Maxwell equations and finite element software systems: object-oriented coding needs well defined objects

In this paper we examine the structure of Maxwell equations in order to find clear signposts how to implement finite element software systems. The aim is to recognize the abstractions involved in Maxwell equations and to exploit concepts of modern programming techniques, such as object-oriented design, to imitate the abstractions in numerical computing. As mathematics is the machinery to model physical phenomena, it is worth to imitate the same machinery in a software system. If a software system is constructed this way, it is partitioned into distinct components whose function is evident. And that is a basis for a software system that is modifiable and understandable, which are the main goals in software design.