Course Syllabus for

# Computational Electromagnetics Elektromagnetiska beräkningar

## ETI260F, 6 credits

Valid from: Autumn 2019
Decided by: Professor Thomas Johansson
Date of establishment: 2019-10-11

## General Information

Division: Electrical and Information Technology
Course type: Third-cycle course
Teaching language: English

## Aim

This course covers a few major computational methods for numerical analysis of electromagnetic ﬁelds for engineering applications. It includes the ﬁnite difference method (and the ﬁnite difference time-domain method in particular), the ﬁnite element method, and the integral equation-based moment method. A central part of this course is to give detailed knowledge of computational electromagnetics which is used as an analysis and simulation tool for dealing with electromagnetic problems. Once the students are familiar with these three methods, their understanding of electromagnetic numerical problems in engineering simulation or scientific research will be more profound. The aim of this course is to give good knowledge concerning principles, concepts, applications, performance and limitations of fundamental computational electromagnetics.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to show sufficiently deep knowledge concerning the mechanisms behind fundamental computational electromagnetics methods.
• be able to critically analyse and describe the advantages and disadvantages of the methods in different electromagnetic application scenarios from an overall perspective.

Competences and Skills

For a passing grade the doctoral student must

• be able to identify and formulate the basic principles of the three numerical methods.
• be able to strengthen theoretical understanding in their current electromagnetic research topics.
• be able to independently work on projects involving oral presentations and a written report, to motivate the topics and discuss the conclusions.

Judgement and Approach

For a passing grade the doctoral student must be able to understand the principles, advantages, limitations, and application scenarios of different computational electromagnetic methods and make the appropriate selection and comparative analysis in the study of practical problems.

## Course Contents

The courses focus on the three fundamental computational electromagnetics methods: The ﬁnite difference time domain method - The basic principle of ﬁnite difference time-domain method is introduced by ﬁrst deriving basic ﬁnite differencing formulas. This is followed by the stability and dispersion analyses. After that, the method is introduced for solving Maxwell’s equations in both two and three dimensions. Finally, we introduce how to truncate the computational domain for the analysis of open-region electromagnetic problems using absorbing boundary conditions and perfectly matched layers, how to excite incident waves in a computational domain, and how to calculate far ﬁelds based on the near-ﬁeld information. The ﬁnite element method - The basic principle of the ﬁnite element method is introduced by considering a simple one-dimensional example. We then describe in detail the formulation of the ﬁnite element analysis of electromagnetic scalar and vector problems in the frequency domain. This is followed by the extension to the time domain, which includes a brief treatment of modeling a dispersive medium. In each case, we present several numerical examples to demonstrate the application and capability of the ﬁnite element method. The method of moment - The basic principle of the method of moment using a simple electrostatic problem. We then formulate a general integral equation for the two-dimensional Helmholtz equation and apply it to a variety of speciﬁc problems. For each speciﬁc problem, we describe its moment-method solution step by step. This is repeated for three-dimensional electromagnetic ﬁeld problems that include scattering by various conducting and dielectric objects. Finally, we use a relatively simple example to illustrate how to apply the method into practice.

## Course Literature

Rylander, T., Ingelstrom, P. & Bondeson, A.: Computational Electromagnetics. ISBN 9781489986023.

## Instruction Details

Types of instruction: Lectures, seminars, self-study literature review

## Examination Details

Examination format: Written report
Examiner: