Regularizing the fast multipole method for use in molecular simulation

The parallel scaling of classical molecular dynamics simulations is limited by the communication of the 3D fast Fourier transform of the particle-mesh electrostatics methods, which are used by most molecular simulation packages. The Fast Multipole Method (FMM) has much lower communication requirements and would, therefore, be a promising alternative to mesh based approaches. However, the abrupt switch from direct particle-particle interactions to approximate multipole interactions causes a violation of energy conservation, which is required in molecular dynamics. To counteract this effect, higher accuracy must be requested from the FMM, leading to a substantially increased computational cost. Here, we present a regularization of the FMM that provides analytical energy conservation. This allows the use of a precision comparable to that used with particle-mesh methods, which significantly increases the efficiency. With an application to a 2D system of dipolar molecules representative of water, we show that the regularization not only provides energy conservation but also significantly improves the accuracy. The latter is possible due to the local charge neutrality in molecular systems. Additionally, we show that the regularization reduces the multipole coefficients for a 3D water model even more than in our 2D example.