Removal of spurious self-interactions in particle–mesh methods

We derive an analytic formula for subtracting the spurious self-forces in particle–mesh methods that use the analytical differentiation scheme, such as the Smooth Particle Mesh Ewald (SPME) method and the Particle–Particle Particle–Mesh (P3M) method with analytical differentiation. The impact of the self-forces on the accuracy of the particle–mesh methods is investigated, and it is shown that subtracting them can improve the accuracy of the calculation for some choices of the methodʼs parameters. It is also suggested to subtract exactly the approximate, mesh-computed, self-energy of each particle, replacing them by the exact value. Subtracting in this way the self-energy and self-force of each particle not only improves the accuracy, but also reduces the violation of momentum and energy conservation in particle–mesh methods with analytical differentiation.