The Evaluation and Optimization of 3-D Jacobi Iteration on a Stream Processor

Stream processors, with the stream programming model, have demonstrated significant performance advantages in the domains signal processing, multimedia and graphics applications, and are covering scientific applications. Jacobi iteration, which is widely used to solve partial differential equations, is an important class of scientific programs. As computers became more powerful, scientists have begun writing 3-D programs to solve PDEs. In this paper we examine the applicability of a stream processor to 3-D Jacobi iteration. In a stream processor system, the management of system resources is the programmers’ responsibility. Compared with 2-D Jacobi iteration, some new issues must be considered, since reuse along the third dimension cannot fit in on-chip memory. We first map 3-D Jacobi iteration in FORTRAN version to the stream processor in a straightforward way. We then present several optimizations, which avail the stream program for 3-D Jacobi iteration, called StreamJacobi, of various aspects of the stream processor architecture. Finally, we analyze the performance of StreamJacobi, with different scales, and the presented optimizations. The final stream program StreamJacobi is from 2.43 to 11.48 times faster than the corresponding FORTRAN programs on a Xeon processor, with the optimizations playing an important role in realizing the performance improvement.