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The Fast Multipole Method
"... 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 ..."
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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 matrixvector product
The fast multipole method: numerical implementation
 J. Comput. Phys
, 2000
"... We study integral methods applied to the resolution of the Maxwell equations where the linear system is solved using an iterative method which requires only matrix–vector products. The fast multipole method (FMM) is one of the most efficient methods used to perform matrix–vector products and accele ..."
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Cited by 85 (2 self)
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We study integral methods applied to the resolution of the Maxwell equations where the linear system is solved using an iterative method which requires only matrix–vector products. The fast multipole method (FMM) is one of the most efficient methods used to perform matrix–vector products
An Overview of Fast Multipole Methods
, 2004
"... Sing, Muse, of the lowrank approximationsOf spherical harmonics and O( N) computation... ..."
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Sing, Muse, of the lowrank approximationsOf spherical harmonics and O( N) computation...
Fast Multipole Methods on Graphical Processors
 Journal of Computational Physics
"... The Fast Multipole Method allows the rapid evaluation of sums of radial basis functions centered at points distributed inside a computational domain at a large number of evaluation points to a specified accuracy ɛ. The method scales as O (N) compared to the direct method with complexity O(N 2), whic ..."
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Cited by 47 (6 self)
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The Fast Multipole Method allows the rapid evaluation of sums of radial basis functions centered at points distributed inside a computational domain at a large number of evaluation points to a specified accuracy ɛ. The method scales as O (N) compared to the direct method with complexity O(N 2
Fast Multipole Method for Multidimensional Integrals
"... We give a fast algorithm to evaluate a class of ddimensional integrals. A direct numerical evaluation of these integrals costs N d where d is the number of variables and N is the number of discrete points of each variable. The algorithm we present in this note permits to reduce this cost from N ..."
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d to a cost of the order O(N). This recursive algorithm takes its inspiration from the wellknown FastMultipole method. At the end of this paper we give some physical applications of such an algorithm. M ethode multipolaire pour des int egrales multidimensionnelles Resume.  On propose un
A pedestrian introduction to fast multipole methods
, 2012
"... Abstract This paper provides a conceptual and nonrigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions. Both the nonoscillatory and the oscillatory kernels are considered. For nonoscillatory kernel, we outline the main ideas of th ..."
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Abstract This paper provides a conceptual and nonrigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions. Both the nonoscillatory and the oscillatory kernels are considered. For nonoscillatory kernel, we outline the main ideas
Scalable Distributed Fast Multipole Methods
"... evaluation to any arbitrary precision of Nbody interactions that arises in many scientific contexts. These methods have been parallelized, with a recent set of papers attempting to parallelize them on heterogeneous CPU/GPU architectures [1]. While impressive performance was reported, the algorithms ..."
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. Numerical simulations on a heterogeneous cluster empirically demonstrate the performance of our algorithm. Keywordsfast multipole methods; GPGPU; Nbody simulations; heterogeneous algorithms; scalable algorithms; parallel data structures; Figure 1. Problems in distributing the FMM across two nodes. Left
Encyclopedia entry on “Fast Multipole Methods.”
"... Short definition. The Fast Multipole Method (FMM) is an algorithm for rapidly evaluating all pairwise interactions in a system of N electrical charges. While the direct computation requires O(N2) work, the FMM carries out this task in only O(N) operations. A parameter in the FMM is the prescribed ac ..."
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Short definition. The Fast Multipole Method (FMM) is an algorithm for rapidly evaluating all pairwise interactions in a system of N electrical charges. While the direct computation requires O(N2) work, the FMM carries out this task in only O(N) operations. A parameter in the FMM is the prescribed
Simple recursive implementation of fast multipole method
"... In this paper we present an implementation of the well known “fast multipole” method for the efficient calculation of dipole fields, that uses polynomials in the Cartesian coordinates rather than spherical harmonics. This has considerable efficiency and simplicity advantages. We have implemented it ..."
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In this paper we present an implementation of the well known “fast multipole” method for the efficient calculation of dipole fields, that uses polynomials in the Cartesian coordinates rather than spherical harmonics. This has considerable efficiency and simplicity advantages. We have implemented
The Fast Multipole Method for the Direct E/MEG Problem
 in Proceedings of ISBI
, 2002
"... Reconstructing neuronal activity from MEG and EEG measurements requires the accurate calculation of the electromagnetic field inside the head. The boundary element formulation of this problem leads to a dense linear system which is too large to be solved directly. We propose to accelerate the comput ..."
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Cited by 8 (5 self)
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the computations via the fast multipole method. This method approximates the electromagnetic interaction between surface elements by performing multipole expansions at a coarse resolution. It significantly reduces the computational complexity of the matrixvector products needed for the iterative solution
Results 1  10
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