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6.2.3 Parallel Issues

The code used in this study parallelizes well for a number of reasons. The discretization is static and regular, and the same operations are applied at each grid point, even though the evolution of the system is nonlinear. Thus, the problem can be statically load balanced  at the start of the code by ensuring that each processor's rectangular subdomain contains the same number of grid points. In addition, the physics, and hence the algorithm, is local so the finite difference algorithm only requires communication between nearest neighbors in the hypercube topology. The extreme regularity of the FCT technique means that it can also be efficiently used to study convective transport on SIMD concurrent computers, such as the Connection Machine,   as has been done by Oran, et al. [Oran:90a].

No major changes were introduced into the sequential code in parallelizing it for the hypercube architecture. Additional subroutines were inserted to decompose the problem domain into rectangular subdomains, and to perform interprocessor communication. Communication is necessary in applying the Courant condition to determine the size of the next time step, and in transferring field values at grid points lying along the edge of a processor's subdomain. Single rows and columns of field values were communicated as the algorithm required. Some inefficiency, due to communication latency,  could have been avoided if several rows and/or columns were communicated at the same time, but in order to avoid wasting memory on larger communication buffers, this was not done. This choice was dictated by the small amount of memory (about ) available on each nCUBE-1  processor.

Guy Robinson
Wed Mar 1 10:19:35 EST 1995