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 & J. Andrew McCammon

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

Published online: 2013-01

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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 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.


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@Article{CiCP-13-107, author = {Bo Zhang, Benzhuo Lu, Xiaolin Cheng, Jingfang Huang, Nikos P. Pitsianis, Xiaobai Sun and J. Andrew McCammon}, 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 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 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210711.111111s}, url = {http://global-sci.org/intro/article_detail/cicp/7214.html} }
TY - JOUR T1 - Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver AU - Bo Zhang, Benzhuo Lu, Xiaolin Cheng, Jingfang Huang, Nikos P. Pitsianis, Xiaobai Sun & J. Andrew McCammon JO - Communications in Computational Physics VL - 1 SP - 107 EP - 128 PY - 2013 DA - 2013/01 SN - 13 DO - http://dor.org/10.4208/cicp.210711.111111s UR - https://global-sci.org/intro/cicp/7214.html KW - AB -

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 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.


Bo Zhang, Benzhuo Lu, Xiaolin Cheng, Jingfang Huang, Nikos P. Pitsianis, Xiaobai Sun & J. Andrew McCammon. (1970). Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver. Communications in Computational Physics. 13 (1). 107-128. doi:10.4208/cicp.210711.111111s
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