Lecturer

Stefan Kurz

stefan.kurz@sam.math.ethz.ch

Coordinator

Wouter Tonnon

wouter.tonnon@sam.math.ethz.ch

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. On Discuna you can ask questions to your tutors regarding the theory and exercises. You can also reach the organisers of the course to give feedback, ask questions, or make suggestions. The main reference for the first part of the course (Boundary Element Methods) will be the lecture notes. A secondary reference are these lecture notes. They cover the same material, but for a target audience of engineers. Recordings of the lecture are available at video.ethz.ch. The following folder contains additional (handwritten) notes: Notes.

Content

Boundary Element Methods

Hierarchical Matrices

Hybrid Modeling

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), while some 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.

Exercises(E)

Homework Coding Projects (H)

Tutorials

The code base

The code can be found here. We will mainly work with the master branch.

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)
• Numerical Methods for Non-local Operators by S. Börm (Universität Kiel 2021)
• 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)