Discrete electromagnetism with shape forms of higher polynomial degree

Abstract

The classical Discrete Electromagnetism (DEM) uses a set of discrete differential forms and associated discrete operators for treatment of electromagnetic PDEs. The operators originate from a differential form representation and can be classified as metric-dependent and metric-independent ones. The appearance of the discretised operators depends on the underlying shape functions. While the lowest order version using Whitney elements is well known for its simple structure, a "natural" extension to higher polynomial degrees has yet to be found. We present a higher order Discrete Electromagnetism using a hierarchical set of shape forms. Our focus of interest lies on the magneto(quasi)static formulation of Maxwell's equations. © 2012 Springer-Verlag Berlin Heidelberg.