High Order Compact Multigrid Solver for Implicit Solvation Models.

Abstract

The electrostatic problem defined by the continuum solvation models used in molecular mechanics and ab initio molecular dynamics is solved in real space through multiscale methods. First, the Poisson equation is rewritten as a stationary convection-diffusion equation and discretized by a general mesh size fourth-order compact difference scheme. Then, the linear system associated with such a discrete version of the elliptic partial differential equation is solved by a parallel (geometric) multigrid solver whose convergence rates and robustness are improved by an iterant recombination technique in which the multigrid acts as a preconditioner of a Krylov subspace method. The numerical tests performed on ideal and physical systems described by linear Poisson equations under different boundary conditions show the good performance of this accelerated multigrid solver. Furthermore, nonlinear Poisson equations, like the regular modified Poisson-Boltzmann equation, can also be solved by using in addition simple iterative schemes.