Fast analysis of microwave integrated circuits by use of the inner‐outer flexible GMRES‐FFT method

Mo, Lingfei; Chen, R. S.; Rui, P.L.; Feng, Xiaobing

doi:10.1002/mop.20485

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…If the preconditioner is computed by a certain number of GMRES solvers, it is called the inner-outer FGMRES solver. When the inner-outer FGMRES solver is used to analyze microwave integrated circuits with the moment method [23] and waveguide discontinuity problems with TVFEM [24], it can be found that about five times improvement for convergence can be achieved when compared with the conventional GMRES solver. In Ref.…”

Section: The Flexible Gmres Methodsmentioning

confidence: 99%

The multigrid preconditioned flexible GMRES solver for hierarchical TVFEM analysis

Zhu

Tang

2007

Micro & Optical Tech Letters

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mm, length l ϭ 23.31 mm, substrate height b ϭ 0.254 mm, cylinder spacing W ϭ 1.2 mm, permittivity r ϭ 2.2, and loss tangent tan ␦ ϭ 0.0009; at K band, SIW width a ϭ 6 mm, length l ϭ 8 mm, substrate height b ϭ 0.254 mm, cylinder spacing W ϭ 1 mm, permittivity r ϭ 2.2, and loss tangent tan ␦ ϭ 0.0009.In Figures 5 and 6, we can see that, the difference between calculation and simulation results increase with the cylinder radius and frequency band. However, the deviation is not big even at K-band. At X-band, the maximum deviation is about 1.84%, while it is 2.98% at K-band. The results of calculation and simulation imply the validity and accuracy of our derived formula; all the deviations are less than 3%. There are three potential reasons causing the errors. First, the equations of electromagnetic fields in SIW resonance cavity is not the same as those in RW resonance cavity strictly; second, the current density distribution on metal cylinders change along the radius of cylinders, which definitely have an impact on integral; third, the simulation is implemented by commercial software HFSS, error of the software is also a factor potentially. CONCLUSIONSThe quality factor of the SIW resonance cavity is investigated in this paper. The conductor losses on the sidewalls, front/end walls and top/bottom planes of the cavity have been derived separately, the formula of the quality factor for the SIW cavity is proposed for the first time. The calculations from the derived formula at several frequency bands have been made, good agreements are observed between the calculations and the numerical HFSS simulations. The maximum deviations at S-, X-, and K-bands are 1.52%, 1.84%, and 2.98%, respectively, all less than 3%, demonstrating the validity and the accuracy of our formula. In addition, the error factors are discussed also in the paper. ACKNOWLEDGMENTThe authors express their gratitude to the financial support of the National Science Foundation of China under Grant 60471025 and the Natural Science Foundation of Jiangsu Province under Grant BK2004135. Poling optical fiber to induce a second-order optical nonlinearity allows for fiber-based devices, such as electro-optic modulators, optical switches, and frequency converters, and increased opportunity for more fundamental research into second-order nonlinearity in macroscopic centrosymmetric crystal. Poled silica fiber devices offer low coupling losses and long interaction lengths. Thermally poling is probably the most popular and promising among all poling techniques. Much higher electric fields can be applied by including internal electrodes than is possible with external electrodes because of the high dielectric breakdown of silica compared with that of air. The maximum electro-optic coefficient of 6 pm/V in silica is observed in a fiber with internal electrodes [1]. Internal electrodes are always achieved by inserting thin metal wires into fibers. However, the lengths of electrodes are usually not more than 10 cm. Manufacturing longer fibers for poling is desirable becaus...

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Section: The Flexible Gmres Methodsmentioning

confidence: 99%

The multigrid preconditioned flexible GMRES solver for hierarchical TVFEM analysis

Zhu

Tang

2007

Micro & Optical Tech Letters

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“…This has led to the development of various iterative algorithms with the FFT technique for solving the surface current with computational complexity of O(N log N ), where N denotes the number of unknowns. Here the details are omitted (see [11,[19][20][21][22][23][24][25][26][27]). After the unknown currents are obtained, the transmission coefficient can be calculated from the unknown currents.…”

Section: Analysis Of the Fssmentioning

confidence: 99%

“…The GMRESR-FFT method is used to accelerate the solution of the impedance matrix equation [11][12][13]. This method involves an outer generalized conjugate residual method (GCR) [14] and an inner generalized minimal residual method (GMRES) [15,16], where the inner GMRES acts as a variable preconditioner [13,[17][18][19][20] for the outer GCR. A typical FSS structure is analyzed and the good results demonstrate the validity and efficiency of the proposed algorithm.…”

Section: Introductionmentioning

confidence: 99%

Fast Analysis and Design of Frequency Selective Surface Using the Gmresr-FFT Method

Zhuang¹,

Fan

Ding³

et al. 2009

PIER B

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Abstract-In this paper, frequency selective surfaces (FSSs) are analyzed and designed. The analytical procedure is based on method of moments (MoM). The generalized minimal residual recursive method combined with fast Fourier transform (GMRESR-FFT) is utilized to accelerate the solution of the matrix equation. Our numerical results show that the GMRESR-FFT method can converge at least 3 times faster than the generalized minimal residual fast Fourier transform method (GMRES-FFT). In this paper, the cross dipoles are first used to design the FSS filter with a passband at 300 GHz and a stopband at 450 GHz, and then the Jerusalem cross slots are utilized to avoid grating lobes and improve the bandwidth of FSS. Numerical results demonstrate the validity and efficiency of the presented method.

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“…An important property of FGMRES is that it satisfies the residual norm minimization property over the preconditioned Krylov subspace just as in the standard GMRES algorithm. In this method, the preconditioning matrix is obtained through a few iterations and applied to the GMRES iterative solver flexibly [11,12]. Moreover, the inner-outer flexible GMRES method can be combined with a preconditioner to further improve convergence as the conventional GMRES [13,14].…”

Section: Introductionmentioning

confidence: 99%

The SSOR‐preconditioned inner outer flexible GMRES method for the FEM analysis of EM problems

Xue

Chen

Tsang

et al. 2006

Micro & Optical Tech Letters

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Fast analysis of microwave integrated circuits by use of the inner‐outer flexible GMRES‐FFT method

Abstract: ABSTRACT:In this paper, the microstrip circuit is analyzed in terms of the mixed potential integral equation (MPIE)

Cited by 8 publications

References 24 publications

The multigrid preconditioned flexible GMRES solver for hierarchical TVFEM analysis

The multigrid preconditioned flexible GMRES solver for hierarchical TVFEM analysis

Fast Analysis and Design of Frequency Selective Surface Using the Gmresr-FFT Method

The SSOR‐preconditioned inner outer flexible GMRES method for the FEM analysis of EM problems

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