In this paper we discuss the development and implementation of volumetric integral equations for both dielectric and magnetically permeable materials using curvilinear hexahedral elements. Both piecewise constant and higher order basis functions will be examined in the context of volumetric multilevel fast multipole method implementation. Comparisons with corresponding finite element– boundary ...

This paper introduces two techniques for approximating the Biot–Savart integral for deforming elliptical Gaussian functions. The primary motivation is to develop a high spatial accuracy vortex method. The first technique is a regular perturbation of the streamfunction in the small parameter = a−1 a+1 , where a2 is the aspect ratio of the basis function. This perturbative technique is suitable f...

In this paper, we propose a novel method to extend the fast multipole method (FMM) to calculate the electrostatic potential due to charges inside or outside a dielectric sphere. The key result which allows such an extension is the construction of a small number (two for a 10 2 relative error in reaction potentials inside the sphere) of image point charges for source point charges inside or outs...

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...