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...

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...

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...

Article history: Received 8 March 2010 Received in revised form 1 September 2010 Accepted 15 September 2010

Article history: Received 30 April 2009 Received in revised form 25 June 2009 Accepted 29 June 2009 Available online 2 July 2009 PACS: 02.30.Em 02.30.Rz 02.60.Dc 24.10.Cn

We present a matrix interpretation of the three-dimensional fast multipole method (FMM). The FMM is for efficient computation of gravitational/electrostatic potentials and fields. It has found various applications and inspired the design of many efficient algorithms. The one-dimensional FMM is well interpreted in terms of matrix computations. The threedimensional matrix version reveals the unde...

The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be eliminated by overlapping multipole and local expansion computations with direct kernel evaluations on the finest level grid.

We present a simple and robust method for computing skeletons for arbitrary planar objects and centerlines for 3D objects. We augment the Fast Marching Method (FMM) widely used in level set applications 11 by computing the paramterized boundary location every pixel came from during the boundary evolution. The resulting parameter field is then thresholded to produce the skeleton branches created...