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About 2,280 papers for “Fast multipole method”

Fast Multipole Method

E. J. Hinch · Cambridge University Press eBooks · 2020

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Cited by 0

Generalized fast multipole method

Pierre-David Létourneau, Cristopher Cecka, Eric Darve · IOP Conference Series Materials Science and Engineering · 2010

The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between N points in O(N) or O(N ln N) steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems arising from such formulations. Original FMMs required analytical expansions of the kernel, for example using spherical harmonics or Taylor expansions. In recent years, the range of applicability and the ease of use of FMMs has been extended by the introduction of black box [1] or kernel independent techniques [2]. In these approaches, the user only provides a subroutine to numerically calculate the interaction kernel. This allows changing the definition of the kernel with minimal change to the computer program. In this talk we will present a novel kernel independent FMM, which leads to diagonal multipole-to-local operators. This results in a significant reduction in the computational cost [1], in particular when high accuracy is needed. The approach is based on Cauchy's integral formula and the Laplace transform. We will present a numerical analysis of the convergence, methods to choose the parameters in the FMM given some tolerance, and the steps required to build a multilevel scheme from the single level formulation. Numerical results are given for benchmark calculations to demonstrate the accuracy as a function of the number of multipole coefficients, and the computational cost of the different steps in the method.

Cited by 5Open access

The Fast Multipole Method

Dianne P. O’leary, Xiaobai Sun · 2013

What is the FMM? In many applications, it is important to compute, for example, • the gravitational potential arising from a distribution of masses • electrostatic potential arising from a distribution of charges Picture. We’ll talk about charges, for definiteness. Suppose that the charge on source particle j, which is located at position sj, is qj, j = 1,..., n. Then to compute the potential pk at target particle k, located at position tk, we compute k = 1,..., m. pk = n∑ j=1 qj ‖tk − sj‖β For notational convenience, we take β = 1, but it really doesn’t matter. Notice that computing all of the potentials is just a matrix-vector product

Cited by 0

A Provably Fast Multipole Method

Hachul, Stefan, Jünger, Michael · Kölner Universitäts PublikationsServer (Universität zu Köln) · 2006

The evaluation of potential or force fields in systems of N particles whose interactions are Coulombic or gravitational is very important for several applications in natural science, applied mathematics, and computer science. A naive direct calculation of the interactions needs Theta(N^2) time per time step which is inappropriate for large systems.Therefore, fast hierarchical algorithms (called tree codes) are used that approximate the pairwise interactions in the systems. We present a new multipole-based tree code that runs in O(N) time in the best case and in O(N log N) time in the worst case. This is an improvement in comparison with existing tree codes: Few of them run in Theta(N log N) time. Others are O(N) or O(N log N) in the best case but quadratic or even unbounded in the worst case. Our practical experiments indicate that the new multipole method is faster than several popular hierarchical N -body simulation algorithms for both uniform and highly non-uniform particle distributions.

Cited by 0

Fast multipole method on GPU

Xueqian Zhao, Zhuo Feng · 2011

To facilitate full chip capacitance extraction, field solvers are typically deployed for characterizing capacitance libraries for various interconnect structures and configurations. In the past decades, various algorithms for accelerating boundary element methods (BEM) have been developed to improve the efficiency of field solvers for capacitance extraction. This paper presents the first massively parallel capacitance extraction algorithm FMMGpu that accelerates the well-known fast multipole methods (FMM) on modern Graphics Processing Units (GPUs). We propose GPU-friendly data structures and SIMD parallel algorithm flows to facilitate the FMM-based 3-D capacitance extraction on GPU. Effective GPU performance modeling methods are also proposed to properly balance the workload of each critical kernel in our FMMGpu implementation, by taking advantage of the latest Fermi GPU's concurrent kernel executions on streaming multiprocessors (SMs). Our experimental results show that FMMGpu brings 22X to 30X speedups in capacitance extractions for various test cases. We also show that even for small test cases that may not well utilize GPU's hardware resources, the proposed cube clustering and workload balancing techniques can bring 20% to 60% extra performance improvements.

Cited by 16

Fast Multipole Boundary Element Method

Yijun Liu · Cambridge University Press eBooks · 2009

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.

Cited by 400

Nonsymmetric Algebraic Fast Multipole Method

Reiz, Severin; Biros, George; Bungartz, Hans-Joachim · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2019

Cited by 0Open access