In this paper, we describe the performance and accuracy of the P2M2 tree code. The P2M2 tree code is a highaccuracy tree code based on the pseudoparticle multipole method (P2M2). P2M2 is a method to express multipole expansion using a small number of pseudoparticles. The potential field of physical particles is approximated by the field generated by the pseudoparticles. The primary advantage of...

The atoms in molecules (AIM) theory may be used to derive atomic charges, atomic volumes and molecular dipole moments from the charge density. The theory is applied to theoretical periodic Hartree-Fock (PHF), density-functional (DFT) and experimental X-ray densities of p-nitroaniline using the program TOPOND and a newly developed program, TOPXD, for topological analysis of densities described b...

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case. Using Herberthson’s method we also devel...

A combination of hierarchical tree-like data structures and data access patterns from fast multipole methods and hierarchical low-rank approximation of linear operators from H-matrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations of scientific computing at the exascale. The combination provides asymptotically optimal computat...

A diagonal form fast multipole boundary element method (BEM) is presented in this paper for solving 3-D acoustic wave problems based on the Burton–Miller boundary integral equation (BIE) formulation. Analytical expressions of the moments in the diagonal fast multipole BEM are derived for constant elements, which are shown to be more accurate, stable and efficient than those using direct numeric...

In the analysis of an acoustic radiation mode of a baffled plate, Rayleigh integral with free space Green’s function is involved. The boundary element method (BEM) is one of the approaches to compute its modes and radiation efficiencies. In this paper a fast multipole BEM in conjunction with an iterative solver based on the implicit restart Arnold method is proposed to efficiently and accuratel...

The projected mass of a gravitational lens inside (circular) apertures can be derived from the measured shear inside an annulus which is caused by the tidal eld of the deeecting mass distribution. Here we show that also the multipoles of the two-dimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the s...

In this paper, we present a fast multipole method (FMM) for the half-space Green’s function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (1936). The image structure of this Green’s function is unbounded, so that standard outgoing representations are not easily available. We introduce two such representations here, one inv...

This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ )θ , with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number...

Many models in natural and social sciences are comprised of sets of interacting entities whose intensity of interaction decreases with distance. This often leads to structures of interest in these models composed of dense packs of entities. Fast Multipole Methods are a family of methods developed to help with the calculation of a number of computable models such as described above. We propose a...