Abstract
. This paper summarizes the mathematical and numerical theories and computational
elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver.
We introduce and discuss the following components in order: the Poisson-Boltzmann
model, boundary integral equation reformulation, surface mesh generation, the nodepatch
discretization approach, Krylov iterative methods, the new version of fast multipole
methods (FMMs), and a dynamic prioritization technique for scheduling parallel
operations. For each component, we also remark on feasible approaches for further
improvements in efficiency, accuracy and applicability of the AFMPB solver to largescale
long-time molecular dynamics simulations. The potential of the solver is demonstrated
with preliminary numerical results.