Modern Graduate Electromagnetics Education—A New Perspective

1. Modern Graduate Electromagnetics Education—A 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

2. 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.

3. Physics Based Signal Processing & Imaging Biomedical Engineering & BioTech Computer Chip Design & Circuits Lasers & Optoelectronics Wireless Comm. & Propagation MEMS & Microwave Engineering Electromagnetics RCS Analysis, Design, ATR & Stealth Technology Remote Sensing & Subsurface Sensing & NDE Antenna Analysis & Design EMC/EMI Analysis Importance of Electromagnetics

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

5. IncompleteBrief History of Analysis withMaxwell’s 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+.

6. 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.

7. Sommerfeld Half-Space Problem1949 • Radiation of a Hertzian dipole on top of the half-space earth was solved in terms of Sommerfeld integrals.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. Types of Graduate Students • Types of Graduate Students: • Students who will do A when instructed to do A. • Students who will do A+B when instructed to do A. • Students who will do C when instructed to do A.

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

15. 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.

16. 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.

17. 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.