IBM Research in Tokyo (mgr. Shigenori Shimizu), in collaboration with Dr. Ebisuzaki at the Institute of Physical and Chemical Research (RIKEN), has built an accelerator board that calculates a general force between all pairs of particles in an N-body particle simulation. A PCI-bus version of the board will be completed in July/August 2000 that consists of 4 MD-GRAPE2 chips made at the IBM Microelectronics Division, Burlington, NY, and runs at about 64 Gflops on computers with AIX, Linux, or Solaris operating systems. Production versions of these boards will be built by Advanet, Inc. (Japan). A compact-PCI version of the board consisting of 16 chips is being built by RIKEN during the summer of 2000.

This is a continuation of a project begun at the University of Tokyo 10 years ago under the name GRAPE, which stands for GRAvity PipE. The first accelerators had a pipelined Coulomb force to accelerate N-body problems with gravity, such as galaxy evolution. They made a single-precision version called GRAPE-4 in 1995 that reached a Teraflop speed with 2000 chips. Their first general force chip was also in 1995; they named this MD-GRAPE, where the MD is for molecular dynamics.

The MD-GRAPE2 chip made at Burlington contains 4 pipelines that each evaluate the summed force between 6 particles and all other field particles. Each pipeline holds the positions of the 6 particles, and all other particle positions stream by from the board memory. At each clock cycle, a new force is added to the summed force on the pipelined particle. The result is a summation of all the forces on each of the 6 particles per pipeline. This sum is returned to the host computer when it is finished and new sums for a new set of particles begins.

The force evaluation is made by a 1024-piece, fourth order polynomial in a normalized interval of distance representing the particle separations. Force types can be changed by inputting different coefficients in the polynomials. MD-GRAPE2 will come with coefficients for Coulomb and van der Waals forces, and with coefficients used for the Ewald method. The coefficient sets are entered with a subroutine call in the main program, and can be varied arbitrarily during the operation of the code.

MD-GRAPE2 allows the N-squared part of an N-body calculation to be done at high speed on the accelerator chips, while the order-N part, such as the time-stepping and bonding forces for a molecule, is done on the host. Typically 70-90 percent of a calculation is spent doing the N-squared part, and with MD-GRAPE2, this part is done at extremely high speed. As a result, the whole code runs 3 to 10 times faster with MD-GRAPE2 boards attached.

The board is used with subroutine calls in FORTRAN or C, so the reprogramming of standard code is relatively easy.

A Molecular Dynamics Machine running at 100 Teraflops will be built at RIKEN near Tokyo. The completion date for the MDM is expected to be late 2000.

MDM is designed for the Ewald method of solving for the summed Coulomb force. This is a fast method invented by Ewald in the 1920's for problems that have periodic boundary conditions. Periodic boundary conditions are commonly used for MD simulations that involve a complex molecule in a water bath. To avoid a vacuum boundary around the water, the whole ensemble of molecule and water is repeated infinitely in all directions. The Ewald method allows this infinitely extended system to be modelled using only the force summations for particles that are in one cell. To do this, the problem is divided into a real-space part and a wave-like part. The real-space part involves sums that are done on the MD-GRAPE chip, while the wave-like part involves sums that require a different chip, called WINE2 by RIKEN. The WINE2 chip is simpler than the MD-GRAPE chip, and the entire WINE2 system is already operational with 2688 WINE2 chips running at a total speed of 50 Teraflops. When the MD-GRAPE2 part is finished, it will have 2560 MD-GRAPE2 chips running at an additional 50 Teraflops. Thus the whole MDM will run at 100 Teraflops by the end of 2000.

MD-GRAPE2 can also be used for other problems, such as incompressible fluid simulations with the particle-vortex method, compressible fluid simulations with smoothed particle hydrodynamics, plasma physics with magnetic and electric forces, magnetics, and astrophysics with gravity. Algorithms that have been used include hierarchical tree codes, multipole methods, the Ewald method, and Particle-Particle/Particle-Mesh methods.

There has been a considerable amount of research done with GRAPE boards in the last 5 years. There are about 50 GRAPE boards of various types in use around the world.

For a sample publication, see "Fast and accurate molecular dynamics simulations of a protein using a special purpose computer," by Komeiji, Y., Uebayasi, M., Takata, R., Shimizu, A., Itsukashi,K., and Taiji, M. (Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, Ibaraki, 305 Japan), Journal of Computational Physics, Vol. 18, No. 12, 1546-1563