@Article{CiCP-13-107, author = {}, title = {Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {1}, pages = {107--128}, 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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210711.111111s}, url = {http://global-sci.org/intro/article_detail/cicp/7214.html} }