Massively Parallel Implementation of Divide-and-Conquer Jacobi Iterations Using Particle-Mesh Ewald for Force Field Polarization.

To accelerate the evaluation of the self-consistent polarization in large condensed-phase systems with polarizable force fields, the new divide-and-conquer Jacobi iterations (DC-JI) solver is adapted for periodic boundary conditions with particle-mesh Ewald and implemented in a massively parallel fashion within the Tinker-HP software package. DC-JI captures the mutual polarization of close-range interactions within subclusters of atoms using Cholesky decomposition and couples in the polarization effects between these clusters iteratively. Iterative convergence is accelerated with direct inversion of the iterative subspace (DIIS) extrapolation. Compared to widely used preconditioned conjugate gradient (PCG) or conventional Jacobi iterations (JI/DIIS) algorithms, DC-JI/DIIS solves the polarization equations ∼20-30% faster in protein systems ranging from ∼10,000-175,000 atoms run on hundreds of processor cores. This translates to ∼10-15% speed-ups in the number of nanoseconds of simulation time that can be achieved per day. Not only is DC-JI/DIIS faster than PCG, but it also gives more energetically robust solutions for a given convergence threshold. These improvements make numerically robust polarizable force field simulations more computationally tractable for chemical systems of interest.