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Work in Progress


Ed Hayes, Troy Wu, Ohio State University; Dan Sorensen, Kristy Maschinoff, Zdenko Tomasic, Rice University

CRPC researchers at Rice University, working with Ohio State University researchers, have made considerable progress this past year in developing and testing a new parallel implementation of their surface function and propagation codes for reactive scattering. Led by Ed Hayes and Dan Sorensen, the team has achieved more than 20 gigaflops sustained performance on 512 nodes of the Cray T3D system at the Pittsburgh Supercomputing Center. They are expecting even greater performance levels in the near future. The eigenvalue calculations are done with a new portable parallel version of ARPACK, called P_ARPACK.

In addition to the primary reactive scattering work, the researchers have also performed the quantum mechanical calculations of the bound states of the HO2 molecule under the condition that the total angular momentum J = 0, 1, 2, 3. This is a breakthrough that has resulted directly from the collaborative efforts in eigenvalue calculations.

HO2 is a stable molecule that is energetically accessible from both the reactants and products of the reaction H + O2(right arrow)OH + O. Prior to this work, other groups have computed the bound-state energy levels of HO2 calculated under the condition J = 0. The group has calculated these energy levels with J > 0 for the first time.

The HO2 bound-state calculations are done on the multi-processors of the Cray-T3D. The performance rating of the program scales almost linearly when up to 128 processors are used, and the highest sustained performance rating of the program in the test cases is 3.8 gigaflops. The CPU time is also dramatically reduced, compared with the previous calculations. In the J = 0 case, instead of using tens of hours, the calculation can be finished in four minutes if 128 processors are used.

ARPACK is being used by many other research groups in a number of application areas. Another computational chemistry application is the determination of vibrational eigenstates from first principles, i.e., quantum mechanics. This represents a major computational challenge for most molecules, even ones with as few as four atoms. Such eigenstates determine the observable spectroscopy of molecules, and an understanding of their nature is essential for understanding how molecules behave. Computational scientists R. Lehoucq and S. Gray at Argonne National Laboratory have used an MPI-based parallel implementation of the implicitly restarted Arnoldi algorithm from the software package ARPACK to compute the vibrational levels of the four-atom molecule H+O+C+O (Hydrogen-Oxygen-Carbon-Oxygen). This molecule is important in combustion where it occurs as an intermediate process during the burning of hydrocarbon fuels. The presence of three relatively massive atoms (O and C are 16 and 12 times as massive as H, respectively), makes the problem particularly challenging. So far, a series of experiments has been successfully performed that computes the lowest 41 - 52 vibrational states. The associated matrix eigenvalue problems were of order 1,092,420, 1,638,630, and 2,278,044. These problems took approximately 6, 8.4, and 11 hours using 54 nodes of the IBM SP system at Argonne. The current goal is to generate the first 100 vibrational eigenstates of this system. Once completed, work will begin on other challenging four- atom systems, e.g., acetylene and hydrogen peroxide.

For more information on ARPACK, including instructions on how to download the software, see http://www.caam.rice.edu/~kristyn/parpack_home.html .

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