Unconditionally stable time-domain mixed finite-element method

Abstract

Previous work has developed a time-domain mixed finite-element method using Whitney 1-forms and Whitney 2-forms to represent the electric field and magnetic flux density, respectively in the coupled, first order Maxwell's equations. However, the leapfrog time-stepping scheme used in most of those works is conditionally stable, and the time step size is closely tied to the spatial discretization. In this work, we present an unconditionally stable time-stepping method for the time-domain mixed finite-element method based on the second order Newmark Beta time-stepping algorithm; at the conference, we will present a more elaborate/rigorous proofs on the stability of the algorithm given choices of certain parameters.