The procedure of derivation of the wave equation is reviewed, it been pointed out that, while for a medium at rest there is a clear correspondence between point multipole sources originating from the expansion of a general source term and with multipoles resulting from singularities in the continuity and momentum equations, this is not so for a moving medium. Thus, a classification of source mu...

In this work, we propose a novel and efficient solution for the generalized multipole technique (GMT): the localized iterative generalized multipole technique (LIGMT). In LIGMT, an analytic constraint is imposed on the power radiated by the set of multipole sources sharing the same origin, rendering it minimum over a given angular sector. In this way, the power radiated by each set of multipole...

We consider the problem of interpolating scattered data using spline methods and present a general framework of using the multipole method to accelerate the evaluation of splines. The method depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation. We also illustrate the performance of the ...

We compute the effect of scattering gravitational radiation off static background curvature, up to second order in Newton constant, known literature as tail and tail-of-tail processes, for generic electric magnetic multipoles. Starting from multipole expansion composite compact objects, expected due quadrupole case, both long- short-distance (UV) divergences are encountered. The former disappea...

The N-body simulation has been used extensively in study of the dynamics of galactic systems, uid, and biomolecules. It is known to be computational bound due to direct force calculation among bodies in the system. The time complexity is O(N 2) where N is the number of bodies. Fast multipole algorithm, proposed by Greengard and Rokhlin, reduces the complexity to O(N). Tremendous amount of work ...

Multipole radiofrequency ion traps are a highly versatile tool to study molecular ions and their interactions in a well-controllable environment. In particular the cryogenic 22-pole ion trap configuration is used to study ion-molecule reactions and complex molecular spectroscopy at temperatures between few Kelvin and room temperatures. This article presents a tutorial on radiofrequency ion trap...

A fundamental assumption in cosmology is that of statistical isotropy—that the Universe, on average, looks the same in every direction in the sky. Statistical isotropy has recently been tested stringently using cosmic microwave background data, leading to intriguing results on large angular scales. Here we apply some of the same techniques used in the cosmic microwave background to the distribu...

Dense operators for preconditioning sparse linear systems have traditionally been considered infeasible due to their excessive computational and memory requirements. With the emergence of techniques such as block low-rank approximations and hierarchical multipole approximations, the cost of computing and storing these preconditioners has reduced dramatically. This paper describes the use of mul...