Temporal acceleration of time‐domain integral‐equation solvers for electromagnetic scattering from objects residing in lossy media

Jiang, Peilin; Michielssen, E.

doi:10.1002/mop.20595

Cited by 10 publications

(12 citation statements)

References 19 publications

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“…1. The computational cost associated with a single matrix vector product Z kÀl S l is OðN 2 s Þ and hence the cost of evaluating P k at all N t time steps scales as OðN 2 s N 2 t Þ. Parenthetically, we note that potential evaluators for the wave equation (in both two and three dimensions) and the lossy wave equation take a form that is similar to (8) [31][32][33]23,29]. With simple algebraic manipulation, it is possible to retrofit these fast schemes into marching on in time (MOT) solvers for solving time domain integral equations.…”

Section: Mathematical Preliminariesmentioning

confidence: 97%

“…In the FFT and ACE based spatio-temporal convolution, the multipole-to-local translation operation involves the temporal convolution in (18b) that is evaluated in Fourier domain (23) using FFTs. This evaluation is carried out for each of the (n + 1)(n + 2)/2 tensor components.…”

Section: Multi-level Algorithm and Cost Estimatementioning

confidence: 99%

“…One method used to arrive at such an algorithm relies upon relating the three-dimensional Green's function to the one-dimensional Green's function via a spectral integral and evolving the fields rapidly in one-dimension [22,23]. The asymptotic cost of this approach is OðN s N t logðN s Þ logðN t ÞÞ.…”

Section: Introductionmentioning

confidence: 99%

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Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials

Vikram

Baczewski

Shanker

et al. 2010

Journal of Computational Physics

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a b s t r a c tDiffusion, lossy wave, and Klein-Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green's functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales aswhere N s and N t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The first scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as OðN s N t log 2 N t Þ. Several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.

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Section: Mathematical Preliminariesmentioning

confidence: 97%

Section: Multi-level Algorithm and Cost Estimatementioning

confidence: 99%

See 1 more Smart Citation

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials

Vikram

Baczewski

Shanker

et al. 2010

Journal of Computational Physics

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“…This is simply due to the fact that Green function of such a medium has a temporal tail [7]. Consequently, computation of the convolution of the Green function and currents becomes very costly, and the resulting marching-on-in-time (MOT)-based TDSIE solvers have to be accelerated using blocked fast Fourier transform Manuscript (blocked-FFT) [3], plane-wave time domain (PWTD) [4], and/or Prony-series [5], [6] schemes. The first MOT scheme [2] developed for lossy dielectrics solves four coupled TDSIEs constructed in tangential and normal components of the fields on the interface between the lossy scatterer and the lossless background medium.…”

Section: Introductionmentioning

confidence: 99%

MOT Solution of the PMCHWT Equation for Analyzing Transient Scattering from Conductive Dielectrics

Uysal

Ülkü

Bağcı

2015

Antennas Wirel. Propag. Lett.

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Transient electromagnetic interactions on conductive dielectric scatterers are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation with a marching on-in-time (MOT) scheme. The proposed scheme, unlike the previously developed ones, permits the analysis on scatterers with multiple volumes of different conductivity. This is achieved by maintaining an extra temporal convolution that only depends on permittivity and conductivity of these volumes. Its discretization and computation come at almost no additional cost and do not change the computational complexity of the resulting MOT solver. Accuracy and applicability of the MOT-PMCHWT solver are demonstrated by numerical examples.

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“…In general, for higher speed and higher sensitivity systems such as RF and analog methods, the loss is a crucial factor in determining system specifications and performance. The TDIE approach has been shown to work with lossy material [15][16][17][18] wherein the Green's functions, besides possessing delta functions in time, also include a broadly exponentially decaying 'wake'. This leads to the implementation issue that the spatial integrals at retarded times have to be replaced by temporal convolutions.…”

mentioning

confidence: 99%

Modeling of lossy multiregion substrates in microelectronic circuits using time‐domain surface integral equations

Yang

Jandhyala

2005

Micro & Optical Tech Letters

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In the BiCMOS process, the trade-off in specifications of all kind of circuits can be fully utilized for possible circuit designs. In this paper, the trade-off between the NF and linearity for LNA circuit design have been tested and verified. A good choice in the first stage of the LNA design is an HBT for a better NF, and the last stage is an MOS for better linearity. Furthermore, the circuits (HBT-MOS) designed in this paper are very useful for integration with other subcircuits in 5-6-GHz receivers IC due to its powersaving characteristic and better figure of merit. With the modern microelectronic industry entering a new era featuring progressively higher speed and more highly integrated mixed-signal systems on chip, accurate modeling of distributed electromagnetic behavior of sections, which may include signal traces, power planes, substrates, and so forth, is crucial during the design flow. Driven by broadband and nonlinear circuit design [1][2][3][4][5], time-domain coupled electromagnetic and circuit simulation has been gaining popularity. In particular, integral-equation methods [6 -14] have proven to be useful since radiation conditions are built in and only surface meshing and modeling is needed. In this work, the time-domain integral equation (TDIE) method is enhanced to model realistic loss behavior in substrates, which is a crucial component for quality-factor prediction of integrated passives, as well as potentially for thermal pattern prediction. The EM simulation environment in emerging and future 3D integrated circuits is characterized by multiple piecewise homogeneous regions. Each region is comprised of lossy materials, which may or not have a strong impact on the overall performance. In general, for higher speed and higher sensitivity systems such as RF and analog methods, the loss is a crucial factor in determining system specifications and performance. The TDIE approach has been shown to work with lossy material [15][16][17][18] wherein the Green's functions, besides possessing delta functions in time, also include a broadly exponentially decaying 'wake'. This leads to the implementation issue that the spatial integrals at retarded times have to be replaced by temporal convolutions. This convolution brings not only coding complexity, but also increases the computational cost dramatically [15,17].In the presented work, the multiregion substrate geometry is addressed with a TDIE solver. An equivalent-surface approach for each region is used along with the following method to tackle the lossy medium Green's function. To circumvent the difficulty caused by the convolution in time, the decaying 'wake' in the Green's function is approximated by a sum of decaying exponentials via Prony's method. It is shown that for circuit dimensions and realistic losses, the decaying 'wake' changes slowly with the variation of the distance between the source and observation point. This allows the creation and use of an exponential fitting table for discrete distances. The use of the exponential models permits t...

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Temporal acceleration of time‐domain integral‐equation solvers for electromagnetic scattering from objects residing in lossy media

Cited by 10 publications

References 19 publications

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials

MOT Solution of the PMCHWT Equation for Analyzing Transient Scattering from Conductive Dielectrics

Modeling of lossy multiregion substrates in microelectronic circuits using time‐domain surface integral equations

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