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      Fast multipole methods in service of various scientific disciplines

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      Author
      Gürel, Levent
      Date
      2014
      Source Title
      2014 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium)
      Publisher
      IEEE
      Pages
      287 - 287
      Language
      English
      Type
      Conference Paper
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      Abstract
      For more than two decades, several forms of fast multipole methods have been extremely successful in various scientific disciplines. Reduced complexity solutions are obtained for solving different forms of equations that are derived from Maxwell's equations, such as Helmholtz's equation for electrodynamics and Laplace's equation for electrostatics. Fast multipole solvers are developed for and applied to the integral equations derived from Helmholtz's and Laplace's equations. Fast multipole solvers are kernel-dependent techniques, i.e., they rely on certain analytical properties of the integral-equation kernels, such as diagonalizability. Electromagnetics is not the only discipline benefiting from the fast multipole methods; a plethora of computations in various disciplines, such as the solution of Schroedinger's equation in quantum mechanics and the calculation of gravitational force in astrophysics, to name a few, exploit the reduced-complexity nature of the fast multipole methods. Acoustics, molecular dynamics, structural mechanics, and fluid dynamics can be mentioned as other disciplines served by the fast multipole methods. © 2014 IEEE.
      Keywords
      Astrophysics
      Laplace equation
      Laplace transforms
      Maxwell equations
      Molecular dynamics
      Quantum theory
      Schrodinger equation
      Analytical properties
      Fast multipole method
      Gravitational forces
      Helmholtz's equations
      Laplace's equations
      Maxwell's equations
      Scientific discipline
      Structural mechanics
      Integral equations
      Permalink
      http://hdl.handle.net/11693/26808
      Published Version (Please cite this version)
      https://doi.org/10.1109/USNC-URSI.2014.6955670
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      • Computational Electromagnetics Research Center (BiLCEM) 84
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