Efficient Polarization Solvers for Classical Molecular Dynamics Simulations

The primary focus of this dissertation is the acceleration of the evaluation of the self-consistent polarization energy. Two new variants of Jacobi iterations are proposed here that exploit domain decomposition to accelerate the convergence of the induced dipoles. The first, divide-and-conquer JI (DC-JI), is a block Jacobi algorithm which solves the polarization equations within non-overlapping sub-clusters of atoms directly via Cholesky decomposition, and iterates to capture interactions between sub-clusters. The second, fuzzy DC-JI, achieves further acceleration by employing overlapping blocks. These algorithms employ knowledge of the 3-D spatial interactions to group important elements in the 2-D polarization matrix. These methods can be coupled with direct inversion in the iterative subspace (DIIS) extrapolation to accelerate their convergence.The DC-JI solver is adapted for periodic boundary conditions with particle-mesh Ewald treatment of long-range interactions and implemented in a massively parallel fashion within the Tinker-HP software package. 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. Not only is DC-JI/DIIS faster than PCG, but it also gives more energetically robust solutions for a given convergence threshold. We further demonstrate how one can improve the stability of a polarizable force field molecular dynamics simulation or accelerate the evaluation of self-consistent polarization via a simple extension of the predictor in the Always Stable Predictor-Corrector (ASPC) method. Specifically, increasing the number of prior steps used in the predictor from six to sixteen reduces the energy drift by an order of magnitude. Alternatively, for a given level of energy drift, the induced dipoles can be obtained ~20% faster due to the reduced number of self-consistent field iterations required to maintain energetic stability.Finally, we have developed an averaged condensed phase environment (ACPE) model that address the high computational cost associated with modeling configurational average properties with quantum mechanics/molecular mechanics (QM/MM) simulations. In the domain of embedding techniques ACPE lies in between explicit QM/MM evaluation of sampled configurations and continuum models. The ACPE model constructs an effective polarizable environment directly from explicitly sampled molecular dynamics configurations. ACPE can reduce the need for hundreds of QM/MM calculations to a few representative QM/MM calculations