scholarly journals Fast Multipole Methods for Three-Dimensional N-Body Problems

2000 ◽  
pp. 284-300
Keyword(s):  
Three Dimensional ◽  
Fast Multipole ◽  
Fast Multipole Methods ◽  
Multipole Methods

scholarly journals Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Matthias Kirchhart ◽  
Donat Weniger
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Fast Multipole ◽  
Newton Potential ◽  
Fast Multipole Methods ◽  
Analytic Integration ◽  
Multipole Methods ◽  
Arbitrary Precision ◽  
Three Dimensional Space

Abstract We present simplified formulæ for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-to-use C++ library that allows computations in arbitrary precision arithmetic which is also documented here. We describe how these results can be combined with fast multipole methods to evaluate the Newton potential of more general, non-polynomial densities.

scholarly journals Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

2013 ◽  
Vol 13 (1) ◽  
pp. 107-128 ◽  
Author(s):  
Bo Zhang ◽  
Benzhuo Lu ◽  
Xiaolin Cheng ◽  
Jingfang Huang ◽  
Nikos P. Pitsianis ◽  
...  
Keyword(s):  
Large Scale ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Fast Multipole Methods ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Multipole Methods ◽  
Surface Mesh Generation ◽  
Dynamics Simulations ◽  
Boltzmann Model

AbstractThis 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 large-scale long-time molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.

scholarly journals Fast multipole methods for particle dynamics

2006 ◽  
Vol 32 (10-11) ◽  
pp. 775-790 ◽  
Author(s):  
J. Kurzak ◽  
B. M. Pettitt
Keyword(s):  
Particle Dynamics ◽  
Fast Multipole ◽  
Fast Multipole Methods ◽  
Multipole Methods

On solving continuum-mechanics problems by fast multipole methods

2017 ◽  
Vol 62 (8) ◽  
pp. 400-402
Author(s):  
A. M. Linkov ◽  
E. Rejwer ◽  
L. Rybarska-Rusinek
Keyword(s):  
Continuum Mechanics ◽  
Fast Multipole ◽  
Fast Multipole Methods ◽  
Multipole Methods

Accelerating fast multipole methods for the Helmholtz equation at low frequencies

1998 ◽  
Vol 5 (3) ◽  
pp. 32-38 ◽  
Author(s):  
L. Greengard ◽  
Jingfang Huang ◽  
V. Rokhlin ◽  
S. Wandzura
Keyword(s):  
Helmholtz Equation ◽  
Fast Multipole ◽  
Low Frequencies ◽  
Fast Multipole Methods ◽  
Multipole Methods
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