Fast multipole methods in service of various scientific disciplines
Author
Gürel, Levent
Date
2014Source Title
2014 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium)
Publisher
IEEE
Pages
287 - 287
Language
English
Type
Conference PaperItem Usage Stats
177
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105
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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
AstrophysicsLaplace 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/11693/26808Published Version (Please cite this version)
https://doi.org/10.1109/USNC-URSI.2014.6955670Collections
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