Explicit and implicit time domain finite element methods using Whiteny forms

Abstract

This paper describes the time domain finite element methods based on p-forms of Whiteny (1957) edge and facet elements. The finite element methods are used in modeling homogeneous and non-homogeneous structures arising in computational electromagnetic applications. The time-harmonic electromagnetic fields differential equations are discretized in the spatial domain by the p-forms of Whiteny elements and in the time domain by the finite difference schemes. The finite element time domain equations are reduced to explicit and implicit differential equations which are solved using the leapfrog and Newmark schemes. The accuracy and computational efficiency of the algorithms are discussed and illustrative example is presented for an EM problem.