Application of vector and parallel supercomputers to ground-water flow modeling
A new generation of high-performance computers offers geoscientists new and exciting tools for computationally-intensive scientific problems. This paper presents preliminary results on optimizing the performance for ground-water flow models on a Cray supercomputer. The traditional method of solving a tridiagonal matrix system, that of forward solution and backsubstitution (FB), is intrinsically data dependent, in that the equations at a given grid node depend on values from adjacent grid nodes. This feature effectively prohibits vectorizing and parallelizing the method for solution on vector and parallel processors. An alternative method of solution, that of reduction and backsubstitution (RB), has no data dependence and was implemented in Fortran for vector and parallel processors to solve a tridiagonal matrix system in a ground-water flow model. The vectorized code has an overall execution rate of 110MFLOPs on a Cray Y-MP that is five to sixteen times faster than the scalar code. Implementing the code in vector-parallel mode using eight undedicated processors on a Cray Y-MP results in an overall additional speedup of 2.8 times in wall clock time for a two-dimensional flow problem and 2.2 times for a three-dimensional flow problem. In comparison with the FB code, the RB code requires 26% less CPU time and 66% less wall-clock time on the same flow problem. Demonstrative application of the model is included for two- and three-dimensional flow problems.
finite difference method darcy's law amdahl's law theis