  In preparation to the exascale era, an alternative approach to calculate the
electrostatic forces in Particle Mesh (PM) methods is proposed. While the
traditional techniques are based on the calculation of the electrostatic
potential by solving the Poisson equation, in the new approach the electric
field is calculated by solving the Ampere's law. When the Ampere's law is
discretized explicitly in time, the electric field values on the mesh are
simply updated from the previous values. In this way, the electrostatic solver
becomes an embarrassingly parallel problem, making the algorithm extremely
scalable and suitable for exascale computing platforms. An implementation of a
one dimensional PM code is presented to show that the proposed method produces
correct results, and it is a very promising algorithm for exascale PM
simulations.
