The evolution of computational science over the last fifty years has enabled theoretical physics to expand its scope to include both analytic and numeric solutions to increasingly large and complex problems. One of the earliest developments in computational science was a fast solution to the many body problem called the Particle Mesh (PM) Method, which approximates the position of each particle on a grid in order to speed up computation. Simulations of plasmas and galaxy formation are just two examples of systems that have greatly benefited from PM. The classic PM method is applied to particles that interact according to a gravity-like force. This thesis presents a PM method for magnetic dipoles and elaborates on its differences to the gravity-like PM. The motivation for this method is an investigation into the thermal properties of the hard-sphere magnetic dipole system, such as its relationship between energy, temperature, and entropy. A true analysis of a thermal system requires a very large number of particles, much larger than our current simulation is capable of on a reasonable timescale. The first part of this thesis is an explanation as to how the particle mesh method actually operates, and a description of the particle particle-particle mesh method, which calculates the short range force directly. The second part of this thesis is a comparison of the results of the exact calculation method and the PM to demonstrate is effectiveness. Finally, we present new prospects for future simulations given the newly increased efficiency of simulation.