The Fast Multipole Method (FMM) obeys periodic boundary conditions "natively" if it uses a Green function for computing the multipole expansion in interaction zone of each FMM oct-tree node. One can define "optimal" such method that results numerical solution converges to equivalent Particle-Mesh limit sufficiently high order multipoles. A discrete functional equation optimal be derived, but is...

We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for on-going and future high precious sky surveys. It makes use of truncated Fast Multiple Method (FMM) short-range gravity, incorporating with Particle Mesh (PM) method long-range potential, which is applied to deal extremely large particle number. In this work, we present specific strategy modi...

Vector spline techniques have been developed as general-purpose methods for vector eld reconstruction. However, such vector splines involve high computational complexity, which precludes applications of this technique to many problems using large data sets. In this paper, we develop a fast multipole method for the rapid evaluation of the vector spline in three dimensions. The algorithm depends ...

We present an implementation of the fast multipole method for computing Coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected O(N) scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation ...

In this paper, we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm. When the buffer size is large enough, the error can be controlled and minimized by using the conventional selection rules. On the other hand, if the buffer size is small, the conventional selection rules no longer hold, and the new approach which ...