We present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1/r, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p and 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p (with a > 0) in both two and three dimensions. Our algorithm is an extension of the kernel independent fast multipole method presented in Ying et al. [L. Y...

In this article we develop a method of finding the static axisymmetric space-time corresponding to any given set of multipole moments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static space-time for any g...

Recently, hierarchical capacitance extraction algorithms have been shown an efficient and accurate capacitance extraction algorithm. An improved algorithm is also proposed to remove its runtime dependency on the number of conductors by a combination of hierarchical and multipole expansion algorithm. In this paper, we show that with the introduction of hierarchical merging operation and supernod...

Reconstructing neuronal activity from MEG and EEG measurements requires the accurate calculation of the electromagnetic field inside the head. The boundary element formulation of this problem leads to a dense linear system which is too large to be solved directly. We propose to accelerate the computations via the fast multipole method. This method approximates the electromagnetic interaction be...

We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical ha...

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 field of the deflecting mass distribution. Here we show that also the multipoles of the twodimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the...

In this paper the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on R. We also give a bound on the multipole moments. This gives a proof of the ”necessary part” of a long standing conjecture due to Geroch.

This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order the fast multipole method and its kernel independent variant, the hierarchical matrix framework, the wavelet based method, the high frequency fast multipole method, and the recently proposed multi...

A symmetric Galerkin boundary-element method is used for the solution of boundary-value problems with mixed boundary conditions of Dirichlet and Neumann type. As a model problem we consider the Laplace equation. When an iterative scheme is employed for solving the resulting linear system, the discrete boundary integral operators are realized by the fast multipole method. While the single-layer ...