We perform large-scale finite-difference time-domain (FDTD) simulations with the aid of efficient parallel-computing algorithms for designing optical and acoustic metamaterials, where either electromagnetic or elastic constants in the materials are artificially modulated via nano/micro-structuring. For optical metamaterials, effects of nanostructure on dielectric properties are taken into account by introducing the Drude-Lorentz model and a hybrid quantum-mechanical/classical FDTD method for optical dispersion of simple metal particles. Using these computational methods, we assess the materials dependence of light-confinement efficiency in the recently proposed novel structure that combines dielectrics and metamaterials periodically. In the acoustic case, we perform the parallel FDTD simulations of elastic-wave propagations in 2D phononic crystals. The negative refraction of acoustic wave is shown to occur via a negative effective mass appeared in their phonon band-structures. We demonstrate that the focal intensity by the lens effect and its energy-transfer efficiency can be optimized by adapting the filling fraction of the crystal.