Efficient Solution of Integral Equations in a Localizing Basis

Adams, Robert J.; Zhu, Aiming; Canning, F.X.

doi:10.1163/156939305775537438

Cited by 14 publications

(30 citation statements)

References 3 publications

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“…Previously reported LOGOS-based sparse factorization algorithms for Z at low frequencies utilize nonoverlapped, localizing LOGOS modes [ [3][4][5][6][7]. These modes were obtained by analyzing the impedance matrix to determine surface current modes satisfying (1) for which both the current, J, and the scattered field, ZJ, are localized (within O(ε)) to identical spatial groups.…”

Section: Overlapped Localizing Logos Modesmentioning

confidence: 99%

“…To motivate this algorithm, Section 6.3.1 summarizes the original procedure [3,5] used to determine localizing LOGOS modes from the full columns of the impedance matrix. In so doing, we also make the minor extension of using the associated LOGOS mode calculation algorithm to find the OLL modes described above.…”

Section: Efficient Determination Of Overlapped Localizing Modesmentioning

confidence: 99%

“…(In this paper, the phrase "low-frequency" is used to refer to a situation in which the maximum linear dimension of a scattering configuration is small relative to the wavelength of the harmonic excitation.) The low-frequency factorization and solution strategy discussed below relies on previous work providing sparse implementations of Z −1 using so-called local-global solution (LOGOS) modes [3][4][5][6][7]. A LOGOS mode is a solution (J) of the global boundary condition (1) that is localized to order-ε within a smaller part of the global simulation domain.…”

Section: Introductionmentioning

confidence: 99%

“…In [3][4][5][6][7], a nonradiating LOGOS mode is defined as a solution to (1) in which both the surface current and the associated scattered fields are localized to the same small spatial region. In the following we generalize previous definitions of nonradiating LOGOS modes to include solution modes in which the currents are localized to overlapping spatial regions.…”

Section: Introductionmentioning

confidence: 99%

“…In the following we generalize previous definitions of nonradiating LOGOS modes to include solution modes in which the currents are localized to overlapping spatial regions. However, as in [3][4][5][6][7], the scattered fields remain localized to non-overlapping spatial regions. Such modes are hereinafter referred to as overlapped localizing LOGOS (OLL) modes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sparse Factorization of the TMZ Impedance Matrix in an Overlapped Localizing Basis

Adams¹,

Zhu²,

Canning³

2006

PIER

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Abstract-It has been observed that localized solution modes provide sparse factored representations of the discrete integral equations encountered in the simulation of electromagnetic phenomena at low frequencies.This paper extends these results by incorporating overlapped localizing modes. For TM z scattering from a rectangular array of perfectly conducting obstacles, it is observed that the complexity scaling of the resulting factorization is significantly reduced relative to previously reported results. The memory complexity of the resulting factored representation scales approximately as O(N ) for electrically small arrays. Limitations and possible extensions of these results are discussed.

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Section: Overlapped Localizing Logos Modesmentioning

confidence: 99%

Section: Efficient Determination Of Overlapped Localizing Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sparse Factorization of the TMZ Impedance Matrix in an Overlapped Localizing Basis

Adams¹,

Zhu²,

Canning³

2006

PIER

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Sparse solution of an integral equation formulation of scattering from open PEC targets

Zhu

Adams

Canning³

et al. 2006

Microw. Opt. Technol. Lett.

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seen, and the 10-dB return-loss impedance bandwidth is almost unchanged. It can be concluded that the presence of the RF shielding metal case causes small or negligible effects on the performances of the proposed antenna.The effects of the antenna ground plane on the antenna performances were also studied. The measured results for three different side lengths of G ϭ 22, 26, and 30 mm for the antenna ground plane are shown in Figure 4. It is first seen that the obtained impedance bandwidths for G ϭ 26 and 30 mm are about the same. On the other hand, for the case with a smaller side length (see G ϭ 22 mm in the figure), the impedance matching of the antenna is quickly degraded. This is largely because, with a smaller side length, the antenna ground plane can no longer function as an effective shielding plate for blocking the possible fringing EM fields of the antenna from contacting the system ground plane. In this case, large effects on the antenna performances due to the presence of the RF shielding metal case are expected.The radiation characteristics of the proposed antenna studied in Figure 2 were also measured. Figure 5 plots the measured radiation patterns at 2442 MHz, the center frequency of the 2.4-GHz WLAN band. It is observed that broadside radiation patterns are generally obtained, except that a small dip is seen in the broadside direction. This small dip is mainly contributed by the long feeding strip and the shorting strip of the antenna. Other frequencies over the operating band were also measured, and the obtained radiation patterns were found to be similar to those plotted here, indicating that stable radiation patterns are obtained for the proposed antenna. The antenna gain was also measured, and the result is shown in Figure 6. A stable antenna gain level of about 2.9 dBi over the operating band is obtained. CONCLUSIONA novel compact shorted patch antenna suitable to be mounted above the system ground plane of a wireless communication device for WLAN operation has been proposed, constructed, and tested. The constructed prototype occupied nearly no valuable board space of the system ground plane or circuit board of the wireless device. In addition, the results clearly show that even with the presence of a RF shielding metal case placed under the antenna, the variations in the impedance matching of the antenna are small or negligible. This indicates that the associated components of the wireless device can be placed on the system ground plane or circuit board under the antenna, with the performances of the antenna almost unaffected. It is thus expected that a compact integration of the proposed antenna with associated components in the wireless device can be obtained.

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Sparse direct solution of the electric field integral equation using nonoverlapped localizing logos modes

Adams

et al. 2007

Micro & Optical Tech Letters

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These results are also in agreement with the experimental ones, apart from experimental errors. It is noteworthy that the numerical calculation of the noise figure is very dependent on the initial ASE power of the WDM channels.The noise figure is approximately the same for coherent and incoherent pumping in the counter propagation configuration. CONCLUSIONSWe report an incoherent Raman amplification scheme with a low cost pump source.In agreement with previous works [1-6], our results indicate that incoherent pumping decreases the spectral ripple of the Raman gain, which corresponds to a decrease of the gain slope.Furthermore, a good agreement between experimental and simulation results was achieved with the present numerical model.

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Efficient Solution of Integral Equations in a Localizing Basis

Cited by 14 publications

References 3 publications

Sparse Factorization of the TMZ Impedance Matrix in an Overlapped Localizing Basis

Sparse Factorization of the TMZ Impedance Matrix in an Overlapped Localizing Basis

Sparse solution of an integral equation formulation of scattering from open PEC targets

Sparse direct solution of the electric field integral equation using nonoverlapped localizing logos modes

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