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.