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Computational Electrodynamics

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eBook details

  • Title: Computational Electrodynamics
  • Author : Wim Schoenmaker
  • Release Date : January 05, 2017
  • Genre: Engineering,Books,Professional & Technical,
  • Pages : * pages
  • Size : 100981 KB

Description

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 for computing the properties of elementary particles using the lattice formulation of gauge theories. However, the gauge principle has played a much less pronounced role in performing computation in classical electrodynamics. 


In this work, the author demonstrates 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 will be useful 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 in different materials. Semiconductors are responding to electromagnetic fields in a non-linear way, and the induced complications are discussed in detail. Part 2, using the gauge potentials, presents the transition of electrodynamics theory to a formulation that can serve as the gateway to computational code. In part 3, a collection of microelectronic device designs demonstrate the feasibility and success of the methods in Part 2. 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 


Table of Contents:

Preface

List of Symbols


PART1: Introduction

The Microscopic Maxwell Equations

The microscopic Maxwell equations in integral and differential form

Conservation laws

Potentials and Fields and the Lagrangian

The scalar and vector potential

Gauge invariance

Lagrangian for an electromagnetic field interacting with charges and currents

The Macroscopic Maxwell Equations

Constitutive equations

Boltzmann transport equation

Currents in metals

Charges in metals

Currents in semiconductors

Dielectric and Magnetic media

Wave Guides and Transmission Lines

Transmission line theory

Classical Ghosts Fields

Energy Calculations and the Poynting Vector

The Geometry of Electrodynamics

Integral Theorems

Vector identities


PART 2: The Finite Difference Method

The Finite Element Method

The Finite Volume Method and Finite Surface Method

Finite Volume Method and the Transient Regime


PART 3: Simple Test Cases

Evaluation of Coupled Inductors

Coupled Electromagnetic-TCAD Simulation for High Frequencies

EM-TCAD Solving from 0-100 THz

Large Signal Simulation of Integrated Inductors on Semi-Conducting Substrates

Inclusion of Lorentz Force Effects in TCAD Simulations

Self-Induced Magnetic Field Effects, the Lorentz Force and Fast-Transient Phenomena

EM Analysis of ESD Protection for Advanced CMOS Technology

Coupled Electromagnetic-TCAD Simulation for Fast-Transient Systems

A Fast Time-Domain EM-TCAD Coupled Simulation Framework via Matrix Exponential with Stiffness Reduction


PART 4: Surface-Impedance Approximation to Solve RF Design Problems

Using the Ghost Method for Floating Domains in Electromagnetic Field Solvers

Integrating Factors for the Discretized Maxwell-Ampere Equation

Stability Analysis of the Transient Field Solver

Summary of the Numerical Techniques 


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