Optimal decomposition of the domain in spectral methods or wave-like phenomena

A strategy for determining the optimal number of grid points and subdomains in a spectral method with domain decomposition on a serial computer is pre sented. The rapidly growing computational cost for large numbers of grid po ints in each subdomain is balanced against the exponential convergence for spectral approximation of smooth functions, and the optimum is found as the number of grid points and subdomains that gives the minimal computational cost for a given accuracy. The typical length scale of the problem is found to influence the number of subdomains but not the number of grid points wi thin each subdomain.