Innovation and tradition are two fundamental factors in the design of new digital musical instruments. Although apparently mutually exclusive, novelty does not imply a total disconnection from what we have inherited from hundreds of years of traditional design, and the balance of these two factors often determines the overall quality of an instrument. Inspired by this rationale, in this article we introduce the Hyper Drumhead, a novel augmented virtual instrument whose design is deeply rooted in traditional musical paradigms, yet aimed at the exploration of unprecedented sounds and control. In the first part of the article we analyze the concepts of designing an augmented virtual instrument, explaining their connection with the practice of augmenting traditional instruments. Then we describe the design of the Hyper Drumhead in detail, focusing on its innovative physical modeling implementation. The finite-difference time-domain solver that we use runs on the parallel cores of a commercially available graphics card and permits the simulation of real-time 2-D wave propagation in massively sized domains. Thanks to the modularity of this implementation, musicians can create several 2-D virtual percussive instruments that support realistic playing techniques but whose affordances can be enhanced beyond most of the limits of traditional augmentation.