Modern Graduate Electromagnetics Education—A

New Perspective W.C. ChewW.C. Chew

Director, Center for Computational EM and Director, Center for Computational EM and EM Lab.EM Lab.

Department of Electrical and Computer Department of Electrical and Computer EngineeringEngineering

University of IllinoisUniversity of Illinois

Urbana, IL 61801-2991Urbana, IL 61801-2991

PIERSPIERS

July 7, 2000July 7, 2000

Outline

Importance of electromagnetics.Importance of electromagnetics. History of Electromagnetics.History of Electromagnetics. Roles of physics and mathematics in Roles of physics and mathematics in

electromagnetics.electromagnetics. Role of computer science in electromagnetic Role of computer science in electromagnetic

analysis.analysis. Type of graduate students we have to reckon Type of graduate students we have to reckon

with.with. Roles of graduates in the academe and Roles of graduates in the academe and

industry.industry. Conclusions.Conclusions.

Importance of Electromagnetics

ElectromagneticsElectromagnetics

BiomedicalEngineering& BioTech

WirelessComm. &Propagation

Physics BasedSignalProcessing &Imaging

ComputerChip Design& Circuits

Lasers &Optoelectronics

MEMS &MicrowaveEngineering

RCS Analysis,Design, ATR& StealthTechnology

AntennaAnalysis &Design

EMC/EMIAnalysis

RemoteSensing &SubsurfaceSensing & NDE

Importance of Electromagnetics-Background

Maxwell’s equations remains a fundamental Maxwell’s equations remains a fundamental law that drives electrical engineering, which law that drives electrical engineering, which is the study of the manipulation of electricity.is the study of the manipulation of electricity.

Maxwell’s equations have strong predictive Maxwell’s equations have strong predictive power.power.

EM analysis is important in many engineering EM analysis is important in many engineering and scientific disciplines.and scientific disciplines.

Complete solution of Maxwell’s equations can Complete solution of Maxwell’s equations can expedite many design and analysis process.expedite many design and analysis process.

Electromagnetic analysis has been Electromagnetic analysis has been traditionally performed with either simple traditionally performed with either simple geometry, or approximate pencil-and-paper geometry, or approximate pencil-and-paper methods.methods.

IncompleteBrief History of Analysis with

Maxwell’s Theory

Age of simple shapes: Scattering from Age of simple shapes: Scattering from spheres, cylinders, planes etc.spheres, cylinders, planes etc.– Sommerfeld, 1896,1949, Rayleigh, 1897, Mie, 1908, Debye, Sommerfeld, 1896,1949, Rayleigh, 1897, Mie, 1908, Debye,

1909, Chu & Stratton, 1938, 1941, Marcuvitz, 1951, Wait, 1909, Chu & Stratton, 1938, 1941, Marcuvitz, 1951, Wait, 1955.1955.

– Bowman, Senior & Uslenghi, 1969.Bowman, Senior & Uslenghi, 1969.

Age of approximations: Approximate solution Age of approximations: Approximate solution methods, asymptotic and perturbation theorymethods, asymptotic and perturbation theory– Bremmer, 1951, Keller, 1956, Jones & Kline, 1958, Fock, Bremmer, 1951, Keller, 1956, Jones & Kline, 1958, Fock,

1965, Hanse, Lee & Deschamps, 1976, Felsen & 1965, Hanse, Lee & Deschamps, 1976, Felsen & Marcuvitz, 1973.Marcuvitz, 1973.

Age of numerical methods: MOM, FDTD, FEMAge of numerical methods: MOM, FDTD, FEM– Yee, 1966, Harrington, 1968, Silvester, 1972, Rao, Wilton Yee, 1966, Harrington, 1968, Silvester, 1972, Rao, Wilton

& Glisson, 1983, Mittra, 1980+, Taflove, 1980+.& Glisson, 1983, Mittra, 1980+, Taflove, 1980+.

Scattering by Simple Shapes1890s-1950s

EM theory was predated by theory of fluid EM theory was predated by theory of fluid and theory of sound.and theory of sound.

They were very rich in mathematics, with They were very rich in mathematics, with famous mathematicians such as Euler, famous mathematicians such as Euler, Lagrange, Stokes, Gauss.Lagrange, Stokes, Gauss.

Many mathematics of low-Reynold number Many mathematics of low-Reynold number flow and scalar wave theory of sound can be flow and scalar wave theory of sound can be transplanted with embellishment to EM transplanted with embellishment to EM theory.theory.

Sommerfeld Half-Space Problem

1949

Radiation of a Hertzian dipole on top of the Radiation of a Hertzian dipole on top of the half-space earth was solved in terms of half-space earth was solved in terms of Sommerfeld integrals.Sommerfeld integrals.

| '|

0

1/ 22 2

( ) ( ) ( )z zik z z ik zn

z

dk J k e R k e

k k k

r

Approximate Scattering Theory

1950s-1970s

Physical optics approximation, Kirchhoff Physical optics approximation, Kirchhoff approximation, geometrical optics approximation, geometrical optics approximation, geometrical theory of approximation, geometrical theory of diffraction etc.diffraction etc.

Ansatz based:Ansatz based:

The leading order coefficients are often The leading order coefficients are often obtained from canonical solutions such as obtained from canonical solutions such as the Sommerfeld half-plane problem, the Sommerfeld half-plane problem, scattering by a sphere, Watson scattering by a sphere, Watson transformation, etc.transformation, etc.

