On the optimal number of subdomains for hyperbolic problems on parallel computers

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for the numerical solution of hyperbolic problems. The complexity analysis is based on theoretical results that predict error as a function of (q,n) for problems having wavelike solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q,n) as a function of the number of processors. It is shown that, for present-day multicomputers, the impact of communication overhead does not significantly shift (q,n) from the optimal uniprocessor values and that the effects of granularity are more important.