A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of p...

This paper presents an efficient preconditioning technique in order to couple Partial Element Equivalent Circuit (PEEC) method with Fast Multipole algorithm (FMM).

This year, we have focused on the acceleration of two inverse operators, so that they can be used by the Compressive Sensing (CS) imaging algorithms in the future. In particular, the following activities were performed for this project: 1) Development of a multistatic FFT-based formulation for imaging applications; and 2) Acceleration of the multistatic Inverse Fast Multipole Method (I-FMM) usi...

A fast algorithm for reconstructing the profile of random rough surfaces using electromagnetic scattering data is presented. The algorithm is based on merging a fast forward solver and an efficient optimization technique. The steepest descent fast multipole method (SDFMM) is used as the three-dimensional (3-D) fast forward solver. A rapidly convergent descent method employing a “marching-on” st...

Spherical harmonic transform is the most important orthogonal function transform only except Fourier transform, and is used not only for climate simulation and signal processing but also for a base of several numerical algorithms. Fast Fourier Transform (FFT), which runs in time O(N logN) is quite well known, but, for spherical harmonic transform, there is no fast algorithm which is as simple a...

A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g. crystal structures, or indirectly through the discretization of PDEs. In the analog to solving continuous inhomogeneous differential equations using Green’s functi...

This paper discusses the scalability properties of a novel algorithm for the rapid evaluation of radial basis function interpolants. The algorithm is associated with the problem of force calculation in many-body calculations. Contrary to previously developed fast summation schemes including treecodes and fast multipole methods, this algorithm has simple communication patterns which are achieved...

Abstract. This paper introduces a new fast algorithm for uniform-resolution filtering of functions defined on the sphere. We use a fast summation algorithm based on Nonequispaced Fast Fourier Transforms, building on previous work that used Fast Multipole Methods. The resulting algorithm performs a triangular truncation of the spectral coefficients while avoiding the need for fast spherical Four...

The purpose of this study is to investigate the acoustic performance of mufflers. As a numerical scheme for analyzing an acoustic filter, the boundary element method is more suitable than are domain methods, such as the finite element method, which has to mesh the domain. However, the coefficient matrices established by the boundary element method are full and often non-symmetrical. In order to...