相关论文: A Simple Formulation of the Fast Multipole Method:…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media…
We describe a new implementation of a parallel Tree-SPH code with the aim to simulate Galaxy Formation and Evolution. The code has been parallelized using SHMEM, a Cray proprietary library to handle communications between the 256 processors…
Series expansions have been a cornerstone of applied mathematics and engineering for centuries. In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective. Specifically, we introduce the Fast Continuous…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
Large-scale MIMO systems can yield a substantial improvement in spectral efficiency for future communication systems. Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems have shown…
Raising the order of the multipole expansion is a feasible approach for improving the accuracy of the treecode algorithm. However, a uniform order for the expansion would result in the inefficiency of the implementation, especially when the…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…
Large-scale multi-user multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements for future communication systems. Counter-intuitively, the practical issues of having uncertain channel knowledge,…
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…
We introduce the use of the Fast Multipole Method (FMM) to speed up gravitational lensing ray tracing calculations. The method allows very fast calculation of ray deflections when a large number of deflectors, $N_*$, is involved, while…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
In this report, we describe three encodings of the multiple constant multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and introduce an algorithm to solve the MCM problem optimally. To the best of our knowledge, the…
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.…
A new approach for decoding binary linear codes by solving a linear program (LP) over a relaxed codeword polytope was recently proposed by Feldman et al. In this paper we investigate the structure of the polytope used in the LP relaxation…
We describe a parallel version of our tree-code for the simulation of self-gravitating systems in Astrophysics. It is based on a dynamic and adaptive method for the domain decomposition, which exploits the hierarchical data arrangement used…
The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the…