Integral Equations in Computational Electromagnetics and Their Implementations

Integral equations in Computational Electromagnetics (CEM) are one branch of a diverse field.There are many methods to solve for electromagnetic scattering and transmission, with boundary integral equations being one of the most efficient. This is due to only needing to discretize the object's surface, leading to smaller, dense systems as opposed to the larger, sparse systems encountered with Finite Element Method (FEM). Combining the boundary integral method with FEM leads to the creatively named Finite Element Boundary Integral (FEBI) method. It can use the more appropriate method as needed for a given region of space. We turn our focus to boundary integral methods and their implementations.The subfield of boundary integral equations comprises many subparts, including formulations, representations, testing, singularity treatment, acceleration techniques, solvers, preconditioning, and others.In this thesis, I will present several new and existing formulations using the same formulation framework, demonstrate how to perform the integrals for analytic and piecewise basis and testing functions, modify acceleration techniques for various integral equations, and present supporting results.The new formulations are well-conditioned, free from traditional breakdowns, and comparable to state-of-the-art formulations.Most of the implementation of all the formulations presented is shared to limit unintended comparisons.