The computation of long-range potentials is one of the demanding tasks in Molecular Dynamics. During the last decades, an inventive panoply of methods was developed in order to reduce the CPU time of this task. In this work, we propose a fast method dedicated to the computation of the elec-trostatic potential in adaptively restrained systems. We exploit the fact that, in such systems, only some particles are allowed to move at each timestep. We developed an incremental algorithm derived from a multigrid-based alternative to traditional Fourier-based methods. Our algorithm was implemented inside LAMMPS, a popular molecular dynamics simulation package. We evaluated the method on different systems. We showed that the new algorithm's computational complexity scales with the number of active particles in the simulated system, and is able to outperform the well-established Particle Particle Particle Mesh (P3M) for adaptively restrained simulations.