Program Overview

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Advanced Numerical Methods for CSE Autumn 2025

General Information

The lectures for this course will take place on Fridays from 10:15 to 12:00 and from 14:15-16:00 in HG G19.2. The tutorials take place on Wednesdays from 08:15 to 10:00 or on Thursdays from 08:15-10:00.

Content

Boundary Element Methods

Lecture Date | Lecture Slides/Notes | Topic
---|---|---
19/09/2025 | Introduction | Introduction
Typical Problems | Typical Problems
26/09/2025 | Lecture 2 Aftermath
BEM in a Nutshell | BEM in a nutshell
Potential problems I | Potential problems - derivation of boundary integral equations
03/10/2025 | Recap last week
Potential Problems II
Potential Problems III
10/10/2025 | Recap Notes
Potential Problems IV | Potential problems - lowest order discretization of boundary integral equations
Potential Problems IV
17/10/2025 | Potential Problems IV
Numerical Experiments | Numerical Experiments
24/10/2025 | Potential Problems V | Extensions
Potential Problems V
31/10/2025 | Acoustic wave propagation - Helmholtz Equation | Acoustic wave propagation - Helmholtz equation
Acoustic wave propagation - Helmholtz Equation
07/11/2025 | Electromagnetic wave propagation - Maxwell's equation | Electromagnetic wave propagation - Maxwell's equation
Electromagnetic wave propagation - Maxwell's equation

Hierarchical Matrices

Lecture Date | Lecture Slides | Topic
---|---|---
14/11/2025 | H-Matrices I | H-Matrices I
H-Matrices I | H-Matrices I
21/11/2025 | H-Matrices II | H-Matrices II
H-Matrices II | H-Matrices II
28/11/2025 | H-Matrices III | H-Matrices III
H-Matrices III | H-Matrices III

Hybrid Modeling

Lecture Date | Lecture Slides | Topic
---|---|---
05/12/2025 | Hybrid Modeling I | Hybrid Modeling I
Hybrid Modeling I | Hybrid Modeling I
12/12/2025 | Hybrid Modeling II | Hybrid Modeling II
Hybrid Modeling II | Hybrid Modeling II
19/12/2025 | Hybrid Modeling III | Hybrid Modeling III
Hybrid Modeling III | Hybrid Modeling III

Problem Sets

Every lecture will be accompanied by a set of exercises. These exercises are divided into two groups.

• Exercises (E): These are exercises that we recommend to do. They are helpful in the understanding of the material and their contents might show up at the final exam. However, they are not required to be handed in. These exercises consist of both theory and code. Most exercises will be taken from the ANCSE problem set (includes solutions). Some small, conceptual exercises will be taken from a lecture given at TU Darmstadt (TUD) and can be found here. Solutions are available here. The exercises are related to specific lectures, because they cover the content of the associated lecture! There are no deadlines.
• Homework Coding Projects (H): Students are expected to actively work on the homework coding projects. We encourage collaboration and discussion among students and also with the TAs. For every coding project, there will be a deadline for submission after which the solutions will be made available. The students shall hand in a minimum of 50% of the homework coding projects in order to participate in the mandatory oral code review at the end of the semester. During the code review, the examiners will ask the students to explain specific parts of the code they handed in. The coding projects are to be handed in using the SAM-Upload Tool. Homework Coding Projects are not associated to specific lectures and do have a due date. The homework coding projects will be graded by the TAs with a pass or fail. You need to get a pass for at least two homework coding project in order to participate in the oral code review and the final exam. This year, the oral code reviews will take place on December 17th and 18th.

Exercises(E)

Associated Lecture | ANCSE Problems | TUD Problems
---|---|---
19/09/2025 | 1.1, 1.2, 1.3 | 1, 2, 3, 4, 5
26/09/2025 | 1.4, 1.5 |
03/10/2025 | 1.7, 1.8 |
10/10/2025 | 1.9 |
17/10/2025 | 1.11 |
24/10/2025 | 1.10 |
31/10/2025 | 1.14 (the references refer to the old lecture document) |

Homework Coding Projects (H)

Project Description | Due date
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Homework Project 1 | October 28th, 2025
Homework Project 2 | November 24th, 2025
TBD | TBD
TBD | TBD

Tutorials

time | room | assistant | Files
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We 08-10 | HG F 26.5 | Paul Fischill | files
Th 08-10 | HG G 26.1 | Michael Klein | files

Literature

Boundary Element Methods

• Advanced Numerical Methods for Computational Science and Engineering by R. Hiptmair (ETH Zürich)
• Fast Boundary Element Methods for Engineers by S. Kurz (TU Darmstadt 2017)
• Boundary Element Methods by S. Sauter and C. Schwab (Springer 2011)
• Numerical Approximation Methods for Elliptic Boundary Value Problems by O. Steinbach (Springer 2008)
• The Fast Solution of Boundary Integral Equations by S. Rjasanow and O. Steinbach (Springer 2007)
• Fast Multipole Boundary Element Methods - Theory and Applications in Engineering by Y. Liu (Cambridge University Press 2009)
• The analytical computation of the Galerkin elements for the Laplace, Lamé and Helmholtz equation in 2D-BEM by Matthias Maischak

Hierarchical Matrices

• Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems by M. Bebendorf (Springer 2008)
• Hierarchical Matrices: Algorithms and Analysis by W. Hackbusch (Springer 2015)

Hybrid Modeling

• Gaussian Processes for Machine Learning by C. Rasmussen and C. Williams (The MIT Press 2006)

Lecturer and Coordinator

• Lecturer: Stefan Kurz
• Coordinator: Wouter Tonnon