ABSTRACT
Integrating factors play an important role for discretizing differential equations. This is also the case for partial differential equations despite the fact that is not always clear how such factors should look like in higher-dimensional problems. This chapter presents the construction of the integrating factor that is needed for the Maxwell-Ampere equation in three dimensions. The construction is proposed by considering a simpler case from which one deduce a series of guidelines in order to make an educated guess for the higher dimensional problem. In particular, the chapter considers one of the most successful applications of integrating factors, that is, the Scharfetter-Gummel scheme approach for the simulation of semiconductor devices as a vehicle to identify the essential steps for the construction of the integration factor for the Maxwell-Ampere equation. It then reviews the Scharfetter-Gummel discretization and provides a summary of key observations that will help one to construct the integrating factor for electromagnetic problems.
