Flexible GMRES‐FFT method for fast matrix solution: application to 3D dielectric bodies electromagnetic scattering

Abstract

SUMMARYIn this paper, the electromagnetic wave scattering is analysed by the efficient Krylov subspace iterative fast Fourier transform (FFT) technique in terms of the electric field integral equation (EFIE) for a dielectric body of general shape, inhomogeneity, and anisotropy. However, when the permittivity of the scatter becomes large, the convergence rate of Krylov subspace iterative methods slow down. Therefore, the innerouter flexible generalized minimum residual method (FGMRES) is used to accelerate the iteration. As a result, nearly 10 times convergence improvement is achieved for high permittivity cases.

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

“…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.…”

“…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.…”

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

“…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].…”

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

“…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.…”

“…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. The FGMRES method with FFT technique is applied for the analysis of electromagnetic wave scattering from threedimensional dielectric bodies with the large permittivity [19].…”