This thesis is devoted to the study of processes in the propagation of electromagnetic fields. We do not aim at one particular problem, actually very different kinds of topics are analyzed here. We deal with direct problems as well as with inverse ones, low frequency electromagnetism is discussed and consequently the wave propagation problem in high frequency domain is studied.
Study of electromagnetic materials and their behavior is of a huge interest for the technological world. Its importance originates from the increasing requirements for high performance devices as motors, transformers, radars,... To improve character of electromagnets, new models, accurate numerical schemes and their rigorous analysis are needed to be worked out.
In the first part we aimed at a time dependent eddy current equation of the magnetic field when a non-perfect contact of two different materials is considered on the boundary.
The second part concerning the problems in the high-frequency domain includes the stuyd of elctromagnetic waves and propagation of energy through matter. These problems are mostly posed on an unbounded domain. To solve these problems we use the method of Artificial Boundary Condition (ABC) - widely used for wave problems since 1977.
The third part of the thesis is devoted to the inverse problems in low-frequency electromagnetism. For a design of the material characteristics of the magnetic circuit, such as the electromagnetic loss P, the permeability µ and the electrical conductivity sigma, is essential. In this thesis, the missing material constant turns out to be a measure for the electromagnetic losses.
The end of each part is devoted to numerical examples confirming the theoretical results. All the computations are performed using The Finite Element Toolbox ALBERT
