Numerical Stability of Dual Full-Wave Formulations With Electric Circuit Element Boundary Conditions

We have successfully implemented full-wave (FW) frequency-domain $E$ - and $H$ -based finite-element (FE) formulations with electric circuit element (ECE) boundary conditions (BCs) for high frequency (HF) applications. These formulations are stable and accurate at HF, with an unknown field strictly inside the domain and a scalar potential with support only on the boundary. Aiming at having all-purpose Maxwell’s solvers at hand, we investigate their numerical stability at very low frequencies (LFs). We show that these FW formulations can be used at LF provided that techniques to ensure numerical stability are applied. If only global (energy-based) stability is sought, then just using the excitation which is essential for the finite element method (FEM) might be enough. If a local (field spatial distribution) stability is needed, we show that scaled hybrid versions of these formulations ensure LF stability. Models of increasing complexity are considered: a homogeneous cylinder (2-D axi/3-D), a coaxial cable (2-D axi/3-D), a coplanar waveguide (3-D).