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401-4671-00L 10 Credits MSC D-MATH
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Advanced Numerical Methods for CSE

Lecturers & Examiners: Prof. Dr. Stefan Kurz
VVZ CR 4.0

Last Updated: 2026-06-01 11:31:29

Abstract

This course will focus on teaching different advanced topics in numerical methods for science and engineering. The main aim would be introduce novel algorithms and discuss their implementation.

Objective

* Understanding the mathematical foundations and design principles of a selection of modern numerical methods for challenging problems. * Ability to adapt the presented paradigms and algorithms to modified or new problems arising from applications in computational science and engineering. * Ability to judge the scope, strengths and weaknesses of the numerical methods covered in this course and of methods derived from them. * Skills in translating a high-level description of an algorithm into efficient code.

Content

The course will comprise three main chapters: 1. The Boundary Element Method (BEM): It is a numerical method used to solve boundary value problems for linear PDEs. It focuses only on the boundary, rather than the entire volume of the domain to be modeled. [50%] 2. Hierarchical Matrices (H-matrices): They are an efficient data structure used to approximate dense matrices with a hierarchical block structure, significantly reducing the computational and memory costs for operations like matrix multiplication and inversion. [25%] 3. Hybrid Modeling: The technique combines multiple modeling techniques, such as physics-based models and data-driven approaches, to capitalize on the strengths of each method and improve the accuracy and efficiency of simulations or predictions in complex systems. [25%]

Resources

Lecture Notes

Lecture material will be created during the course and will be made available.

Learning Materials (Links)

General Information

Language
English
Levels
MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes
During the teaching period students are expected to give a 15-minute oral code review and answer questions concerning selected homework programming assignments. The code review is regarded as a mandatory performance element that will contribute 20% of the final grade.

Course Components

Type Title Time & Place Hours
lecture Advanced Numerical Methods for CSE
  • Fri 10:15-12:00 (HG G 19.2)
  • Fri 14:15-16:00 (HG G 19.2)
4 h weekly
exercise Advanced Numerical Methods for CSE
Groups are selected in myStudies. Wed 8-10 or Thu 8-10
  • Wed 08:15-10:00 (HG F 26.5)
  • Thu 08:15-10:00 (HG G 26.1)
2 h weekly
practical/laboratory course Advanced Numerical Methods for CSE No time listed 4 h weekly

Offered In

  • Rechnergestützte Wissenschaften Master
    • Kernfächer (Von den angebotenen Kernfächern müssen mindestens zwei Lerneinheiten erfolgreich abgeschlossen werden. Höchstens eine der beiden Lerneinheiten 263-5210-00L Probabilistic Artificial Intelligence bzw. 252-0535-00L Advanced Machine Learning darf als Kernfach angerechnet werden. Eine Anrechnung der anderen Lerneinheit in einer anderen Kategorie ist jedoch zulässig.)