Solving the Poisson Equation on the FPS-164 (Floating Point System-164)

摘要

The architectural differences between a serial and a parallel machine raise a number of questions regarding the efficiency of established algorithms. This paper explores several algorithms which solve the Poisson equation on rectangular regions in two dimensions. The solution of the Poisson problem is an example of one of the simplest nontrivial computations which frequently occur in innermost loops of large scale scientific codes, and hence is a useful test of different architectures for scientific computation. Compared are solution times on the Vax 11/780 with solution times on the Floating Point System 164 (FPS-164) attached processor. Since the FPS-164 supports a sufficiently large memory and the host/attached processor I/O is relatively slow, it is of interest to solve large problems entirely on the FPS-164. We explore the performance of the FPS-164 on both portable FORTRAN programs which have not been tuned to its architecture and on moderately tuned FORTRAN programs which make calls to the FPS assembly language math library, MATHLIB. Use of MATHLIB results in shorter programs which are usually more efficient. We show that the speedup in execution time is more uniform across the algorithms than might be anticipated and hence the choice of algorithm is still highly significant.