Abstract: Electromagnetics is the cornerstone of modern electrical and electronic systems, shaping how we live, work, and interact with the world. As the foundational principle behind electronic design and innovation, solving electromagnetic problems is not just essential—it is transformative. Over the past four decades, computational electromagnetics (CEM) has made remarkable strides in solving electromagnetic problems, with numerous techniques emerging to tackle increasingly complex challenges. In this talk, I will present a unifying theoretical framework that integrates diverse computational methods under a single mathematical structure, offering deeper insight into their connections and hybridization. I will then describe a novel computational approach that leverages the equivalence principle to simplify multilayer structure analyses into single-layer computations, significantly enhancing efficiency without sacrificing accuracy. Finally, I will explore the groundbreaking potential of time-reversal techniques for shape reconstruction, opening new possibilities in imaging and inverse scattering.
