Application of the Dual-Equation Equivalent-Current Reconstruction to Electrically Large Structures by Fast Multipole Method Enhancement [AMTA Corner]

2014 ◽  
Vol 56 (5) ◽  
pp. 264-273 ◽  
Author(s):  
L. J. Foged ◽  
L. Scialacqua ◽  
F. Saccardi ◽  
J. L. Araque Quijano ◽  
G. Vecchi
Keyword(s):  
Fast Multipole Method ◽  
Fast Multipole ◽  
Equivalent Current ◽  
Dual Equation ◽  
Large Structures ◽  
Multipole Method ◽  
Current Reconstruction

scholarly journals Algebraic preconditioners for the Fast Multipole Method in electromagnetic scattering analysis from large structures: trends and problems

2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Bruno Carpentieri
Keyword(s):  
Electromagnetic Scattering ◽  
Fast Multipole Method ◽  
Practical Interest ◽  
Iterative Solution ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Preconditioning Techniques ◽  
Large Structures ◽  
Multipole Method ◽  
Memory Complexity

<div>The Fast Multipole Method was introduced by Greengard and Rokhlin in a seminal paper appeared in 1987 for studying large systems of particle interactions with reduced algorithmic and memory complexity [60]. Developments of the original idea are successfully applied to the analysis of many scientific and engineering problems of practical interest. In scattering analysis, multipole techniques may enable to reduce the computational complexity of iterative solution procedures involving dense matrices arising from the discretization of integral operators from O(n2) to O(n log n) arithmetic operations. In this paper we discuss recent algorithmic developments of algebraic preconditioning techniques for the Fast Multipole Method for 2D and 3D scattering problems. We focus on design aspects, implementation details, numerical scalability, parallel performance on emerging computer systems, and give some minor emphasis to theoretical aspects as well. Thanks to the use of iterative techniques and efficient parallel preconditioners, fast integral solvers involving tens of million unknowns are nowadays feasible and can be integrated in the design processes. Keywords: algebraic preconditioners, Fast Multipole Method, Krylov solvers, electromagnetic scattering applications, Maxwell&#39;s equations.</div>

scholarly journals Fast computation of electromagnetic near-fields with the multilevel fast multipole method combining near-field and far-field translations

2006 ◽  
Vol 4 ◽  
pp. 111-115 ◽  
Author(s):  
A. Tzoulis ◽  
T. F. Eibert
Keyword(s):  
Electromagnetic Compatibility ◽  
Fast Multipole Method ◽  
Near Field ◽  
Boundary Integral ◽  
Far Field ◽  
Discrete Elements ◽  
Fast Multipole ◽  
Equivalent Current ◽  
Multipole Method ◽  
Current Densities

Abstract. In Electromagnetic Compatibility (EMC) problems, computation of electromagnetic near-fields in the vicinity of complex radiation and scattering systems is often required. Numerical solution of such problems is achieved using Boundary Integral (BI) based approaches, where the involved Integral Equations (IE's) are solved with the Method of Moments (MoM). The MoM solution process is speeded up by fast IE solvers such as the Multilevel Fast Multipole Method (MLFMM). In the end the desired amplitudes of the expansion of the equivalent current densities on the discrete elements all over the Huygens' surfaces are known. Computation of the electromagnetic fields produced by the equivalent currents at observation points being in the near-field regions requires integration of the current densities over the Huygens' surfaces. Numerical evaluation of the near-field integrals using conventional integration rules can become extremely time consuming for large objects and large number of observation points. In this contribution, acceleration of the near-field integration of the equivalent current densities is provided using a postprocessing MLFMM, where near-field and far-field translations are combined in order to achieve optimum performance. The proposed approach was applied in the postprocessing stage of a powerful Finite Element Boundary Element (FEBI) method, resulting in significant decrease of the postprocessing computation time. The formulation of the proposed acceleration is presented and numerical results are shown.

A Fourier-series-based kernel-independent fast multipole method

2011 ◽  
Vol 230 (15) ◽  
pp. 5807-5821 ◽  
Author(s):  
Bo Zhang ◽  
Jingfang Huang ◽  
Nikos P. Pitsianis ◽  
Xiaobai Sun
Keyword(s):  
Fourier Series ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak
Keyword(s):  
Canonical Ensemble ◽  
Yukawa Potential ◽  
Direct Method ◽  
Fast Multipole Method ◽  
Parallel Computers ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Massively Parallel Computers ◽  
Multipole Method ◽  
Execution Times

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

A new version of the Fast Multipole Method for the Laplace equation in three dimensions

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 229-269 ◽  
Author(s):  
Leslie Greengard ◽  
Vladimir Rokhlin
Keyword(s):  
Laplace Equation ◽  
Fast Multipole Method ◽  
High Accuracy ◽  
Three Dimensions ◽  
Potential Fields ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Reasonable Cost ◽  
Multipole Method ◽  
Translation Operators

We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

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