Computational Electrodynamics is a vast research field with a wide variety of tools. In physics the principle of gauge invariance plays a pivotal role as a guide towards a sensible formulation of the laws of nature as well as computing the properties of elementary particles using the lattice formulation of gauge theories, yet the gauge principle has played a much less pronounced role in performing computation in classical electrodynamics. In this work the author will demonstrate that starting from the gauge formulation of electrodynamics using the electromagnetic potentials leads to computational tools that can very well compete with the conventional electromagnetic field-based tools. Once accepting the formulation based on gauge fields, the computational code is very transparent due to the mimetic mapping of the electrodynamic variables on the computational grid. Although the illustrations and applications originate from microelectronic engineering, the method has a much larger range of applicability. Therefore this book is of interest to everyone having interest in computational electrodynamics. The volume is organized as follows: In part 1, a detailed introduction and overview is presented of the Maxwell equations as well as the derivation of the current and charge densities is different materials. Semiconductors are responding to electromagnetic fields in a non-linear way and the induced complications are discussed in detail. In part 2, the transition of the theory of electrodynamics, using the gauge potentials, to a formulation that can serve as the gateway to computational code is presented. In part 3, the feasibility and success of the methods of part 2 are demonstrated by a collection of microelectronic device designs. Part 4 focuses on a set of topical themes that brings the reader to the frontier of research in building the simulation tools using the gauge principle in computational electrodynamics.
Technical topics discussed in the book include:
Electromagnetic Field Equations
Constitutive Relations
Discretization and Numerical Analysis
Finite Element and Finite Volume Methods
Design of Integrated Passive Components

Computational Electrodynamics

Wim Schoenmaker spent about one third of his carrier in physics working on several aspects of gauge theories. The other two-third of his professional life he worked in the ¿eld of microelectronics, starting in IMEC as a researcher in technology computer-aided design. When being confronted with numerous design problems in microelectronics that were induced by the increasing demand of high-frequency applications, he developed the numerical methods that are discussed in this book by exploiting his expertise in (lattice) gauge theories by adapting these methods for performing numerical simulations. Encouraged by the successful outcomes of these calculations, he co-founded the company MAGWEL that provides electronic design automation tools for microelectronic industry. He is presently the Chief-Technology Of¿cer
and member of the Board of Directors of MAGWEL. Wim Schoenmaker is the principal or co-author of ¿175 peer-reviewed journal and conference contributions. He is the co-author of one book, several book chapters and three patents.