Error control of the translation operator in 3D MLFMA

Hastriter, M.L.; Ohnuki, Shinichiro; Chew, Weng Cho

doi:10.1002/mop.10862

Cited by 39 publications

(42 citation statements)

References 15 publications

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“…For a cluster of size a l = 2 l−3 λ at level l, the truncation number is determined by using the excess bandwidth formula [10] for the worst-case scenario and the one-box-buffer scheme [11], i.e.,…”

Section: Solutions Of Surface Integral Equations Via Mlfmamentioning

confidence: 99%

“…This cannot be predicted by the excess bandwidth formula in (3), which suggests significantly large truncation numbers, as listed in Table 1. This is because the excess bandwidth formula is based on the worst-case scenario for the positions of the basis and testing functions inside the clusters [11]. In fact, the ordinary MLFMA must use the truncation numbers obtained with (3) to guarantee the desired level of accuracy.…”

Section: Strategies For Building a Less-accurate Mlfmamentioning

confidence: 99%

“…There are many studies that further improve the reliability of the implementations by refining formulas for the truncation numbers, especially for small clusters [11]. In most cases, the purpose is to obtain accurate results by suppressing the error sources in MLFMA.…”

Section: Strategies For Building a Less-accurate Mlfmamentioning

confidence: 99%

See 2 more Smart Citations

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Ergül¹,

Malas²,

Gürel³

2010

PIER

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Abstract-We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectlyconducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems.In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.

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Section: Solutions Of Surface Integral Equations Via Mlfmamentioning

confidence: 99%

Section: Strategies For Building a Less-accurate Mlfmamentioning

confidence: 99%

See 1 more Smart Citation

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Ergül¹,

Malas²,

Gürel³

2010

PIER

View full text Add to dashboard Cite

show abstract

“…For example, the excess bandwidth formula, presented in [13] provides an initial estimate for the high-frequency (HF) case. In [14,15], the excess bandwidth formula is supplemented with additional formulas such that L can be estimated for medium frequencies also. For low frequencies (LF), dedicated formulas can also be derived.…”

Section: Introductionmentioning

confidence: 99%

Error Control of the Vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm

Bogaert¹,

Peeters²,

Zutter³

2011

PIER

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Abstract-Novel formulas are presented that allow the rapid estimation of the number of terms L that needs to be taken into account in the translation operator of the vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA). This is especially important for low frequencies, since the L needed for errorcontrollability can be substantially higher than the L required in the scalar case. Although these formulas were originally derived for use in the NSPWMLFMA, they are equally useful in at least three other fast matrix multiplication methods.

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“…By increasing the number of buffer boxes, i.e., by increasing D, one could improve the accuracy, but at the same time the computational cost is increasing because more outer-to-inner translations need to be performed, and more nearby interactions need to be calculated directly. The error control can be improved somewhat at lower frequencies or levels by choosing a more optimal truncation order L, as described in [11], but ultimately this so called low-frequency breakdown limits the minimum division cube side length to about λ/10 . .…”

Section: Representations For the Green's Functionmentioning

confidence: 99%

Translation Procedures for Broadband Mlfma

Wallén¹,

Sarvas²

2005

PIER

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Abstract-The multilevel fast multipole algorithm (MLFMA) is used in computing acoustic and electromagnetic fields with integral equation methods. The traditional MLFMA, however, suffers from a lowfrequency breakdown that effectively limits the minimum division cube side length to approximately one wavelength. To overcome this low-frequency breakdown and get a broadband MLFMA, we propose an efficient and relatively straightforward implementation of the field translations based on the spectral representation of the Green's function. As an alternative we also consider the so called uniform MLFMA, which has a lower computational cost but limited accuracy. We consider the essential implementation details and finally provide numerical examples to demonstrate the error controllability of the translations.

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Error control of the translation operator in 3D MLFMA

Cited by 39 publications

References 15 publications

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Error Control of the Vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm

Translation Procedures for Broadband Mlfma

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