Topological Approach to Computational Electromagnetism
T. Tarhasaari, Lauri Kettunen · Electromagnetic waves · 2001
Abstract—Software systems designed to solve Maxwell’s equations need abstractions that accurately explain what different kinds of electromagnetic problems really do have in common. Computational electromagnetics calls for higher level abstractions than what is typically needed in ordinary engineering problems. In this paper Maxwell’s equations are described by exploiting basic concepts of set theory. Although our approach unavoidably increases the level of abstraction, it also simplifies the overall view making it easier to recognize a topological problem behind all boundary value problems modeling the electromagnetic phenomena. This enables us also to construct an algorithm which tackles the topological problem with