Multilevel Fast Multipole Method for Higher Order Discretizations

Borries, Oscar; Meincke, Peter; Jørgensen, Erik; Hansen, Per Christian

doi:10.1109/tap.2014.2330582

Cited by 32 publications

(8 citation statements)

References 31 publications

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“…The MLFMM implementation is described in detail in [13], but the discussion in the present paper focuses on practical considerations and includes a comparison with other results from the litterature.…”

Section: Resultsmentioning

confidence: 99%

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

Borries

Meincke²,

Jørgensen³

et al. 2014

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

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The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion being that going above 2 nd order is not worthwhile. In this paper, we challenge this conclusion, providing results that demonstrate the potential performance gains with Higher-Order MLFMM and showing some modifications to the traditional MLFMM that can benefit both Higher-Order and standard discretizations.

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Section: Resultsmentioning

confidence: 99%

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

Borries

Meincke²,

Jørgensen³

et al. 2014

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

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“…The results are based on the implementation detailed in , but the implementation does not utilize the storage of basis functions using spherical harmonics expansions (SHEs) , as we want to isolate the effects of using adaptive grouping compared to standard Octree grouping at the finest level. However, these two techniques (adaptive grouping and SHE) can easily be combined, and their combination allows use of the SHE to reduce the computational cost of adaptive grouping.…”

Section: Numerical Resultsmentioning

confidence: 99%

Adaptive grouping for the higher‐order multilevel fast multipole method

Borries

Jørgensen²,

Meincke³

et al. 2014

Micro & Optical Tech Letters

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Abstract-An alternative parameter-free adaptive approach for the grouping of the basis function patterns in the MultiLevel Fast Multipole Method is presented, yielding significant memory savings for most discretizations. Results from both a uniformly and non-uniformly meshed scatterer are presented, showing how the technique is worthwhile even for regular meshes, and demonstrating that there is no loss of accuracy in spite of the large reduction in memory and relatively low computational cost.

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“…The standard translation operator is used at the level h = 1. The group structure is described in Borries et al [2014]. standard translation operators, respectively.…”

Section: Scattering Problemmentioning

confidence: 99%

“…We shall now show numerical examples to illustrate the benefits of the Gaussian translation operator for both the scanning problem discussed above and the scattering problem of [ Borries et al , ].…”

Section: Numerical Examplementioning

confidence: 99%

“…The goal is to determine the far‐field pattern of the source (antenna under test) from the recorded probe output. The problem of plane wave scattering by a perfectly conducting sphere will be solved by augmenting the multilevel FMM scheme from Borries et al [] to include the Gaussian translation operator. This scattering example illustrates that the Gaussian translation operator can be incorporated into in an existing FMM code in a straightforward manner.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian translation operator in a multilevel scheme

Hansen¹,

Borries²

2015

Radio Science

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A multilevel computation scheme for time-harmonic fields in three dimensions will be formulated with a new Gaussian translation operator that decays exponentially outside a circular cone centered on the line connecting the source and observation groups. This Gaussian translation operator is directional and diagonal with its sharpness determined by a beam parameter. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard fast multipole method translation operator. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The use of the computation scheme will be illustrated through a near-field scanning problem where the far-field pattern of a source is determined from near-field measurements with a known probe. Here the Gaussian translation operator improves the condition number of the matrix equation that determines the far-field pattern. The Gaussian translation operator can also be used when the probe pattern is known only in one hemisphere, as is common in practice. Also, the Gaussian translation operator will be used to solve the scattering problem of the perfectly conducting sphere.

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Multilevel Fast Multipole Method for Higher Order Discretizations

Cited by 32 publications

References 31 publications

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

Adaptive grouping for the higher‐order multilevel fast multipole method

Gaussian translation operator in a multilevel scheme

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