## Computational Methods in Electromagnetics

Module number: EI73181

Duration: 1 Semester

Occurence: Winter Semester

Language: English

Number of ECTS: 6

## Staff

Professor in charge: Thomas Eibert

## Amount of work

Contact hours: 75

Self-study hours: 105

Total: 180

## Description of achievement and assessment methods

The examination consists of an oral examination of 25 min duration.

In the oral examination, students demonstrate by answering questions under time pressure and without helping material the theoretical knowledge of computational and analytical methods for the solution of electrostatic as well as acoustic and electromagnetic field and wave problems. By describing solution concepts for particular field problems, they demonstrate the understanding of the relevant solution principles.

During the semester, students get the opportunity to participate in voluntary project tasks, in which they can solve different field problems in more detail. These project tasks can be used to improve the final grade.

The final grade consists of the grade of the oral exam (100%).

The overal grade for the project task will count with 20% of the final grade, if the average grade of the oral exam (80%) and of the project task grade (20%) will lead to an improvement of the grade.

## Recommended requirements

Mathematics

- Electrodynamics

The successful participation in the following modules is recommended:

- Technische Felder und Wellen

## Contents

1) Mathematical and physical basics

- Maxwells Equations

- Boundary conditions

- Vector spaces

- Distributions and complex analysis

- Uniqueness of field solutions

- Green's functions

- Radiation of electromagnetic sources

- Huygens' principle

2) Numerical solvers

- Finite-difference method

- Finite-difference time-domain method

- Finite element method

- Integral equation method

- Method of moments

3) Field solutions by Green's functions

- Orthogonal series representations of Green's functions

- Solution of the Laplace-/Helmholtz equation in Cartesian cylindrical and spherical coordinates

- Surface and volume integral equation formulations of radiation and scattering problems

4) Vector wave solutions in Cartesian and spherical coordinates

- Mie series solutions

- Dyadic Green's functions in planar multilayered media

- Spectral domain immitance approach

- Transmission line representation

- Sommerfeld integral representation

- Michalski's mixed potential representation

- Dipole over a halfspace (earth)

5) Basics of Variational Calculus

- Functional formulation of field solutions

- First variation of functionals

- Stationary field representations

- Direct solution of variational problems

- Rayleigh-Ritz procedure

- Finite element method

## Study goals

At the end of the module students understand advanced computational and analytical methods for the solution of electromagnetic field problems. They are able to apply these methods to develop field solutions for modified geometrical and material configurations within the scope of the methods. They understand the relationship and the mutual utilization of mathematical and physical considerations in order to develop field solutions of practical relevance. They understand the importance of analytical concepts for the development of advanced numerical methods in electromagnetics.

## Teaching and learning methods

Teaching method:

During the lectures students are instructed in a teacher-centered style. The tutorials are held in a student-centered style. The students are expected to give tutorials themselves.

Learning method:

In addition to the individual methods of the students, consolidated knowledge is aspired by repeated lessons in excercises and tutorials

## Media formats

Presentation (online available), selected problems with solutions, practical work with MATLAB and commercial solvers. Software demonstration of leading EM software tools with hands-on tutorial.

## Literature

- Jin, J.-M.: Theory and Computation of Electromagnetic Fields, Wiley 2010

- Chew, W.C.: Waves and Fields in Inhomogeneous Media,IEEE Press, 1995

- Jackson, J.D.: Classical Electrodynamics, Wiley, 1962

- Tai, C.-T.: Dyadic Green Functions in Electromagnetic Theory, IEEE Press, 1994

- Peterson, Ray: Computational Methods for Electromagnetics, IEEE Press, New York, 1997

- Collin, R.E.: Field Theory of Guided Waves, IEEE Press, 1991

- Thomas Rylander, Pär Ingelström, Anders Bondeson: Computational Electromagnetics, Springer, 2013

- Felsen, L.B., Marcuvitz, N.: Radiation and Scattering of Waves, IEEE Press, 1994