Computational electromagnetism plays a crucial role in many areas of scientific research and industrial applications, including antennas, radar, metamaterials, integrated circuit design, quantum computing, energy generation and transmission, optics, medical imaging, sensing, radioastronomy. This course focuses on integral equation methods for solving Maxwell's equations, covering theory, implementation, applications and recent research developments. Electrostatic problems are first used to introduce students to fundamental concepts: integral formulations of Maxwell's equations, the Green's function, discretization and testing aspects, computation of singular integrals. After a review of direct and iterative methods to solve linear systems, we discuss the most prominent techniques for accelerating integral equation methods, including fast multipole algorithms, FFT-based approaches, and hierarchical matrices. The general case of electrodynamics is considered next, including the choice of basis functions, modeling of excitations, postprocessing of results, modeling penetrable objects. Finally, selected topics from recent research will be presented.

Throughout the course, examples drawn from real applications will be presented, related to integrated circuit design, antenna modeling, and metamaterials. The course engages students in lectures with an active, hands-on approach based on learning notebooks that both exemplify the concepts covered in lectures, as well as require students to immediately put them into practice. Students will be required to solve 3 to 4 assignments and work on a final project, typically related to their research interests. The project deliverables will be: an IEEE-formatted report, a presentation, and the submission of the developed codes.