Parameter multi-domain hp' empirical interpolation

In this paper, we introduce two parameter multi-domain hp techniques for the empirical interpolation method (EIM). In both approaches, we construct a partition of the original parameter domain into parameter subdomains: h-refinement. We apply the standard EIM independently within each subdomain to yield local (in parameter) approximation spaces: p-refinement. Further, for a particularly simple case, we introduce a priori convergence theory for the partition procedure. We show through two numerical examples that our approaches provide significant reduction in the EIM approximation space dimension and thus significantly?reduce the computational cost associated with EIM approximations. Copyright (C) 2012 John Wiley & Sons, Ltd.