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 Poi...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.展开更多
In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated wi...In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.展开更多
基金supported by NSF,DOE,HHMI,and NIH(B.Z./X.S./N.P.:NSF 0905164,B.Z./J.H.:NSF 0811130 and NSF 0905473,J.A.M.:NSF MCB1020765 and NIH GM31749)the NSF Center of Theoretical Biological Physics(CTBP)partially funded by the Chinese Academy of Sciences,the State Key Laboratory of Scientific/Engineering Computing,and the China NSF(NSFC1097218).
文摘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.
基金This work is partially supported by Hong Kong Research Grants Council General Research Fund 604208 and the Nano Science and Technology Program at HKUST.
文摘In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.
