Smectic liquid crystals vividly illustrate the subtle interplay of broken translational and orientational symmetries, by exhibiting defect structures forming geometrically perfect confocal ellipses and hyperbolas. Here, we develop and numerically implement an effective theory to study the dynamics of focal conic domains in smectic-A liquid crystals. We use the information about the smectic's structure and energy density provided by our simulations to develop several novel visualization tools for the focal conics. Our simulations accurately describe both simple and extensional shear, which we compare to experiments, and provide additional insight into the coarsening dynamics of focal conic domains. © 2015 American Physical Society.