Operator index reduction in electromagnetism

The aim of this work is introducing an index reduction technique in the operator level, thereby regularization of the high index differential-algebraic equations (DAEs) which are derived by spatial semi-discretization of the partial differential equations (PDEs) in electromagnetism can be avoided. The introduced technique is applied to the obtained operator DAE system which is resulted by considering the PDE system in the weak sense for the suitable Hilbert spaces. In addition, for the discretization, the Galerkin method is applied which in turn provides automatically nice properties of the discrete operators for the index determination.