Gaussian translation operator for Multi-Level Fast Multipole Method

Borries, Oscar; Hansen, Per Christian; Sørensen, Stig B.; Meincke, Peter; Jørgensen, Erik

doi:10.1109/aps.2014.6905403

Cited by 2 publications

(6 citation statements)

References 7 publications

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“…In FMM computations one should preselect a sampling rate for each group level and determine the beam parameter for each group to group interaction to achieve this sampling rate. Future publications [13], [14] will further investigate the effectiveness of the new plane-wave expansion.…”

Section: Discussionmentioning

confidence: 98%

“…Naturally, depends on , and . Since (9), (13), and (15) are exact, we can always find to ensure a relative error that is less than any positive .…”

Section: Truncation and Samplingmentioning

confidence: 98%

“…We next consider the problem of determining the proper truncation limit for the summations in (9), (13), and (15) to ensure a relative error less than . Naturally, depends on , and .…”

Section: Truncation and Samplingmentioning

confidence: 99%

“…From (13) we see that if a transmitting antenna with far-field pattern is confined to the region , its electric field can be computed in as (52) where the integral can be computed through the use of the Gauss-Lengendre rule to get (53)…”

Section: Truncation and Samplingmentioning

confidence: 99%

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Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

Hansen¹

2014

IEEE Trans. Antennas Propagat.

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A new exact plane-wave expansion is presented for general time-harmonic electromagnetic fields radiated by an arbitrary finite source region in three dimensions. The plane-wave expansion employs a directional spectrum that is proportional to the far-field pattern of the source. The directionality is achieved through an exact representation that involves a beam parameter, which determines the sharpness of the spectrum. When the beam parameter is set to zero, the new expansion becomes identical to the plane-wave expansion employed in the fast multipole method. The expansion is exact for observations points all the way up to the source region and includes evanescent waves. An antennaantenna transmission formula follows straightforwardly. Numerical examples demonstrate that the new plane-wave expansion requires fewer plane waves than previously derived plane-wave expansions.

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Section: Discussionmentioning

confidence: 98%

“…Naturally, depends on , and . Since (9), (13), and (15) are exact, we can always find to ensure a relative error that is less than any positive .…”

Section: Truncation and Samplingmentioning

confidence: 98%

“…We next consider the problem of determining the proper truncation limit for the summations in (9), (13), and (15) to ensure a relative error less than . Naturally, depends on , and .…”

Section: Truncation and Samplingmentioning

confidence: 99%

Section: Truncation and Samplingmentioning

confidence: 99%

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Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

Hansen¹

2014

IEEE Trans. Antennas Propagat.

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“…The numerical computation of should be performed using normalized Bessel and Hankel functions to avoid overflow. Specifically, one should use the normalized Hankel function in (16) and the corresponding normalized Bessel function (32) Then the product of a Bessel and a Hankel function can be computed as (33) Numerical experimentation shows that even with the normalization for the Bessel function introduced in (32), the Bessel factor in (29) can become extreme. Therefore, it would be advantageous to create a subroutine that computes the logarithm of the Bessel function.…”

Section: Methods For Determining To Achieve Any Desired Precisionmentioning

confidence: 99%

Numerical Properties of a Gaussian Translation Operator for the 2D FMM

Hansen¹

2014

IEEE Trans. Antennas Propagat.

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A diagonal Gaussian translation operator for the time-harmonic fast multipole method (FMM) in two dimensions is examined numerically. The Gaussian translation operator depends on a beam parameter that determines its sharpness. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard FMM translation operator. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The required number of plane waves depends strongly on the actual source-receiver locations, not just on the diameter of the source and receiver regions. Index Terms-Electromagnetic propagation, electromagnetic theory.0018-926X

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Gaussian translation operator for Multi-Level Fast Multipole Method

Cited by 2 publications

References 7 publications

Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

Numerical Properties of a Gaussian Translation Operator for the 2D FMM

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