A rigorous solution to the low-frequency breakdown in full-wave finite-element-based analysis of general problems involving inhomogeneous lossy dielectrics and non-ideal conductors

State-of-the-art methods for solving the low-frequency breakdown problem of full-wave solvers rely on low-frequency approximations, the accuracy of which is a great concern. A rigorous method is developed in this work to fundamentally eliminate the low frequency breakdown problem for full-wave finite-element based analysis of general 3-D problems involving inhomogeneous lossy dielectrics and non-ideal conductors. In this method, the frequency dependence of the solution to Maxwell´s equations is explicitly derived from DC to any high frequency. The rigor of the proposed method has been validated by the analysis of realistic on-chip circuits at frequencies as low as DC. Moreover, the proposed method is applicable to both low and high frequencies, and hence constituting a universal solution to Maxwell´s equations in a full electromagnetic spectrum.