We describe a wideband version of the Fast Multipole Method for the Helmholtz equation in three dimensions. It unifies previously existing versions of the FMM for high and low frequencies into an algorithm which is accurate and efficient for any frequency, having a CPU time of O(N) if low-frequency computations dominate, or O(N logN) if high-frequency computations dominate. The performance of t...

The Fast Multipole Method (FMM) designed by V. Rokhlin rapidly computes the field scattered from an obstacle. This computation consists of solving an integral equation on the boundary of the obstacle. The main result of this paper shows the convergence of the FMM for the two dimensional Helmholtz equation. Before giving the theorem, we give an overview of the main ideas of the FMM. This is done...

An image method due to Allen and Berkley (1979) is often used to simulate the effect of reverberation in rooms. This method is relatively expensive computationally. We present a fast method for conducting such simulations using multipole expansions. For M real and image sources and N evaluation points, while the image method requiresO(MN) operations, our method achieves the calculations in O(M ...

The evaluation of sums (matrix–vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

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...

We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numerically. We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numericall...

We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT solution by taking advantage of the isotropy of the scattering kernel, and solve the integral equation with a fast multipole method (FMM). In the second step, we s...

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts...

A method for the computation of the band structure of two-dimensional photonic crystals is presented. It is well suited for crystals including materials with arbitrary frequency-dependent dielectric constants. The technique can be applied to study photonic crystals with irregularly shaped ~noncircular! elements. This method is based on the multiple multipole method. In order to find the solutio...

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 ...