Fast solvers for integral equations in electromagnetics

The purpose of this thesis is the advancement of numerical techniques in computational electromagnetics (CEM), specifically in the area of integral equation formulations in the frequency domain. The research has been focused on the solution of multi-scale, realistic, 3D surface problems using the Method of Moments (MoM). Several state of the art (e.g. with computational costs lower than N2, with N the number of unknowns in the problem) solutions to well-known issues are proposed. The research addresses two important branches in CEM: compression techniques and convergence improvement for iterative solutions. In the compression techniques area, the objective were the so called kernel independent schemes, which work directly on matrix entries (e.g. MoM matrix elements) rather than modifying the computation of these; this kind of schemes is applicable to a broad span of problems (with different kernels) without substantial modifications. The convergence acceleration of iterative solutions was tackled from the low frequency stabilization of kernel independent solvers to a new Domain Decomposition scheme for intermediate and high frequencies.