Broadband MLFMA With Plane Wave Expansions and Optimal Memory Demand

A broadband multilevel fast multipole algorithm (MLFMA) in 3D is presented based on plane wave expansions and diagonal translations on all division levels. The radiation and incoming wave patterns on all levels are presented by trigonometric polynomials, and optimal sampling rates and translator deg...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2009-03, Vol.57 (3), p.742-753
Main Authors: Dufva, T., Sarvas, J.
Format: Article
Language:English
Subjects:
Acceleration
Applied classical electromagnetism
Broadband
Computational efficiency
Division
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Error correction
Exact sciences and technology
Fast Fourier transforms
Fast multipole method
fast solvers
Fundamental areas of phenomenology (including applications)
Integral equations
Mathematical models
MLFMA
Multipoles
Optimization
Partial differential equations
Physics
Plane waves
Polynomials
Sampling methods
Testing
Translations
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Summary:A broadband multilevel fast multipole algorithm (MLFMA) in 3D is presented based on plane wave expansions and diagonal translations on all division levels. The radiation and incoming wave patterns on all levels are presented by trigonometric polynomials, and optimal sampling rates and translator degrees are found and tabulated. On the super-wavelength levels the memory need and the computational cost are lowered more than by half compared to the traditional approach. On the sub-wavelength levels also a novel saving method for the field patterns is presented which is as efficient as saving the multipole series coefficients while all translations with the proposed method can still be carried out in the fast diagonal form. Also the direction dependence of the radiation and incoming wave patterns is lowered by half. The proposed broadband MLFMA has a very good error control on all division levels which we demonstrate by numerical testing.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2009.2013426