The consistent and computationally economical analysis of demanding amplification and filtering structures is introduced in this paper via a new spectrally-precise finite-volume time-domain algorithm. Combining a family of spatial derivative approximators with controllable accuracy in general curvilinear coordinates, the proposed method employs a fully conservative field flux formulation to derive electromagnetic quantities in areas with fine structural details. Moreover, the resulting 3-D operators assign the appropriate weight to each spatial stencil at arbitrary media interfaces, while for periodic components the domain is systematically divided to a number of nonoverlapping subdomains. Numerical results from various real-world configurations verify our technique and reveal its universality.