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Electromagnetism has a strong geometrical structure which, however, is hidden when the theory is examined in terms of classical vector analysis. Consequently a more powerful framework of algebraic topology and differential geometry is needed to view the subject. Recently, the geometric view has become rather popular among the community of computational electromagnetism, but still it has been asked, whether the more generic view truly enables one to develop new tools applicable to pragmatic field and wave analysis which could not be discovered otherwise. In other words, is the investment needed to study the new subject justified by the advantages brought by the more accurate viewpoint? Such a question is, evidently, not trivial to answer. Not because the larger framework did not have clear advantages, but rather for it takes a considerable effort to understand the difference between the "old" and "new" approach. Second, the advantages tend to be rather generic in the sense, that the geometric viewpoint tends to be more useful in building a software system to solve electromagnetic boundary value problems instead of in finding some handy techniques to solve certain specific problems. This paper makes an attempt to highlight some keypoints of the geometric nature of electromagnetism and to explain which way the geometric viewpoint is known to be useful in numerical analysis of electromagnetic field and wave problems. We start from the basics of electromagnetism and end up with more specific questions related to computing.
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