EEL 766 Numerical Methods in Electromagnetics 2014-15 Semester II
Lectures: Tu 4:30-6p, Fr 5-6:30p (Slot K-ish), Block IIA - 305 (Bharti). Instructor: Uday Khankhoje


News
  1. Major on 06 May 2015, 3:30-5:30pm in Block I/336. Portion: Lecture topics 5-9, open notes.
  2. Course presentations, phase 3 on 17 April 2015.
  3. Homework 3 is out on 01 April 2015, due on 20 April 2015. Latex users, please use the following header to prepare your report "\documentclass[11pt,a4paper,onecolumn]{IEEEtran}". Hardcopy submission is required.
  4. Course presentations, phase 2 on 27 March 2015.
  5. Homework 2 is out on 25 Feb 2015, due on 12 March 2015.
  6. Mid semester exam on 10 March 2015.
  7. Course presentations, phase 1 on 27 Feb 2015.
  8. Homework 1 is out on 29 Jan 2015, due on 10 Feb 2015.
  9. Please note the new class timings above.
  10. The course has a Facebook group: please join!
Lecture Topics
  1. An overview of computational electromagnetics (CEM). Ch. 1 of Chew. (Lecture 1 06.01.15)
  2. Review material: Vector calculus (Ch. 1 of Griffiths, and URL, videos); Maxwell's equations (Ch. 7 of Griffiths) and electromagnetic wave propagation (Ch. 9 of Griffiths). (Lecture 2 07.01.15)
  3. Finite difference time domain method (FDTD). Ch. 12 of Peterson for the 2D method. See the 1D method from Ch. 3 here (upto 3.3) and a general overview of the 3D method here. Refer to Ch. 5 of Gedney for absorbing boundary conditions, and Ch. 4 for source specifications.
    1. 2D formulation (differential and integral), time update equations, numerical stability. (Notes on 2D) (Lecture 3 10.01.15)
    2. von Neumann stability, Lax-Richtmyer theorem for convergence conditions, divergence conditions in FDTD. (Lecture 4 13.01.15)
    3. Numerical dispersion, handling conducting materials and imposing PEC boundary conditions. (Lecture 5 16.01.15)
    4. Modeling dispersive media, 1st order absorbing boundary condition (notes). (Lecture 6 20.01.15)
    5. Failure of ABC, formulation of PML (paper on coordinate stretching interpretation). (Lecture 7 21.01.15, Lecture 8 28.01.15)
    6. Sources in FDTD: volume currents, total/scattered field formulations (notes) and a short tutorial on meep. (Lecture 9 30.01.15)
  4. Finite element method (FEM): frequency domain formulation. Instructor notes on the 2D vector FEM. Handout on shape functions and 1D/2D formulations.
    1. FEM formulation, weak forms. (Lecture 10 03.02.15)
    2. Example of a 2D scalar formulation (see sec IIA of this and ignore the stochastic part), shape functions (Ch. 2 of Volakis1). (Lecture 10 03.02.15)
    3. 2D vector FEM implementation, computation of matrix elements and matrix assembly (sec III of Instructor's notes). (Lecture 11 10.02.15)
