A numerical study on the performances of the flexible BiCGStab to solve the discretized E-field integral equation

To efficiently solve the large, dense and non-Hermitian matrix system provided by the E-field Integral Equation (EFIE) modelization of the electromagnetic scattering by arbitrarily shaped perfect conducting bodies, the Generalized Minimal Residual method (GMRES) with preconditioning is usually employed. Nonetheless, even if optimal in a broad sense, the GMRES suffers of the drawback that its memory space demand grows linearly with the number of iterations. To avoid possible out-of-memory errors, a Krylov subspace method involving a fixed amount of memory per iteration has to be used. This is the case of the Bi-Conjugate Stabilized (BiCGStab) method. Although this method has been exploited with success to handle dense matrix system arising from EFIE discretization, its flexible version, the Flexible-BiCGstab, at the best of the authors knowledge, has not received any attention within this context. In this work, a study on the performances of the Flexible BiCGStab to solve the discretized EFIE is presented. Numerical results demonstrate that the Flexible BiCGStab is, at least in the examined cases, a workable alternative to the the standard BiCGStab with ILUT preconditioning.