scholarly journals The fast multipole method (FMM) for electromagnetic scattering problems

1992 ◽  
Vol 40 (6) ◽  
pp. 634-641 ◽  
Author(s):  
N. Engheta ◽  
W.D. Murphy ◽  
V. Rokhlin ◽  
M.S. Vassiliou
Keyword(s):  
Electromagnetic Scattering ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Multipole Method

Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

2007 ◽  
Vol 55 (6) ◽  
pp. 1810-1816 ◽  
Author(s):  
Caleb Waltz ◽  
Kubilay Sertel ◽  
Michael A. Carr ◽  
Brian C. Usner ◽  
John L. Volakis
Keyword(s):  
Electromagnetic Scattering ◽  
Fast Multipole Method ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Multipole Method

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>

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