  5. Linear vector space viewpoint of computational methods (handout). Ch.2 of Chew. (Lecture 12 25.02.15)
  6. Integral equation method (IEM): frequency domain formulation.
    1. Equivalence between scattering and radiation problems, concept of Green's function. Instructor notes on deriving the electric field integral equation (EFIE) in the special case of TM polarization. (Lecture 13 13.03.15)
    2. Deriving Green's functions in 2 and 3 dimensions. Useful handout: link (local copy). (Lecture 14 14.03.15)
    3. Solving the forward problem: the method of moments. See one of the early papers on the subject here (local copy). Introduction to the Born Iterative method for solving the inverse problem. See the original paper here (local copy). (Lecture 15 17.03.15)
    4. Electric field integral equation for perfectly conducting surfaces (TM pol, and 2D): Ch 1.7 of Peterson. Solution by method of moments, and computation of radar cross-section: Ch 2.1 of Peterson. (Lecture 16 24.03.15)
  7. Methods of solving linear equations: matrix condition number, steepest descent and conjugate gradient methods (link). Extra material: See topics 11.4-6 here. (Lecture 17 07.04.15, Lecture 18 10.04.15)
  8. Introduction to periodic media, quantitative derivation of photonic bandgap in 1D structures. See lecture notes here, sec 2.2. (Lecture 19 21.04.15)
  9. Band structure calculations in periodic media; use of the tight-binding model in cases where the operator in the master equation is not Hermitian. Slides, link1, link2. (Guest lecture by Sayak Bhattacharya: Lecture 20 25.04.15)
Course Presentations
  1. Rahul Trivedi: Non-local hydrodynamic models in Finite Element Methods. Slides
  2. Suman Shekhar: Finite-difference time-domain methods in Organic LEDs. Slides
  3. Phani Kiram: Transformation Media Based Approach for Efficient Monte Carlo Analysis of Scattering From Rough Surfaces With Objects. Slides
  4. Yaswanth Kalepu: FEM based contrast-source inversion for microwave imaging. Slides.
  5. Divyanshu Mund: Four-Level Two electron FDTD model of losing action in a semiconductor. Slides
  6. Shivam Khare: Dielectric relaxation in dielectric mixtures.Slides.
  7. Nidhi Dua: Adaptive FEM for Schrodinger Equation. Slides.
Course flyer
  • Topics (this is a broad outline and a subset of these topics will be covered) :
    Review of vector calculus, review of electromagnetism, advanced concepts in EM: Uniqueness, reciprocity, reaction, volume equivalence, surface equivalence (Huygen's theorem), image theory, finite difference time domain method (FDTD), frequency domain eigen solutions of Maxwell's equations for periodic structures, finite element method (FEM), integral equation methods and the method of moments (MoM), geometric theory of diffraction (GTD), numerical methods of solving matrix equations.
  • Reference material:
    Advanced Engineering Electromagnetics - C A Balanis, 1st ed.
    Computational Methods for Electromagnetics - Peterson, Ray, Mitra
    Introduction to the FDTD for Electromagnetics - Gedney
    Integral Equation Methods for Electromagnetic and Elastic Waves - Chew, Tong, Hu
    Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications - Volakis1, Chatterjee, and Kempel
    Frequency Domain Hybrid Finite Element Methods for Electromagnetics - Volakis2, Sertel, Usner
    Photonic Crystals: Molding the Flow of Light - Joannopoulos, Johnson, Winn, and Meade, 2nd ed
    Introduction to Electrodynamics - Griffiths, 4th ed
Grading
  • Exams: Mid sem: 25%, End sem: 25%
  • Assignments/projects: 45%, Class interaction: 5%
Policies
  • As per institute rules, 75% attendance (minimum) is mandatory and will be enforced.
  • All emails to the instructor or TAs must have EEL766 in the subject line. And read this ;-).
  • Collaboration policy: For the purpose of assignments and projects, students are free to: Look up any reference texts or Internet resources, use any computational software (Mathematica/MATLAB), and discuss with faculty or fellow students. However, the assignments turned in must be entirely original. Strictly off limits are: Looking at the final work of a fellow student, or the solution manuals of any reference text, or past assignment/examination material of any courses.
  • Academic misconduct: There will be zero tolerance towards any unethical means, such as plagiarism (COPYING in plain and simple terms). Read these links to familiarize yourself, there will be no excuse for ignorance: URL1, URL2, URL3. Penalties incude: receiving a zero in a particular assignment/examination, receiving a fail grade for the entire course, having a note placed in your permanent academic record, suspension, or all of the above. All electronic submissions will be via a plagiarism detection software, TurnItIn. Details will be discussed in class.

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