0 1 21 2

1 1( ) ,

( )

ikrsca e

a a a krr kr kr

r

Numerical Methods1960s

Method of moments (Harrington, 1960s)Method of moments (Harrington, 1960s)– Integral equation based.Integral equation based.

– Versatile geometry handling.Versatile geometry handling.

– Small number of unknowns.Small number of unknowns.

– Cons: DENSE MATRIX SYSTEM.Cons: DENSE MATRIX SYSTEM.

Finite Difference Time Domain Method (Yee, Finite Difference Time Domain Method (Yee, 1960s)1960s)– Differential equation based.Differential equation based.

– Simplicity (euphoric).Simplicity (euphoric).

– Sparse matrix system.Sparse matrix system.

– Cons: LARGE NUMBER OF UNKNOWNS.Cons: LARGE NUMBER OF UNKNOWNS.

– Cons: GRID DISPERSION ERROR.Cons: GRID DISPERSION ERROR.

Basic Physics Knowledge of a Student

Modern physicsModern physics– Understand the thought processes and abstractions that Understand the thought processes and abstractions that

go on in the field of physics.go on in the field of physics.

Physics of classical electromagneticsPhysics of classical electromagnetics– Fundamental solutions of simple shapes and geometries.Fundamental solutions of simple shapes and geometries.

– Physics that arises from approximate method, surface Physics that arises from approximate method, surface waves, creeping waves, lateral waves, Goubaud waves, waves, creeping waves, lateral waves, Goubaud waves, guided modes, evanescent modes (tunneling), radation guided modes, evanescent modes (tunneling), radation modes, leaky modes, specular reflections, edge modes, leaky modes, specular reflections, edge diffractions.diffractions.

Metamorphosis of the physics over different Metamorphosis of the physics over different lengthscaleslengthscales– Physics of electrostatics and magnetostatics.Physics of electrostatics and magnetostatics.

– Physics of mid frequency and high frequency Physics of mid frequency and high frequency electromagnetics.electromagnetics.

– Physics of optics and rays.Physics of optics and rays.

Basic Math Knowledge of a Student

Mathematical analysis:Mathematical analysis:– Understand the finesse, care and precautions that Understand the finesse, care and precautions that

mathematicians go through in their work.mathematicians go through in their work.

– Harmonic analysis, complex variables.Harmonic analysis, complex variables.

– Perturbation and asymptotic methods.Perturbation and asymptotic methods.

– Linear algebra, linear vector spaces.Linear algebra, linear vector spaces.

Modern demands:Modern demands:– Functional analysis.Functional analysis.

– PDE theory.PDE theory.

– Approximation theory, error bounds.Approximation theory, error bounds.

– Topology.Topology.

Computer Science Knowledge

Knowledge of modern programming Knowledge of modern programming languages--object oriented programming languages--object oriented programming paradigm.paradigm.

Parallel computing and large scale Parallel computing and large scale computing.computing.

Algorithms, fast algorithms.Algorithms, fast algorithms. Computer architecture.Computer architecture. Computational geometry.Computational geometry.

Types of Graduate Students

Types of Graduate Students:Types of Graduate Students:

I.I. Students who will do A when instructed to Students who will do A when instructed to do A.do A.

II.II. Students who will do A+B when instructed Students who will do A+B when instructed to do A.to do A.

III.III. Students who will do C when instructed to Students who will do C when instructed to do A.do A.

How do we stimulate creativity?

We should work to bring the best people in to We should work to bring the best people in to work in our field.work in our field.

Good people will always create new areas to Good people will always create new areas to work on and forge new frontiers.work on and forge new frontiers.

Cultivate independent thinking--old Chinese Cultivate independent thinking--old Chinese adage:adage:– If you believe completely in your book, it’s better not to If you believe completely in your book, it’s better not to

have books.have books.

– If you believe completely in your teacher, it’s better not to If you believe completely in your teacher, it’s better not to have teachers.have teachers.

Roles of Grad Students in Academe

Software research.Software research.– Study and develop algorithms and methodology.Study and develop algorithms and methodology.

– Apply methodology to applications.Apply methodology to applications.

– Computer programming.Computer programming.

Hardware research.Hardware research.– Building a component of a larger system.Building a component of a larger system.

– Designing a component using existing CAD tools.Designing a component using existing CAD tools.

Roles of graduates in industry

Most graduates work as system and Most graduates work as system and component design engineers.component design engineers.

Hence, it is imperative that graduate students Hence, it is imperative that graduate students understand the physics of electromagnetics.understand the physics of electromagnetics.

Understanding the physics deeply means Understanding the physics deeply means understanding the mechanism behind how understanding the mechanism behind how things work.things work.

Therefore, in addition to mathematical Therefore, in addition to mathematical analysis and computer programming, and EM analysis and computer programming, and EM students has to understand the physics students has to understand the physics behind a problem.behind a problem.

Conclusions

Electromagnetics will always remain important in Electromagnetics will always remain important in electrical engineering technologies.electrical engineering technologies.

The long and rich history of electromagnetics offers us The long and rich history of electromagnetics offers us a challenge to impart our knowledge to graduate a challenge to impart our knowledge to graduate students.students.

The selected Important knowledge changes with The selected Important knowledge changes with changing times.changing times.

Imparting physical insight into our students is Imparting physical insight into our students is important.important.

It is imperative that we bring the best and the most It is imperative that we bring the best and the most creative people to work in our field.creative people to work in our field.

There is no limit to problems we can work on, and There is no limit to problems we can work on, and creative people will forge new frontiers to rejuvenate creative people will forge new frontiers to rejuvenate the field.the field.