Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver
نویسندگان
چکیده
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. AMS subject classifications: 45B05, 65Y05, 68W10, 90B10, 92C05, 92C40
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