HYDROLOGIC APPLICATIONS OF THE CONNECTION MACHINE CM-2

Massively parallel computers will play an increasingly dominant role in hydrological computing. One such computer is the Connection Machine model CM-2, a single-instruction stream, multiple-data stream computer with up to 65,536 processors, as much as 8 gigabytes (Gbyte) of random access memory distributed among the processors, and a FORTRAN compiler based on the proposed FORTRAN-90 standard. One-, two-, and three-dimensional examples from hydrology are used in this paper to present a tutorial on programming for the CM-2. The problem of saturated, steady flow in a randomly heterogeneous three-dimensional porous medium is explored here in some detail. A diagonally preconditioned conjugate gradient (DPCG) iterative solver is applied to this problem for up to 128(3) nodes. Less than 1 min of CM-2 time is required to reduce the error by a factor of 10(-6) for a 128 x 128 x 128 grid with heterogeneous hydraulic conductivity. Measured CPU times for the DPCG method are significantly smaller than those reported in the literature for a polynomial PCG solver applied to the same domain with different boundary conditions and executed on a Cray X-MP/48 and an Alliant FX/8. The measured performance is also much greater than that reported in the literature for a strongly implicit procedure solver applied to a similar problem on a Cray 2. The need for continued development of massively parallel algorithms, including effective iterative solution of linear systems of equations and problems with irregular domains, is indicated.