Numerical Methods for Maxwell's Equations


Numerical methods for Maxwell equations, Winter 2016/17

Current announcements

  • Lecture notes updated, Section 5.5 on implementation issues is now online.
  • Questions for exams for Chapter 5 added.
  • Lecture notes updated (9th February).
  • The Tutorial of Monday, Jan 30 is again rescheduled to Monday, Feb 6 because of sickness.
  • The registration for the exam is now open. Please make sure to register to examination number 340 (there is yet another open exam with the same title but less credit points). The deadline for registration is February 28.
  • Questions for exams for Chapters 1-4 added.
  • Lecture notes updated. First part of Chapter 5 is now online.
  • Slides added here
  • Solution of problem sheet 6 revised
  • Chapter 4 revised
  • Lecture notes updated, Chapter 4 is now complete
  • Problem sheet 4 and its solution updated
  • Lecture notes updated (Dec 22)
  • Schedule updated
  • Lecture notes updated, Lemma 4.1 revised
  • Typos in Chapter 3 corrected and Section 3.6 revised
  • Lecture notes updated, Chapter 3 is now complete
  • Lecture notes updated, version now ends with Section 3.4
  • Corrected signs in problem 12 and added sketch of solution for tutorial 3
  • Sketch of solutions added for tutorial 1 and 2
  • Schedule updated until Christmas
  • Lecture notes updated, Chapter 1 and 2 are now complete, added first part of Chapter 3 (Nov 15)
  • In order to avoid frequent replacements due to obligations of Prof. Hochbruck for the DFG, there will be an alternative date for lectures. The schedule will be discussed in the first lecture on Wednesday, Oct 19. The lecture dates are always announced here.


Weekly hours

2h lecture + 2h problem class (6 credit points)

Contents and Prerequisites

Maxwell equations are a set of vector valued partial differential equations that are fundamental for the propagation of electromagnetic waves in media. In this lecture we start to derive Maxwell equations in integral- and differential form, discuss examples of material laws, boundary conditions, and study the well-posedness in suitable function spaces. For the numerical solution of Maxwell equations, we employ finite element methods for the spatial discretization. Our emphasis is on discontinuous Galerkin methods. Favorable methods for time discretization are splitting methods, (locally) implicit schemes, and exponential integrators. We construct and analyse these methods and discuss their efficient implementation.

The course is meant for advanced Master students who are familiar with the basics of finite element methods and numerical methods for differential equations. Some knowledge on functional analysis is also helpful.



Monday, 15:45-17:15 in SR 3.061, building 20.30
Wednesday, 9:45-11:15 in SR 3.061, building 20.30
Thursday, 11:30-13:00 in SR 3.069, building 20.30 (alternative date)

The problem class is split into a part integrated into the lecture and a biweekly tutorial.

Concrete dates

Please note that the dates for the lectures and problem classes may vary from week to week. The dates for the next weeks are listed below. If changes to already announced dates are required they will be highlighted by color.

cw 42: Wednesday 19.10. (lecture) and Thursday 20.10. (lecture)
cw 43: Monday 24.10. (tutorial) and Wednesday 26.10. (lecture)
cw 44: Monday 31.10. (lecture) and Wednesday 02.11. (lecture)
cw 45: Monday 07.11. (tutorial) and Wednesday 09.11. (lecture)
cw 46: Monday 14.11. (lecture) and Wednesday 16.11. (lecture)
cw 47: Monday 21.11. (tutorial) and Wednesday 23.11. (lecture)
cw 48: Monday 28.11. (lecture) and Wednesday 30.11. (lecture)
cw 49: Monday 05.12. (lecture) and Wednesday 07.12. (tutorial)
cw 50: Wednesday 14.12. (lecture) and Thursday 15.12. (lecture)
cw 51: Monday 19.12. (tutorial) and Wednesday 21.12. (lecture)
cw 02: Monday 09.01. (lecture) and Wednesday 11.01. (lecture)
cw 03: Monday 16.01. (tutorial) and Wednesday 18.01. (lecture)
cw 04: Monday 23.01. (lecture) and Wednesday 25.01. (lecture)
cw 05: Wednesday 01.02. (lecture)      
cw 06: Monday 06.02. (tutorial)
  Wednesday 08.02. (lecture) and Thursday 09.02. (lecture)


The format of the exams will be the following:

  • Until the end of the semester, we will provide you with a list of possible questions for each chapter of the lecture.
  • You randomly draw three questions from this list, each from another chapter. One question can be redrawn from the same chapter with the possibility to answer the original question.
  • Then you are given 20 minutes for preparation (without any aid). Any notes that you prepare during this time can be used in the oral exam.
  • The actual oral exam will last additional 20 minutes during which you have to answer the questions. This leaves approximatly 7 minutes for each question. If the answer is too short we expect you to present further details of the topic. In order to assure that you understand all aspects of the topic in question, you can always be asked further questions.
  • The final grade will be the mean of the grades (1-6) from the three answered questions.

The list of questions can be found here: Questions

Lecture notes

The lecture notes provided here are a draft version, since they are written when the lecture progresses. This includes corrections shortly after the corresponding topic was discussed.

We are grateful for any suggested corrections and improvements.

Problem sheets

sheet 1, sheet 2, sheet 3, sheet 4, sheet 5, sheet 6, sheet 7

Sketch of solutions

solution 1, solution 2, solution 3, solution 4, solution 5, solution 6, solution 7