The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less thanO (N) operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the mult...

This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We ...

We give a fast numerical algorithm to evaluate a class of multivariable integrals. A direct numerical evaluation of these integrals costs Nm, where m is the number of variables and N is the number of the quadrature points for each variable. For m = 2 and m = 3 and for only one-dimensional variables, we present an algorithm which is able to reduce this cost from Nm to a cost of the order of O((−...

A diagonal form fast multipole boundary element method (BEM) is presented in this paper for solving 3-D acoustic wave problems based on the Burton–Miller boundary integral equation (BIE) formulation. Analytical expressions of the moments in the diagonal fast multipole BEM are derived for constant elements, which are shown to be more accurate, stable and efficient than those using direct numeric...

In the analysis of an acoustic radiation mode of a baffled plate, Rayleigh integral with free space Green’s function is involved. The boundary element method (BEM) is one of the approaches to compute its modes and radiation efficiencies. In this paper a fast multipole BEM in conjunction with an iterative solver based on the implicit restart Arnold method is proposed to efficiently and accuratel...

In this paper, we describe the performance and accuracy of the P2M2 tree code. The P2M2 tree code is a highaccuracy tree code based on the pseudoparticle multipole method (P2M2). P2M2 is a method to express multipole expansion using a small number of pseudoparticles. The potential field of physical particles is approximated by the field generated by the pseudoparticles. The primary advantage of...