A novel flexible GMRES with deflated restarted for efficient solution of electromagnetic problems

Abstract

resonators are required to achieve a very low oscillator phase noise. However, they exhibit multiple resonances at the harmonics of the fundamental resonant frequency, which can cause the oscillation to start at an undesired frequency. Using the proposed technique, the oscillation is guaranteed to start at only the selected frequency. Furthermore, with the switching function implemented in the shaping resonator, a multiband Colpitts VCO with very low phase noise can be realized. CONCLUSIONSA switched negative resistance shaping technique is presented to design a dual-band Colpitts VCO. The shaping of the negative resistance guarantees oscillation to start at only the selected resonant mode when a multimode resonator is used at the input of the Colpitts oscillator. Using the proposed technique, a dualband VCO is designed with center frequencies of 440 and 640 MHz. A measured continuous frequency tuning range of 15.8 and 16.3% and phase noise of À122 dBc/Hz and À120 dBc/Hz at 100 kHz offset are achieved for the lower band and the upper band respectively. residual with deflated restarted (FGMRES-DR), which can greatly improve the convergence of those large dense complex linear systems. Based on physical mechanism of the scattering problems, in inner iteration of FGMRES-DR, an iterative solution of the near-field matrix in MLFMA is adopted. In outer iteration, deflation method which is purely algebraic is used to eliminate the influence on convergence because of the smallest eigenvalues. Numerical experiments indicate that FGMRES-DR is very effective and can reduce the number of MVP compared with the FGMRES in large-scale electromagnetic problems.

Multiple‐directions asymptotic phase basis functions for efficient analysis of scattering from electrically large objects

“…This scheme leads to a significant reduction in the number of unknowns without compromising the accuracy of geometry modelling. The resultant system matrix is then solved using the inner-outer flexible generalised minimal residual (FGMRES) algorithm accelerated by the MLFMM [26][27][28][29]. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method in monostatic radar cross-section (RCS) calculations.…”