Particle–mesh interpolations are fundamental operations for particle-in-cell codes, as implemented in vortex methods, plasma dynamics and electrostatics simulations. In these simulations, the mesh is used to solve the field equations and the gradients of the fields are used in order to advance the particles. The time integration of particle trajectories is performed through an extensive resampling of the flow field at the particle locations. The computational performance of this resampling turns out to be limited by the memory bandwidth of the underlying computer architecture. We investigate how mesh–particle interpolation can be efficiently performed on graphics processing units (GPUs) and multicore central processing units (CPUs), and we present two implementation techniques. The single-precision results for the multicore CPU implementation show an acceleration of 45–70×, depending on system size, and an acceleration of 85–155× for the GPU implementation over an efficient single-threaded C++ implementation. In double precision, we observe a performance improvement of 30–40× for the multicore CPU implementation and 20–45× for the GPU implementation. With respect to the 16-threaded standard C++ implementation, the present CPU technique leads to a performance increase of roughly 2.8–3.7× in single precision and 1.7–2.4× in double precision, whereas the GPU technique leads to an improvement of 9× in single precision and 2.2–2.8× in double precision.