OPTIMIZATION OF CONNECTION MACHINE PERFORMANCE

Abstract

The Connection Machine CM-2 computer represents the state of the art in supercomputer performance at this time, with peak rates of over 20 Gflops in 32-bit precision. While theoretical peak rates are essentially never attained, remarkable performance is possible on real applications. We discuss a number of CM-2 applications including implicit and explicit PDE solvers as well as spectral methods. We demonstrate delivered performance over a gigaflop in each case, and ranging as high as 3.8 gigaflops in the case of conjugate gradient solution of elliptic PDE.We describe 2D and 3D Fast Helmholtz and Poisson Direct Solvers for the CM-2 and provide performance data for them on grids with up to 4 million points and using 65,536 processors. Performance of 1.1 Gflops is attained in 2D, and over 850 Mflops in 3D. The solution of the Helmholtz equation on a 2048×2048 grid takes under half a second, and on a 128×128×256 3D grid it requires .54 seconds. We have iteratively solved more general elliptic PDE by conjugate gradient methods at 3.8 Gflops. The fast solver has been used to provide a pre-conditioner for the conjugate gradient solver, which is then limited in performance to 1.3 Gflops, but results in far fewer iterations.We also describe several partial and complete applications ranging from oil reservoir simulation to oceanographic modeling. In the latter case we present the first results of spectral models running on the CM-2. We emphasize the issues involved in attaining these levels of performance and compare in most cases with CRAY-XMP performance for the same algorithm. All results are for algorithms written in a high-level language.