possible singular behavior of the three- dimensional equations of motion. A significant difference between two- dimensional and three-dimensional flow is the possibility of vortex amplification through vortex stretching. It is not yet known whether divergent vorticities can be attained in a finite time as a result of such stretching. The computational capabilities of the Delta are providing sufficient resolution to address these issues.

A third project involves the translation of the parallel algorithms described above to the Fortran M language for parallel computation. Fortran M is a dialect of Fortran 77 developed by CRPC researchers Mani Chandy and Ian Foster. The language adds a few extensions to the Fortran 77 language which allow one to construct parallel programs in which message passing can be performed in a way which is independent of the underlying architecture. In this way it is possible to guarantee that parallel programs written in Fortran M will perform deterministically. In collaboration with Chandy and a group of undergraduate students, this group has been developing "templates" in the Fortran M language that allow one to write parallel code for various common data distributions and have all aspects of communications hidden in the low level details of the underlying template. This approach to parallel programming has the advantage that, as long as one interfaces with the data structures and utilities provided through the template, parallel programs in Fortran M appear at the source level to be more or less identical with their sequential counterparts. The group is in the process of constructing templates for several common regular data distributions used in scientific computing. The scientific problems described above both possess data distributions that are amenable to this approach.

Currently they are implementing these codes on networks of workstations but plan to port these codes to the high-performance SP1 machine at Argonne.

Numerical Simulations of Quantum Gravity Using Random Surfaces
Paul Coddington, Enzo Marinari, Mark Bowick, Leping Han, Geoff Harris, Syracuse University

String theories are quantum field theories in which the fundamental particles are tiny one-dimensional strings, rather than points with no dimension. There has been great theoretical interest in string theories, since together they provide a long-awaited quantum theory of gravity, as well as reproduce the standard quantum model of the other fundamental forces of nature, and thus provide a possible TOE (Theory of Everything). However, string theories have a major problem--calculations are usually analytically intractable. Methods are currently being developed to alleviate this problem by doing numerical calculations using computer simulation.

String theory calculations involve integrating over all possible two- dimensional surfaces swept out by the string in some higher dimensional space-time. In order to compute this integral numerically, the surfaces are discretized as a triangulated mesh. The integral is then approximated by a sum over a large number of different meshes, which are obtained by making random changes to the mesh throughout the calculation, using a Monte Carlo method. The mesh is thus referred to as a dynamically triangulated random surface.

Currently, the research group is running simulations on the Intel Delta and on networks of workstations by using the trivial parallelism of averaging the results of independent simulations on different processors. However, this can only be done effectively for small meshes. The group is currently working on a data parallel algorithm for larger meshes. Since both the data and the algorithm are dynamic and irregular, this is a challenging problem, which requires parallel algorithms for graph coloring, graph partitioning, load balancing, adaptive mesh generation, as well as the Monte Carlo update.

Parallelization of an All-electron Density-functional Program
Peter Nordlander, Richard Smalley, Liang Lou, Rice University

This group is developing a parallel version of software program that calculates the electronic and geometric structures of polyatomic systems, specifically semiconductor and transition metals as well as hollow-cage carbon structures, new materials known as metcars. The parallelization of the program arises from the use of a recently introduced multi-center numerical integration scheme that is inherently suited for vectorized parallel processing. This numerical integration scheme is based on the discretization of the one-electron Schršedinger equation on a grid of sampling/integration points. This scheme has yielded the most streamlined code out of several possible approaches for partitioning the space and setting up the integration points.

The sequential version of this program has been implemented on several different workstations and used in the study of clusters of various types and sizes, such as C60 structures (Buckminsterfullerene, or "Bucky balls"), small gallium arsenide clusters, NH3-cluster chemisorption systems, GaAs clusters, and some organometallic cage structures. Although program performance is very high on sequential computers, a single CPU limits the calculations involved in accurately describing the electronic structures; these calculations involve several hundred basis functions. The Delta, however, provides sufficient computational power to run these functions. This has allowed the researchers to systematically study cluster systems with extended size range.

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