ECE 5340/6340 (Spring 2012)

Numerical Methods for Electromagnetics

Department of Electrical and Computer Engineering

University of Utah, Salt Lake City, Utah

 

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For Spring 2010 webpage, click here.

 


Term Project Information

 

Term Project Oral Presentation schedule. Presentations start on Monday 4/16.

 

Term Project information. Deadlines, rules, and deliverables for term projects.

 

2D Biological models for EM simulations. These two models represent anatomically correct chest and head slices of a human male, to be used for the projects on implantable antennas.Explanation on the content of the files.

 

Wireless Power Transfer (WPT) and Energy Harvesting projects: You are highly encouraged to participate in the WPT meetings held by Dr. Gandhi and Dr. Cela. In these, information and opportunities specific about these topics is discussed. Contact Dr. Cela to add your email to the meeting list.

 

 


 

 

This schedule may be adjusted throughout the semester. Watch the web for changes. If you find broken links, please email either james.nagel@utah.edu or carlos.cela@utah.edu.

 

 

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Date/
Instructor

Lecture Notes

Reading/Lecture Notes

 

Project Information

(Homework)

 

1

Jan 9
Cela/Nagel

 

Class Overview
Numerical EM Applications
Programming Review

 

Syllabus

createscalarfield.m

plotvectorfield.m

loadandplot.m (good code)

stuff.m (bad code)

2

Jan 11
Cela

 

EM Review: E-field, permittivity, Coulombís Law, Flux of a vector field, Gaussís Law for E fields (Integral), divergence, Gaussís Law for E fields (Differential)

 

Gaussís Law E (integral)

Divergence

Gaussís Law E (differential)

HW 1

HW 1 Solution

HW 1 Matlab code P1

HW 1 Matlab code P2

Matlab note on array indexing

 

Jan 16

 

Holiday (MLK Day)

No Class

 

3

Jan 18
Cela

 

EM Review: B-field,permeability,

Biot-Savart law, Gaussís law for B fields (integral and differential), Divergence Theorem, circulation of a vector field, curl, Stokes Theorem.

Gaussís Law B (integral)

Gaussís Law B (differential)

Divergence Theorem

Circulation and curl

Stokes Theorem

HW 2

HW 2 Solution

HW 2 Matlab code

4

Jan 23
Cela

 

EM Review: Gradient. Laplacian. Poisson and Laplace equations. Ampere-Maxwell Law, Faraday-Maxwell Law. Continuity equation. Constitutive equations.

 

Gradient, Laplacian, Poisson

Faraday-Maxwell Law

Ampere-Maxell Law

Constitutive relations and continuity equation

5

Jan 25
Cela

 

Numerical Differentiation: Forward difference, backward difference, central difference. Higher order derivatives. Partial derivatives. Solution of Linear Systems: Matrix equivalent. Solution sets. Direct vs iterative methods. Sparse matrices. Libraries. Gaussian Elimination. Gauss-Seidel method.

 

Numerical differentiation

Linear systems

Direct vs iterative methods

Gaussian elimination

Gauss-Seidel method

Gauss-Seidel code from book (may be buggy, but will help for HW3)

 

 

 

 

 

HW 3

HW 3 Solutions

6

Jan 30
Nagel

 

Numerical Integration

Riemann Sums

Left/right-point rules

Midpoint, trapezoid, Simpsonís rules

Error bounds

 

Introduction to Numerical Integration

 

7

Feb 1
Nagel

 

Numerical Integration Examples

 

Introduction to the Finite Difference Method (FDM)

Laplace/Poisson Equations
Five-Point Star
Matrix Inversion

Boundary Conditions
Programming Examples

 

Solving the Generalized Poisson Equation using FDM

 

 

 

 

 

HW 4

HW 4 Solutions

HW 4 Matlab Codes

solarData.mat

8

 

Feb 6
Nagel

 

Sparse Matrices
Successive Over-Relaxation
(SOR)
Numerical Gradient

 

9

 

Feb 8
Nagel

 

Capacitance with FDM

Program Examples

Pseudo code for SOR

Pseudo code for gradient

HW 5

HW 5 Solutions

HW 5 Matlab Codes

10

Feb 13
Nagel

 

