Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle mesh multipole method: An efficient solver for
  gravitational/electrostatic forces based on multipole method and fast
  convolution over a uniform mesh   We propose an efficient algorithm for the evaluation of the potential and its
gradient of gravitational/electrostatic $N$-body systems, which we call
particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as
an extension of the particle mesh (PM) method and as an optimization of the
fast multipole method (FMM).In the former viewpoint, the scalar density and
potential held by a grid point are extended to multipole moments and local
expansions in $(p+1)^2$ real numbers, where $p$ is the order of expansion. In
the latter viewpoint, a hierarchical octree structure which brings its
$\mathcal O(N)$ nature, is replaced with a uniform mesh structure, and we
exploit the convolution theorem with fast Fourier transform (FFT) to speed up
the calculations. Hence, independent $(p+1)^2$ FFTs with the size equal to the
number of grid points are performed.
  The fundamental idea is common to PPPM/MPE by Shimada et al. (1993) and FFTM
by Ong et al. (2003). PMMM differs from them in supporting both the open and
periodic boundary conditions, and employing an irreducible form where both the
multipole moments and local expansions are expressed in $(p+1)^2$ real numbers
and the transformation matrices in $(2p+1)^2$ real numbers.
  The computational complexity is the larger of $\mathcal O(p^2 N)$ and
$\mathcal O(N \log (N/p^2))$, and the memory demand is $\mathcal O(N)$ when the
number of grid points is $\propto N/p^2$.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys