Description
Book SynopsisThis book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach.As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials.
Table of ContentsMathematical modelling of the electromagnetic field in continuous media - Maxwell equations and constitutive relations; mathematical framework for electromagnetism; stationary scattering problems with bounded obstacles; waveguide problems; stationary scattering problems on unbounded obstacles; evolution problems; appendix: differential geometry for electromagnetism.
