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 EquationsConstitutive RelationsDiscretization and Numerical AnalysisFinite Element and Finite Volume MethodsDesign of Integrated Passive Components

Dr Akshara Makrariya has a PhD in Mathematics from the National Institute of Technology (SVNIT) Surat, India, specializing in computational and bio mathematics. She completed her Post-Doctoral Research under the Young Scientist Fellowship (NPDF) programme, from the Science & Engineering Research Board (SERB), DST, and Government of India. Her research interest includes computational models to study temperature distribution in extended spherical and ellipsoidal shaped human organs, computational models to study thermal disturbances due to tumours, and their modelling with different numerical methods like fractional calculus, and the finite volume method, and by using optimization techniques.

Dr Jha obtained his PhD in Mathematics in the year 2013 from the National Institute of Technology (SVNIT) Surat, India. His research area includes mathematical modelling and simulation of calcium dynamics in astrocytes, finite element modelling of biological problems, and fractional differential equations and their applications in physiological problems.

Dr Rabia Musheer has a Doctorate in Applied Mathematics from Maulana Azad National Institute of Technology, Bhopal, India. Her research interests include mathematical machine learning and data science application of mathematical modelling and optimization, soft computing, big data and bioinformatics.

Dr Anant Kant Shukla has a Doctorate from the VIT Vellore and CSIR-Fourth Paradigm Institute, Bengaluru. His research is in the area of analytical solutions and nonlinear systems.

Dr Jha obtained his PhD in Mathematics in the year 2013 from National Institute of Technology (SVNIT) Surat, India. Her research area includes mathematical modeling and simulation of calcium dynamics in neuron cell, and finite element modelling of biological problems.

Dr Parvaiz Ahmad Naik is working as Assistant Professor in Mathematics at the School of Mathematics and Statistics, Xi’an Jiaotong University P. R. China. He received his PhD in Applied Mathematics (Mathematical Biology) in 2015. His interest areas include differential equations, mathematical biology, fractional calculus, calcium dynamics, transmission dynamics of infectious diseases, etc.