To extract useful information which really contribute to the target issue from huge amounts of data or text description is an important task towards a number of research fields (e.g., genomics study and text mining). In this paper, a general feature matrix model (FMM) is proposed aiming to provide partial answer to this task. Specifically, one instantiation of FMM is used for identifying featur...

Fast multipole methods (FMM) on distributed memory have traditionally used a bulk-synchronous model of communicating the local essential tree (LET) and overlapping it with computation of the local data. This could be perceived as an extreme case of data aggregation, where the whole LET is communicated at once. Charm++ allows a much finer control over the granularity of communication, and has a ...

An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the ...

The Fourier modal method (FMM) is based on Fourier expansions of the electromagnetic field and is inherently built for infinitely periodic structures. When the infinite periodicity assumption is not realistic, the finiteness of the structure has to be incorporated into the model. In this paper we discuss the recent extensions of the FMM for finite periodic structures and analyze their complexit...

In this paper we describe an efficient algorithm for computing the potentials of the form r−λ where λ ≥ 1. This treecode algorithm uses spherical harmonics to compute multipole coefficients that are used to evaluate these potentials. The key idea in this algorithm is the use of Gegenbauer polynomials to represent r−λ in a manner analogous to the use of Legendre polynomials for the expansion of ...

We present an adaptive fast multipole method for inverting the square root of the Laplacian in two dimensions. Solving this problem is the dominant computational cost in many applications arising in electrical engineering, geophysical fluid dynamics, and the study of thin films. It corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity. Our algorithm ...

In this paper we describe a new approach to implement the O(N) fast multipole method and O(N logN) tree method, which uses pseudoparticles to express the potential field. The new method is similar to Anderson’s method, which uses the values of potential at discrete points to represent the potential field. However, for the same expansion order the new method is more accurate and computationally ...

Higher order panel methods are used to solve the Laplace equation in the presence of complex geometries. These methods are useful when globally accurate velocity or potential fields are desired as in the case of vortex based fluid flow solvers. This paper develops a fast multipole algorithm to compute velocity fields due to higher order, two-dimensional vortex panels. The technique is applied t...

A method is presented for the computation of Schwarz–Christoffel maps to polygons with tens of thousands of vertices. Previously published algorithms have CPU time estimates of the order O(N3) for the computation of a conformal map of a polygon with N vertices. This has been reduced to O(N logN) by the use of the fast multipole method and Davis’s method for solving the parameter problem. The me...

This paper presents a new method for the fast evaluation of univariate radial basis functions of the form s(x) = ∑N n=1 dnφ(|x− xn|) to within accuracy . The method can be viewed as a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data. The method has the advantage of being adaptive to changes in ...