Towards A Unified Theory that Reveals the Essence of Numerical Methods in Electromagnetics

Maxwell's equations provide the fundamental framework for describing electromagnetic phenomena, including RF and microwave structures. Solving these equations typically involves numerical methods based on diverse and seemingly unrelated mathematical approaches. This presentation introduces a unified theory of numerical methods in computational electromagnetics, demonstrating that the essence of numerical methods is to approximate solutions using projections in an inner product space, with basis functions via the process of weighted residuals. By offering a single mathematical framework, this theory bridges various numerical methods, paving the way for hybrid approaches and providing new insights into programming, learning, and applying numerical methods.