Parameter multi‐domain ‘hp’ empirical interpolation

SUMMARY 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.