We present the first (3 + 1)-dimensional numerical simulations of scalar fields with nonminimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld inflaton coupled to a canonical matter field. The simulations represent the full nonlinear theory in the presence of an expanding universe. We show that parametric resonance in the matter field along with self-resonance in the inflaton repopulate the universe with matter particles as efficiently as in traditional preheating.Scalar fields need not be Klein-Gordon-like in four dimensions; theories that include extra dimensions, whether large or small, have effective four-dimensional kinetic terms that are nonminimal. This has led to an increased interest in the dynamics of nonminimal models both to describe inflation, e.g. Dirac-Born-Infeld (DBI) inflation [1], and even more recently, dark energy [2][3][4]. In this Letter, we will focus on DBI inflation, as an example of a system for which we have a scalar degree of freedom whose behavior is self-consistent and stable and whose nonminimal behavior is central to the dynamics of the model. Here, we focus on what happens at the end of inflation when the scalar inflaton becomes inhomogeneous and its couplings to other fields are important. To our knowledge, these are the first three-dimensional lattice simulations of this type of field theory.Preheating [5][6][7][8][9][10][11][12][13][14][15][16][17] provides a mechanism by which the cold postinflationary universe can quickly and efficiently transfer energy into a matter sector, via a period of parametric resonance or a regime of tachyonic instability. For the most part, studies of preheating have focused on the existence and stability of these processes in the presence of different inflationary potentials, e.g., Refs. [17][18][19][20][21][22], multiple fields [23], and multiple decay channels [24]. DBI inflation might end with a coherently oscillating scalar field, and it has been unclear whether preheating can persist in the presence of nonlinear terms in its equation of motion. The search for preheating in nonminimal models began in the work of Ref. [25], where the authors showed that a canonical scalar field can enhance the effects of parametric resonance in a coupled nonminimal matter field.