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

Xue, Ping; Chen, R. S.; Tsang, Kim Fung; Yung, E.K.N.

doi:10.1002/mop.21758

Cited by 10 publications

(9 citation statements)

References 16 publications

(17 reference statements)

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“…To accelerate the convergence rate of iterative methods, preconditioning techniques are usually employed [17,21,22,[27][28][29][30][31][32][33]. One widely used preconditioner is the incomplete LU (ILU) decomposition of the coefficient matrix and its block variants [21,28].…”

Section: Gmresr Algorithmmentioning

confidence: 99%

“…The multigrid preconditioned CG method was used to analyze the scattering of electromagnetic wave but the improvement is limited since the problem is of time-harmonic [32,33]. Like diagonal or block diagonal matrix preconditioner, the symmetric successive overrelaxation (SSOR) preconditioner can also directly be derived from the coefficient matrix without additional cost and can lead to convergence improvement for sparse linear systems [17,[29][30][31]. But FFT technique cannot be applied into Krylov subspace algorithms if SSOR preconditioner is used.…”

Section: Gmresr Algorithmmentioning

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%

See 2 more Smart Citations

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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Section: Gmresr Algorithmmentioning

confidence: 99%

Section: Gmresr Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…This preconditioning strategy is combined with both the sparse approximate inverse (SAI) [9,10] and the symmetric successive over-relaxation (SSOR) [11,12] preconditioning techniques in two successive steps to obtain a better preconditioner for the original matrix equations. The newly constructed preconditioner combines the advantages of both the SAI and SSOR preconditioners with less computational complexity without the breakdowns of incomplete factorization technique.…”

Section: Introductionmentioning

confidence: 99%

Extend two-step preconditioning technique for the Crank-Nicolson finite-difference time-domain method to analyze the 3D microwave circuits

Yang

Fan

Ding

et al. 2009

Int J RF and Microwave Comp Aid Eng

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The increase of the time-step size significantly deteriorates the property of the coefficient matrix generated from the Crank-Nicolson finite-difference time-domain method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. The main purpose of this article is to show that the two-step preconditioner can greatly accelerate the convergence of the iterative method, such as GMRES. Numerical simulations show that this two-step preconditioned GMRES iterative method has a faster convergence speed than those methods when the preconditioner is used alone.

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“…It is desirable to be able to switch within the outer iteration instead of restarting. For the generalized minimum residual method (GMRES) algorithm, this can be easily accomplished with the help of a rather simple modification of the standard algorithm, referred to as the flexible GMRES (FGMRES) [18][19][20][21]. 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.…”

Section: Introductionmentioning

confidence: 99%

Ssor Preconditioned Inner-Outer Flexible Gmres Method for MLFMM Analysis of Scattering of Open Objects

Ding¹,

Chen²,

Fan³

2009

PIER

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Abstract-To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations. The inner-outer flexible generalized minimum residual method (FGMRES) is combined with the symmetric successive overrelaxation (SSOR) preconditioner based on the near-part matrix of the EFIE in the inner iteration of FGMRES to speed up the convergence rate of iterative methods. Numerical experiments with a few electromagnetic scattering problems for open structures are given to demonstrate the efficiency of the proposed method.

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

Cited by 10 publications

References 16 publications

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

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

Extend two-step preconditioning technique for the Crank-Nicolson finite-difference time-domain method to analyze the 3D microwave circuits

Ssor Preconditioned Inner-Outer Flexible Gmres Method for MLFMM Analysis of Scattering of Open Objects

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