The Gmres Iterative Algorithm To Accelerate The Application Of Technology In The Fast Fourier Transform Analysis Of Media Scattering

The method of moment (MoM) is often effectively used for solving electromagnetic scattering problems. This problem, however, involves a dense system of linear equations. To solve the three-dimensional (3-D) weak-form volume electric field integral equation, there is a traditional method named Generalized Minimum Residual Method (GMRES) except the conjugate gradient method (CG). But we always use the restarted GMRES (GMRES( m)) for the increasing memory requirement in GMRES method. However, the GMRES( m) slower the convergence because the orthonormal subspace calculated in the former computation is discarded when the restarting occurs. The accelerative GMRES( m) with the fast Fourier transform (FFT) for solving electromagnetic scattering of three dimensional dielectric bodies is developed. Three kinds of accelerative techniques including eight methods are introduced. For several electromagnetic scattering problems, the accelerative Krylov-FFT method converges more than two times faster than the conventional conjugate gradient (CG)-FFT method, and more than one time faster than GMRES(m)-FFT.In the end, we introduce two new methods, and one of which is the improvement of the Flexible Generalized Minimum Residual (FGMRES) method. It is well known that the deflated technique can throw off the infection of the minimum eigenvalues. It抯natural to combine the FGMRES with the deflated technique, and the new kind of FGMRES converges about three times faster than CG-FFT method. Furthermore, numerical results show that the new method is more efficient than FGMRES. There is another new Krylov-FFT method, GMRES with Explicitly Restarting (GMRES-ER). The improving form of SOFGMRES (GMRES with initial Subspace, Orthonormal columns, and Filtering) method converges 3-6 times faster than the conventional CG-FFT method and 1-12 times faster than GMRES( m )-FFT method. Because GMRES-ER not only throws off the influence of minimum Ritz Values, but also takes off the inflection of Maximum singular values, the condition number becomes smaller and consequently the new method makes convergence faster. Numerical results also demonstrate that the GMRES-ER-FFT method is more efficient compared with other improved Krylov-subspace iterative fast Fourier transforms methods.