Finite element methods for electromagnetic scattering problems: Investigation of approximations for the radiation conditions

This work is concerned with the numerical solution of Maxwell's equations. The emphasis is on the study of approximate techniques for truncation of unbounded domains. The original contribution of this study is the treatment, adaptation, analysis and implementation of absorbing boundary conditions using perfectly matched layers in the frequency domain using finite element methods. Previous works have been mainly concerned with the finite difference methods with no foundation to justify truncating the unbounded domains with perfect matched layers with absorbing boundary conditions.; With this goal, weak formulations for the curl-curl wave equation are studied in the context of scattering problems. The finite element method framework is used to discretize the weak formulas. In particular, edge vector functions are used to represent the unknowns in a mesh in the three dimensional space. The well-known Stratton-Chu formula was used to obtain the near to far field transformation using the results obtained with the finite element method.; To simulate the infinite domain, absorbing boundary conditions and perfectly matched layers techniques are considered. A comparative study is presented for three different approaches used to model the perfectly matched layers. The scalar and vector absorbing boundary conditions for rectangular domains are reviewed. Absorbing boundary conditions to terminate absorbing layer regions are developed. Analysis of the theoretical reflection coefficient shows that the combination of these two techniques has better absorbing properties than each one considered separately.; To verify the numerical effectiveness of the combination (absorbing boundary condition and perfectly matched layers); object-oriented software using the studied theory is implemented. The results are given for three canonical problems: the near field of a thin dipole, the scattering by a plate and the penetration of an incident wave through an aperture.