Fast multipole method pdf

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CBMS Conference on Fast Direct Solvers DartmouthCollege June23-June27,2014 Lecture2:TheFastMultipoleMethod GunnarMartinsson TheUniversityofColoradoatBoulder
Encyclopedia entry on “Fast Multipole Methods.” Per-Gunnar Martinsson, University of Colorado at Boulder, August 2012 Short de?nition. 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
Fast multipole preconditioners for sparse matrices arising from elliptic equations 215 futurehardwareconstraints,anditislikelythatmultigridwill remain competitive. Complementing this evolution, hierarchical low-rank approximation (HLRA) of the off-diagonal blocks of a matrix leads to a whole new variety of O(N) solvers or preconditioners.
The fast multipole method (FMM) is investigated in detail for the solution of elec-tromagnetic scattering problems involving arbitrarily shaped three-dimensional conducting surfaces. This method is known to reduce the computational com-plexity and the memory requirement of the solution without sacri?cing the accu-racy.
4. Construction of fast methods The problems of moving information up and down the tree in the fast multipole method and finding a suitable quadrature (sk , wk ) are related. There are probably many ways to approach this question. We chose to use a spectral decomposition. The function esx for example is not suitable, without making some
A fast multipole method for Maxwell equations stable at all frequencies 605 method similar to White & Headgordon (1996)) and on a plane-wave expansion, which provides a diagonal multipole-to-local operator. Zhao & Chew (2000b) applied a matrix-rotation scheme to reduce the requirement. For the Helmholtz equation, Greengard et al. (1998) propose
The multilevel fast multipole method (MLFMM) is used along with method of moments (MoM) a numerical computational method of solving linear partial differential equations which have been formulated as integral equations of large objects almost faster without loss in accuracy. This method is an alternative formulation of the technology behind the MoM and is applicable to much larger structures Fast methods have been developed for BE formulations, which reduces the complexity to almost linear order. Here, the fast multipole method (FMM) is applied to reduce the complexity of the poroelastodynamic BEM also to an almost linear order. Due to the complicated fundamental solutions a black-box type FMM is preferable.
A A Distributed Memory Fast Multipole Method for Volume Potentials DHAIRYA MALHOTRA, The University of Texas at Austin, Austin, TX 78712 GEORGE BIROS, The University of Texas at Austin, Austin, TX 78712 The solution of a constant-coef?cient elliptic partial differential equation (PDE) can be computed using
Fast Multipole Method Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Department of Computer Science Department of Physics & Astronomy Department of Chemical Engineering & Materials Science Department of Biological Sciences University of Southern California Email: anakano@usc.edu Objectives: Space-time multiresolution algorithms
Fast multipole method (FMM) • Can we do better than Nlog(N)? • The previous algorithm is of Nlog(N) complexity because all particles are “accessed” at every level of re?nement. • We can avoid this by some more analytical manipulations. • In particular Translation of a multipole expansion (M2M)
Request PDF on ResearchGate | The black-box fast multipole method | A new O(N)O(N) fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y
Request PDF on ResearchGate | The black-box fast multipole method | A new O(N)O(N) fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y
A black-box fast multipole method (bbFMM) can be constructed by combining this multilevel scheme with the FMM tree structure as detailed in [1]. Our method is a black-box in the sense that the functional form of the low-rank approximation (6) is independent of the kernel.

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