Realistic applications of numerical modeling of acoustic wave dynamics usually demand high-performance computing because of the large size of study domains and demanding accuracy requirements on simulation results. Forward modeling of seismic motion on a given subsurface geological structure is by itself a good example of such applications, and when used as a component of seismic inversion tools or as a guide for the design of seismic surveys, its computational cost increases enormously. In the case of finite difference methods (or any other volumen-discretization scheme), memory and computing demands rise with grid refinement, which may be necessary to reduce errors on numerical wave patterns and better capture target physical devices. In this work, we present several implementations of a mimetic finite difference method for the simulation of acoustic wave propagation on highly dense staggered grids. These implementations evolve as different optimization strategies are employed starting from appropriate setting of compilation flags, code vectorization by using streaming SIMD extensions Advanced Vector Extensions (AVX), CPU parallelization by exploiting the Open Multi-Processing framework to the final code parallelization on graphics processing unit platforms. We present and discuss the increasing processing speed up of this mimetic scheme achieved by the gradual implementation and testing of all these performance optimizations. In terms of simulation times, the performance of our graphics processing unit parallel implementations is consistently better than the best CPU version. Copyright © 2016 John Wiley & Sons, Ltd.