Volume 13, Issue 1
Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Bo Zhang ,  Benzhuo Lu ,  Xiaolin Cheng ,  Jingfang Huang ,  Nikos P. Pitsianis ,  Xiaobai Sun and J. Andrew McCammon


Commun. Comput. Phys., 13 (2013), pp. 107-128.

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  • Abstract

This paper summarizes the mathematical and numerical theories and computational elementsoftheadaptivefastmultipole 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 discretizationapproach, 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 ef´Čüciency, 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.

  • History

Published online: 2013-01

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