Broadband MLFMA with plane wave expansions and optimal memory demand

Tommi Dufva, Jukka Sarvas

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)742 - 753
Number of pages12
JournalIEEE Transactions on Antennas and Propagation
Volume57
Issue number3
DOIs
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed

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Data storage equipment
Radiation
Wavelength
Polynomials
Sampling
Testing
Costs

Keywords

  • Fast multipole method
  • fast solvers
  • integral equations

Cite this

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Broadband MLFMA with plane wave expansions and optimal memory demand. / Dufva, Tommi; Sarvas, Jukka.

In: IEEE Transactions on Antennas and Propagation, Vol. 57, No. 3, 2009, p. 742 - 753.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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KW - integral equations

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