Modern Graduate Electromagnetics Education

1
Modern Graduate Electromagnetics EducationA New
Perspective 

• W.C. Chew
• Director, Center for Computational EM and EM Lab.
• Department of Electrical and Computer Engineering
• University of Illinois
• Urbana, IL 61801-2991
• PIERS
• July 7, 2000

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Outline

• Importance of electromagnetics.
• History of Electromagnetics.
• Roles of physics and mathematics in
  electromagnetics.
• Role of computer science in electromagnetic
  analysis.
• Type of graduate students we have to reckon with.
• Roles of graduates in the academe and industry.
• Conclusions.

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Importance of Electromagnetics
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Importance of Electromagnetics-Background

• Maxwells equations remains a fundamental law
  that drives electrical engineering, which is the
  study of the manipulation of electricity.
• Maxwells equations have strong predictive power.
• EM analysis is important in many engineering and
  scientific disciplines.
• Complete solution of Maxwells equations can
  expedite many design and analysis process.
• Electromagnetic analysis has been traditionally
  performed with either simple geometry, or
  approximate pencil-and-paper methods.

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IncompleteBrief History of Analysis
withMaxwells Theory

• Age of simple shapes Scattering from spheres,
  cylinders, planes etc.
• Sommerfeld, 1896,1949, Rayleigh, 1897, Mie, 1908,
  Debye, 1909, Chu Stratton, 1938, 1941,
  Marcuvitz, 1951, Wait, 1955.
• Bowman, Senior Uslenghi, 1969.
• Age of approximations Approximate solution
  methods, asymptotic and perturbation theory
• Bremmer, 1951, Keller, 1956, Jones Kline, 1958,
  Fock, 1965, Hanse, Lee Deschamps, 1976, Felsen
  Marcuvitz, 1973.
• Age of numerical methods MOM, FDTD, FEM
• Yee, 1966, Harrington, 1968, Silvester, 1972,
  Rao, Wilton Glisson, 1983, Mittra, 1980,
  Taflove, 1980.

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Scattering by Simple Shapes1890s-1950s

• EM theory was predated by theory of fluid and
  theory of sound.
• They were very rich in mathematics, with famous
  mathematicians such as Euler, Lagrange, Stokes,
  Gauss.
• Many mathematics of low-Reynold number flow and
  scalar wave theory of sound can be transplanted
  with embellishment to EM theory.

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Sommerfeld Half-Space Problem1949

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

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Approximate Scattering Theory1950s-1970s

• Physical optics approximation, Kirchhoff
  approximation, geometrical optics approximation,
  geometrical theory of diffraction etc.
• Ansatz based
• The leading order coefficients are often obtained
  from canonical solutions such as the Sommerfeld
  half-plane problem, scattering by a sphere,
  Watson transformation, etc.

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Numerical Methods1960s

• Method of moments (Harrington, 1960s)
• Integral equation based.
• Versatile geometry handling.
• Small number of unknowns.
• Cons DENSE MATRIX SYSTEM.
• Finite Difference Time Domain Method (Yee, 1960s)
• Differential equation based.
• Simplicity (euphoric).
• Sparse matrix system.
• Cons LARGE NUMBER OF UNKNOWNS.
• Cons GRID DISPERSION ERROR.

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Basic Physics Knowledge of a Student

• Modern physics
• Understand the thought processes and abstractions
  that go on in the field of physics.
• Physics of classical electromagnetics
• Fundamental solutions of simple shapes and
  geometries.
• Physics that arises from approximate method,
  surface waves, creeping waves, lateral waves,
  Goubaud waves, guided modes, evanescent modes
  (tunneling), radation modes, leaky modes,
  specular reflections, edge diffractions.
• Metamorphosis of the physics over different
  lengthscales
• Physics of electrostatics and magnetostatics.
• Physics of mid frequency and high frequency
  electromagnetics.
• Physics of optics and rays.

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Basic Math Knowledge of a Student

• Mathematical analysis
• Understand the finesse, care and precautions that
  mathematicians go through in their work.
• Harmonic analysis, complex variables.
• Perturbation and asymptotic methods.
• Linear algebra, linear vector spaces.
• Modern demands
• Functional analysis.
• PDE theory.
• Approximation theory, error bounds.
• Topology.

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Computer Science Knowledge

• Knowledge of modern programming languages--object
  oriented programming paradigm.
• Parallel computing and large scale computing.
• Algorithms, fast algorithms.
• Computer architecture.
• Computational geometry.

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Types of Graduate Students

• Types of Graduate Students
• Students who will do A when instructed to do A.
• Students who will do AB when instructed to do A.
• Students who will do C when instructed to do A.

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How do we stimulate creativity?

• We should work to bring the best people in to
  work in our field.
• Good people will always create new areas to work
  on and forge new frontiers.
• Cultivate independent thinking--old Chinese
  adage
• If you believe completely in your book, its
  better not to have books.
• If you believe completely in your teacher, its
  better not to have teachers.

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Roles of Grad Students in Academe

• Software research.
• Study and develop algorithms and methodology.
• Apply methodology to applications.
• Computer programming.
• Hardware research.
• Building a component of a larger system.
• Designing a component using existing CAD tools.

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Roles of graduates in industry

• Most graduates work as system and component
  design engineers.
• Hence, it is imperative that graduate students
  understand the physics of electromagnetics.
• Understanding the physics deeply means
  understanding the mechanism behind how things
  work.
• Therefore, in addition to mathematical analysis
  and computer programming, and EM students has to
  understand the physics behind a problem.

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Conclusions

• Electromagnetics will always remain important in
  electrical engineering technologies.
• The long and rich history of electromagnetics
  offers us a challenge to impart our knowledge to
  graduate students.
• The selected Important knowledge changes with
  changing times.
• Imparting physical insight into our students is
  important.
• It is imperative that we bring the best and the
  most creative people to work in our field.
• There is no limit to problems we can work on,
  and creative people will forge new frontiers to
  rejuvenate the field.