Singularity subtraction for evaluation of Green's functions for multilayer media

Şimşek, Ergün; Liu, Qing; Wei, Baodian

doi:10.1109/tmtt.2005.860304

Cited by 134 publications

(80 citation statements)

References 33 publications

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“…As an illustration, Figure 9a shows the magnitude of the E x and E z electric field components due to VED, while Figure 9b plots |E x |, |E y | and |E z | generated by HED. In both panels, the result of present calculations is compared to those shown by Simsek et al [2006], Paulus et al [2000], and Simsek (E. Simsek, personal communication, 2010). Again, overall the agreement between the results is good, thus verifying the fidelity of the proposed analytical and computational treatment.…”

Section: Resultsmentioning

confidence: 95%

“…In particular, it follows from the results in section 5.1 that u p m j,r and v p m j ,r behave as O( −a )e À z , a ⩾ 2, as → ∞. As a result, the decay of the residual field-form spectra u p m j ,r J n ( ) and v p m j ,r J n ( ) along the Re( )-axis is commensurate with that of the respective potential-form residual kernels described by Simsek et al [2006]. From (53) and its magnetic field counterpart, it thus follows that the improper integrals comprising the residual components of (54) and (55) remain unconditionally regular and can be consistently approximated as…”

Section: Numerical Scheme To Evaluate the Residual Componentmentioning

confidence: 83%

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Field forms of the layered electromagnetic Green's functions by TE and TM potentials

Cao

Guzina

2011

Radio Science

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[1] A complete set of 3D layered electromagnetic Green's functions in the spatial domain is derived by way of transverse electric and transverse magnetic potentials, featuring a "direct" formulation for the field forms of the spectral Green's functions. The improper integrals underpinning the computation of the corresponding point-load solutions in the spatial domain are evaluated via the method of asymptotic decomposition, wherein the singular behaviors are entirely extracted and integrated analytically-so that the remaining residual components can be computed effectively and accurately via adaptive numerical quadrature over a suitable contour path. It is also found that, in the spectral domain, the decay of the (numerically-integrated) residual field forms is commensurate with that of their potential-form counterparts, which eliminates the perceived gap between the computation of the field forms and respective potential forms of the Green's functions in the spatial domain. The effectiveness and accuracy of the proposed methodology is evaluated via comparison with relevant examples in the literature.Citation: Cao, Y., and B. B. Guzina (2011), Field forms of the layered electromagnetic Green's functions by TE and TM potentials, Radio Sci., 46, RS6003,

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Section: Resultsmentioning

confidence: 95%

Section: Numerical Scheme To Evaluate the Residual Componentmentioning

confidence: 83%

Field forms of the layered electromagnetic Green's functions by TE and TM potentials

Cao

Guzina

2011

Radio Science

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“…[3] Extensive research has been devoted to the evaluation of these integrals through methods such as singularity extraction techniques [Simsek et al, 2006;Polimeridis et al, 2007], the fast Hankel transform [Hanson, 2004;Boix et al, 2007], the steepest descent path [Cui and Chew, 1999;Tsang et al, 2006], the discrete complex image method [Chow et al, 1991;Aksun and Mittra, 1992;Yuan et al, 2006;Zhuang et al, 2007], and acceleration techniques for unbounded integration of oscillating functions [Michalski, 1998]. In particular, the poles and branch points can be avoided by deforming the integration path in the complex k r plane using, for example, rectangular or elliptic contours, and by applying Cauchy's integral theorem [GayBalmaz and Mosig, 1997;Paulus et al, 2000;He et al, 2005;Simsek et al, 2006].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the poles and branch points can be avoided by deforming the integration path in the complex k r plane using, for example, rectangular or elliptic contours, and by applying Cauchy's integral theorem [GayBalmaz and Mosig, 1997;Paulus et al, 2000;He et al, 2005;Simsek et al, 2006]. However, while all these techniques have proven to be accurate and efficient, they are usually valid only for particular layered configurations or sourcereceiver relative positions.…”

Section: Introductionmentioning

confidence: 99%

“…The definition of the integration contours often remains partly subjective. For instance, Paulus et al [2000] and Simsek et al [2006] considered an empirical ratio of 10 À3 between the semi-minor and semi-major axes of an elliptic integration path, leaving the contour in relatively close vicinity to the real axis in order to avoid significant increase in the Bessels functions.…”

Section: Introductionmentioning

confidence: 99%

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Fast evaluation of zero‐offset Green's function for layered media with application to ground‐penetrating radar

Lambot

Slob

Vereecken

2007

Geophysical Research Letters

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We propose an efficient integration path for the fast evaluation of the three‐dimensional spatial‐domain Green's function for electromagnetic wave propagation in layered media for the particular case of zero‐offset, source‐receiver proximal ground‐penetrating radar (GPR) applications. The integration path is deformed in the complex plane of the integration variable kρ so that the oscillations of the dominant exponential term in the spectral Green's function are minimized. The contour does not need to be closed back on the real kρ axis as the complex integrand rapidly damps. The accuracy and efficiency of the technique have been confirmed by comparison with traditional elliptic integration contours. The proposed algorithm appears to be promising development for fast, full‐wave modeling and inversion of GPR data.

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A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages

Liu

Aygün

Yılmaz

2019

Int J Numerical Modelling

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A parallel iterative layered‐medium integral‐equation solver is presented for fast and scalable network parameter extraction of electronic packages. The solver, which relies on a 2‐D fast Fourier transform (FFT)‐based algorithm and a sparse preconditioner to reduce computational complexity, is parallelized using three workload decomposition strategies, including a pencil decomposition that increases the scalability of the computationally dominant FFT‐based multiplication stage. A set of increasingly difficult benchmark problems, which require network parameter computations for Ntrace = 1 to 257 package‐scale interconnects, are solved on a petaflop scale computer to quantify the solver's accuracy, efficiency, and scalability. The total serialized computation time is observed to scale asymptotically as Ntrace2.6logNtrace. For the largest problem, using ~1.14 million unknowns and 1536 processes, the solver requires a wall‐clock time of ~0.05 s per iteration, ~1 minute per excitation, ~9 h per frequency, and ~424 hours to extract the 514‐port network parameters at 40 sample frequencies between 1 to 40 GHz.

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Singularity subtraction for evaluation of Green's functions for multilayer media

Cited by 134 publications

References 33 publications

Field forms of the layered electromagnetic Green's functions by TE and TM potentials

Field forms of the layered electromagnetic Green's functions by TE and TM potentials

Fast evaluation of zero‐offset Green's function for layered media with application to ground‐penetrating radar

A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages

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