  Tachyonic preheating is realized when the inflaton repeatedly returns to a
convex region of the potential during the post-inflationary oscillating phase.
This will induce a strong tachyonic instability and lead to a rapid
fragmentation of the coherent field that can complete within a fraction of an
$e$-fold. In this paper, we study the linear regime of this process in a
model-independent way. To this purpose, we construct simplified models that
provide an analytic Floquet theoretic description of mode growth. This approach
captures the essential features of well-motivated tachyonic preheating
scenarios, including scenarios in which the inflaton is part of a larger scalar
multiplet. We show that tachyonic preheating is efficient if the field
excursions are sub-Planckian, can produce gravitational waves in the frequency
range of current and future gravitational wave interferometers, and can be
consistent with any experimentally allowed tensor-to-scalar ratio.
