Notes on solving Maxwell equations, part I, finite elements method using vector elements

The content of this document is a brief description of the steps taken in the process of designing and writing a simulation program for solving the Maxwell equations using the finite element method (FEM). It covers the theory from the literature by various authors. It deals with the conversion to certain conventions, like the orientation of axis and the time convention for time-harmonic solutions and the non-dimensionalization process. The mathematical foundation is far from complete, but the reader is referred to the literature for the details. The application is the scattering by an object of electromagnetic waves. Part 2 will cover the far-field calculation given the near-field solution obtained by the FEM.