Multiple Dielectrics with FDM

 

11

Feb 15

Nagel


Characteristic Impedance with FDM

Quasi-Static Conductors with FDM

Magnetic Fields with FDM

Numerical Curl

Pozar Microstrip Z0

Impedance calculations with FDM

HW 6

HW 6 Solutions

HW 6 Matlab Codes

Feb 20

Holiday (Presidentís Day)

No Class

12

Feb 22

Nagel/Cela

 

Helmholtz Equation

Waveguide Eigenmodes with FDM

Project Outlines

Term Project

 

HW 7

HW 7 Solutions

HW 7 Matlab Codes

Poisson_FDM_Solver_2D.m

13

 

Feb 27

Cela

 

 

FDTD: One-dimensional, free space E-H formulation of Finite-Difference Time-Domain method. Courant condition. Determining cell size. Examples.

 

FDTD 1D simple example

14

Feb 29

Cela

 

FDTD: Soft and hard sources. Simple Absorbing Boundary Condition. Excitation sources. Review of wave reflection and transmission. Formulation for propagation in dielectric mediums. Examples.

FDTD notes

Simple ABC

Notes on waveforms

Reflection and transmission

FDTD in non-lossy dielectric

HW8

HW8 Solution

Gaussian.m

15

Mar 5

Cela

 

FDTD: Propagation in lossy dielectrics. D-H formulation. Frequency-domain and FDTD.

 

FDTD and PML articles

FDTD in lossy dielectric

D-H formulation

Frequency domain

FDTD D-H code (1D) code

FDTD D-H code w/ frequency domain analysis code

16

Mar 7

Cela

 

FDTD: Complex media. Debye formulation for dispersive materials. Example: Quarter-wavelength and Half-wavelength filters using dielectric slabs.

 

Link to Debye formulation presentation from Oregon State University

 

FDTD in dispersive lossy media (Debye model) notes

HW9

HW9 Solution

FDTD 1D Debye (dispersive medium) code

Band-pass filter code

Band-stop filter code

Mar 12-16

 

Spring Break

 

17

Mar 19

Cela

 

FDTD: 2D D-H formulation. Perfect Matched Layer (PML).

 

 

 

FDTD 2D TM w/PML code

18

Mar 21

Cela

 

FDTD: Modeling using FDTD. DFT/FFT using Matlab. Advanced excitation sources. Review of rectangular waveguide modes.

 

 

HW/Project Study Session: Friday 23, 11am-12:30pm

WEB 1460

 

 

MEEP MIT FDTD software (Linux/OS X) - Google for instructions on how to install on a Windows PC, it can be done but is a bit more involved.

 

MEEP article.

 

Rectangular waveguide cutoff frequency calculation.

 

HW10 problem 2: building floorplant layout example.

 

HW 10

HW 10 Solution

 

FFT example code

 

Rising sinusoid code

 

Code to build a Gaussian pulse for a given BW and center frequency

19

Mar 26

Nagel

 

Method of Moments (MoM)

 

MoM Lecture Notes

20

Mar 28

Nagel

 

Method of Moments (MoM)

 

HW 11

HW 11 Answer Key

21

Apr 2

Nagel

 

Finite Element Method (FEM)

 

FEM Lecture Notes

 

22

Apr 4

Nagel

 

Finite Element Method (FEM)

 

 

HW 12

23

Apr 9

Cela

 

Admittance Method: Systematic network solving review. Building linear systems from circuit networks.

 

Systematic circuit network solving notes (resistors and current sources)

24

Apr 11

Cela

 

Admittance Method: The quasistatic approximation. From bulk model to network model. Examples.

3D Admittance Method. Static, frequency domain, time-stepping, adaptive multi-resolution meshing, etc.

 

2D Admittance Method example code (includes network solver from previous lecture)

25

Apr 16

Cela/Nagel

 

Project Presentations

 

26

Apr 18

Cela/Nagel

 

Project Presentations

 

 

27

Apr 23

Cela/Nagel

 

Project Presentations

 

 

28

Apr 25

Cela/Nagel

 

Project Presentations