Compatibility Relations for Time-Domain and Static Electromagnetic Field Problems

摘要

When computing an electromagnetic field using a numerical method, e. g. thefinite element method, it is possible that, although Maxwell's equations are discretized accurately, highly inaccurate computational results are obtained. In those cases it can easily be shown that (some of) the electromagnetic compatibility relations (field properties that follow from Maxwell's equations) are not satisfied. The divergence condition on the fluxes, for instance, follows directly from the field equations but not necessarily from their discretized counterparts. This necessitates inclusion of the compatibility relations in the finite-element formulation of the field problem. First a survey is given of all electromagnetic compatibility relations for the time-domain electromagnetic field equations. Subsequently the compatibility relations for the static field equations are discussed.