Initial results (MUSICO )

We tested a splitting of the electrostatics using the splitting of [6] for the short-range electrostatics. The splitting of the electrostatic force is

$$F^{\mathrm{elect}}=F^{\mathrm{short,elect}}(\vec{x}_{n+1/2}+\alpha\Delta t^{2}F^{\mathrm{short,elect}})+F^{\mathrm{long,elect}}(\vec{x}_{n+1/2}),$$ (5)

where $\alpha\neq0$. The implicit part was solved as the minimization to a dynamics function [74,98]. Since $F^{\mathrm{short,elect}}$ has been linearized by the splitting, it can be expressed as the inversion of a sparse linear system. The resulting matrix is symmetric but indefinite. We solved this system using a Krylov subspace method, namely a preconditioned conjugate residual method [5]. Our analysis of time steps possible predicts that using a splitting cutoff of 12Å time steps of 84fs should be possible [44]. These time steps do not necessarily correlate with true MD, since we only incorporate the electrostatic force, but they are encouraging preliminary results. Also, because of the symmetry and the good behavior of the splitting, each Krylov step was nearly the same work as a step of integration using leapfrog. The approach to extend this method is presented in Section 3.2.