An Efficient Mixed Finite-Element Time-Domain Method for Complex Electrically Small Problems

A new mixed finite-element time-domain (FETD) method is developed to eliminate the low-frequency breakdown phenomenon in the conventional finite-element method when solving electrically small transient problems. Constructed by Gauss's law and the current continuity equation, the divergence constraint equation is incorporated into the wave equation for the electric field in the form of a Lagrange multiplier. Curl-conforming vector basis functions and nodal basis functions are chosen for spatial discretization and the implicit Newmark-beta algorithm is adopted for time integration. It is shown that the terms constituted by the divergence constraint equation in the system matrix help to suppress the effect of the singularity of the stiffness matrix, and the property of the system matrix is significantly improved. Numerical results show that for electrically small problems that cannot be solved by the conventional FETD method, the proposed method not only obtains a stable numerical solution but also achieves a faster convergence rate when an iterative solver is used, thus improving the computational efficiency.