An implicit finite element time-domain method with unconditional stability

Volume discretization techniques have been used extensively for the full wave analysis of microwave circuits and resonators. Most predominately, the finite-difference time-domain method, has proven to be a highly efficient technique. Finite element methods have also been used in the frequency domain and in the time domain using implicit methods. For an implicit method to be competitive computationally with an explicit method, the number of time iterations required to converge to a final solution must be significantly less. Unfortunately, the implicit finite element time-domain (FETD) methods presented are all conditionally stable. An unconditionally stable FETD algorithm is presented. The variational formulation is based on the vector wave equation. A time integration technique is proposed which leads to an unconditionally stable solution. Some numerical examples based on a cavity resonator problem are presented to demonstrate the efficiency and accuracy of the method.