5 Complexity reduction of electromagnetic systems

: This chapterhas two main objectives: first, topropose a computer-aidedcon-sistent and accurate description of the behavior of electromagnetic devices at various speeds or frequencies and, second, to describe procedures to generate compact electrical circuits for them, with an approximatively equivalent behavior. The extracted models should have a finite complexity as low as possible, while yielding an acceptable accuracy, as well as preserve essential characteristics, such as passivity. A suc-cessful complexity reduction can be obtained if a priori and on-the-fly reduction strategies are applied before and during the model discretization, followed by a posteriori complexity reduction.