TY - JOUR T1 - Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver JO - Communications in Computational Physics VL - 1 SP - 107 EP - 128 PY - 2013 DA - 2013/01 SN - 13 DO - http://doi.org/10.4208/cicp.210711.111111s UR - https://global-sci.org/intro/article_detail/cicp/7214.html KW - AB -

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 node-patch 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 large-scale long-time molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.