A Three-Dimensional Precorrected FFT Algorithm for Fast Method of Moments Solutions of the Mixed-Potential Integral Equation in Layered Media

Okhmatovski, Vladimir; Yuan, Mengtao; Jeffrey, Ian; Phelps, R. R.

doi:10.1109/tmtt.2009.2033882

Cited by 60 publications

(40 citation statements)

References 33 publications

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“…It is important to point out that the distinction between "near-zone" and "far-zone" interactions in the PFFT algorithm is not based on electrical distance [33]- [35]. Thus, the method can be applied without loss of effectiveness for structures ranging from electrically large to sub-wavelength [35].…”

Section: Fft-enhanced Msos Of Ufftmentioning

confidence: 99%

“…For evaluation of the near interactions between elements nonconformal to the uniform grid, the approach based on subtraction and analytic integration of the Green's function singularity followed by quadrature-based integration [49] of the nonsingular part of the DGF is commonly used [33]- [35]. First, the components are expressed in terms of the scalar potentials [50] as in (21) where is the wavenumber of the media at the observation point.…”

Section: Evaluation Of Green's Function Samples Via Dcim Fitting and mentioning

confidence: 99%

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The Unified-FFT Algorithm for Fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

Rautio

Okhmatovski

Cangellaris

et al. 2014

IEEE Trans. Microwave Theory Techn.

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The unified fast Fourier transform (UFFT) methodology is proposed for fast method of moments analysis of dense integrated circuits embedded in layered media inside perfectly electric conducting or perfectly magnetic conducting enclosures of rectangular cross section. The pre-corrected fast Fourier transform (FFT) method is modified to handle the dyadic Green's function (DGF) of shielded layered media through factorization of the DGF into four convolution/correlation terms enabling fast matrix solve operations (MSOs). Calculation of the impedance matrix elements in the form of an infinite series of waveguide modes is cast into the form of a 2-D discrete Fourier transform allowing for fast FFT-accelerated matrix fill operations (MFOs). Fast FFT-enhanced MSOs and MFOs used in conjunction form the UFFT method. The computational complexity and memory requirements for the proposed UFFT solver scale as and , respectively, where is the number of unknowns in the discrete approximation of the governing integral equation. New criteria specific to shielded circuits for the projection of the current expansion functions on a uniform FFT grid are developed. The accuracy and efficiency of the solver is demonstrated through its application to multiple examples of full-wave analysis of large planar circuits. Index Terms-Computer-aided design (CAD), CAD algorithms and techniques, fast algorithms, numerical analysis, RF integrated circuit (RFIC) modeling.

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Section: Fft-enhanced Msos Of Ufftmentioning

confidence: 99%

Section: Evaluation Of Green's Function Samples Via Dcim Fitting and mentioning

confidence: 99%

The Unified-FFT Algorithm for Fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

Rautio

Okhmatovski

Cangellaris

et al. 2014

IEEE Trans. Microwave Theory Techn.

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“…In this section it is of interest to demonstrate the efficient calculation of the MVP, , by using this decomposition and physically interpret the operations involved. The MVP is evaluated as below (20) For convenience, consider one part of the column vector, namely , that corresponds to the receiver group (21) In (21), contains the excitation coefficients of the basis elements in the transmitter group . In the first step , the collective beam weights of the transmitter group are computed by scaling beam weights of the individual elements with the corresponding excitation coefficients.…”

Section: E Matrix-vector Multiplication and Its Physical Interpretationmentioning

confidence: 99%

“…The efficiency in storage and computational time can be attributed to the computationally attractive algebraic properties of the translation matrix and/or the interpolation coefficient matrices (e.g., sparseness, Toeplitz property). The efficient methods belonging to this class have also been extended to inhomogeneous space problems as for example in [21], [22].…”

Section: Introductionmentioning

confidence: 99%

Complex Source Beam-Moment Method Procedure for Accelerating Numerical Integral Equation Solutions of Radiation and Scattering Problems

Tap¹,

Pathak²,

Burkholder³

2014

IEEE Trans. Antennas Propagat.

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A new hybrid complex source beam-moment method (CSB-MoM) procedure is presented to accelerate the matrix-vector product (MVP) computation in the iterative solution of moment method integral equation problems. The scattering object in this CSB-MoM algorithm is partitioned into groups in a manner similar to the fast multipole method (FMM). However, unlike FMM, the interactions between well separated groups are computed by using the complex source beams (CSBs), which represent the radiation from the basis elements in the group. The directional properties of CSBs allow a fast evaluation for these interactions such that the overall MVP is computed very efficiently. The direct solution time and the storage requirement of the CSB-MoM method is numerically shown to be by optimally selecting the number of groups. A low-memory version of the CSB-MoM method is also presented wherein separated group interactions are computed on-the-fly.Index Terms-Complex source beams (CSBs), moment method (MoM).

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“…Typically, the Green's function explicitly satisfies the radiation conditions, which eliminates the need for discretization of surrounding volumes and localizes the unknown field quantities to the material interface surfaces only. This includes the case of interconnects embedded in multilayered substrates for which the Green's function can be precomputed numerically and reutilized in subsequent MoM solutions for various layout topologies [3]. A proper choice of the Green's function in conjunction with selection of an appropriate acceleration algorithm [3], [4] makes the IE approach the provably fastest existing way to solve certain types of interconnect modeling problems [5].…”

Section: Introductionmentioning

confidence: 99%

A Novel Skin-Effect Based Surface Impedance Formulation for Broadband Modeling of 3-D Interconnects With Electric Field Integral Equation

Al-Qedra

Aronsson

Okhmatovski

2010

IEEE Trans. Microwave Theory Techn.

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The problem of interconnect modeling embedded in multilayered substrate is initially formulated in terms of the volume integral equation (IE) with respect to 3-D conduction current density. One out of three degrees of freedom in volumetric current variation is then eliminated by approximating the current behavior over the coordinate normal to the conductor surface according to the skin-effect. The remaining two degrees of freedom in the volumetric current variation constitute the unknown current distribution on the conductor surface for which a governing surface electric field integral equation is obtained directly from the volume IE via restriction of the volumetric operator's range to the conductor surface. The resultant surface IE features a global to the conductor cross section surface impedance operator, which is shown to approximate the relationship between tangential electric and magnetic field components on the conductor surface. The proposed novel surface IE featuring multilayered media dyadic Green's function is amenable to various discretization schemes including the Rao-Wilton-Glisson method of moments. In this paper the latter is implemented by casting the scattered field operator into Michalski-Zheng's mixed-potential form in conjunction with enforcement of global relationships between the basis and testing functions in conductor cross sections according to the surface impedance operator. Numerical comparisons to alternative conductor loss models show that the method achieves volumetric solution accuracy within the framework of a boundary-element formulation.Index Terms-Integral equation (IE), interconnect, method of moments (MoM), multilayered media, skin-effect, spiral inductor, surface impedance.

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A Three-Dimensional Precorrected FFT Algorithm for Fast Method of Moments Solutions of the Mixed-Potential Integral Equation in Layered Media

Cited by 60 publications

References 33 publications

The Unified-FFT Algorithm for Fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

The Unified-FFT Algorithm for Fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

Complex Source Beam-Moment Method Procedure for Accelerating Numerical Integral Equation Solutions of Radiation and Scattering Problems

A Novel Skin-Effect Based Surface Impedance Formulation for Broadband Modeling of 3-D Interconnects With Electric Field Integral Equation

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