Lehrveranstaltungen im Wintersemester 2022/23
Unsere Arbeitsgruppe bietet im Wintersemester 2022/23 folgende Lehrveranstaltungen an:
Differential-Algebraic Equations
Differential-Algebraic Equations
Contents
The theory and numerical analysis of differential-algebraic equations are discussed, in particular:
- application fields (electrical circuits and multibody mechanical systems)
- relation with singularly perturbed problems
- solution theory and index concepts
- normal form for linear DAEs
- numerical aspects
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered irregularly in winter term.
Links / Contact
Lehrveranstaltungen im Sommersemester 2022
Unsere Arbeitsgruppe bietet im Sommersemester 2022 folgende Lehrveranstaltungen an:
Scientific Computing in Solid Mechanics
Spline Functions
Scientific Computing in Solid Mechanics
Contents
Mathematical modelling, numerical methods, and software for the following topics:
- elastic bodies
- special cases of beams and plane strain/stress state
- finite element space discretisation
- specific time integration schemes
Contact time
2 SWS Lecture
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Numerical Methods"
- "Numerics of ODE"
- "Introduction to PDE"
Formal:
- None
Frequency
This course is offered irregularly.
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Scientific Computing in Solid Mechanics
Course in OLAT:
TUK Scientific Computing in Solid Mechanics SS 2022
Spline Functions
Contents
The following topics will be covered:
- spline functions and spline spaces
- B-splines
- Bézier splines (Bézier polynomials, de Casteljau's algorithm, Bézier curves, Bézier polynomials over triangles, tensor product Bézier surfaces)
- B-spline smoothing (de Boor's algorithm)
Contact time
2 SWS Lecture
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Numerical Methods"
- "Numerics of ODE"
- "Introduction to PDE"
Formal:
- None
Frequency
This course is offered irregularly.
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Spline Functions
Course in OLAT:
TUK Spline Functions SS 2022
Lehrveranstaltungen im Wintersemester 2021/22
Unsere Arbeitsgruppe bietet im Wintersemester 2021/22 folgende Lehrveranstaltungen an:
Numerical Methods for Ordinary Differential Equations
Differential-Algebraic Equations
Proseminar "B-Splines und NURBS"
Numerical Methods for Ordinary Differential Equations
Contents
Most problems in science, technology, and engineering can be modeled by a set of differential equations. In general, these equations are too complex to be solved analytically. This course provides the necessary tools and methods to treat initial value problems numerically.
The following topics will be covered:
- explicit and implicit one-step methods (Runge-Kutta methods)
- error estimation and step size control
- multistep methods (Adams and BDF methods)
- consistency, stability, and convergence
- methods for stiff problems
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Numerical Methods"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered every winter term.
Differential-Algebraic Equations
Contents
The theory and numerical analysis of differential-algebraic equations are discussed, in particular:
- application fields (electrical circuits and multibody mechanical systems)
- relation with singularly perturbed problems
- solution theory and index concepts
- normal form for linear DAEs
- numerical aspects
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered irregularly in winter term.
Links / Contact
Proseminar "B-Splines und NURBS"
Inhalte
Eine Vorstellung des Proseminars kann unter dem folgenden Link aufgerufen werden.
Kontaktzeit
2 SWS Seminar
Inhaltliche Voraussetzungen
Formal:
- "Grundlagen der Mathematik"
- einfache Programmierkenntnisse
Informal:
- Keine
Links / Kontakt
Dozent: Prof. Dr. Bernd Simeon
Hier geht es zum KIS-Eintrag: Proseminar B-Splines und NURBS (Seminar)
Hier geht es zum OLAT-Kurs:
TUK Proseminar "B-Splines und NURBS" WS 2021/22
Lehrveranstaltungen im Sommersemester 2021
Unsere Arbeitsgruppe bietet im Sommersemester 2021 folgende Lehrveranstaltungen an:
Numerical Methods for Partial Differential Equations I
Scientific Computing in Solid Mechanics
Numerical Methods for Partial Differential Equations I
Contents
To describe real-world processes, one often makes use of partial differential equations, which, in general, cannot be solved analytically. In this course, we will discuss and study the mathematical techniques required for solving such equations numerically. The focus lies on the discretization of boundary value problems for elliptic differential equations with finite difference or finite element methods. At the end of the course, these ideas will be applied to parabolic differential equations.
The following topics will be covered:
- approximation methods for elliptic problems
- theory of weak solutions
- consistency, stability, and convergence
- approximation methods for parabolic problems
Contact time
4 SWS Lecture
2 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Numerics of ODE"
- "Introduction to PDE"
- Some functional analysis
Formal:
- None
Frequency
This course is offered every summer term.
Scientific Computing in Solid Mechanics
Contents
Mathematical modelling, numerical methods, and software for the following topics:
- elastic bodies
- special cases of beams and plane strain/stress state
- finite element space discretisation
- specific time integration schemes
Contact time
2 SWS Lecture
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Numerical Methods"
- "Numerics of ODE"
- "Introduction to PDE"
Formal:
- None
Frequency
This course is offered irregularly.
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Scientific Computing in Solid Mechanics
Course in OLAT:
TUK Scientific Computing in Solid Mechanics SS 2021
Lehrveranstaltungen im Wintersemester 2020/21
Unsere Arbeitsgruppe bietet im Wintersemester 2020/21 folgende Lehrveranstaltungen an:
Einführung in Numerische Methoden
Einführung in Numerische Methoden
Inhalte
In dieser Lehrveranstaltung werden die grundlegenden Methoden und Algorithmen zur numerischen Lösung von Fragestellungen aus der Linearen Algebra und der Analysis behandelt. Zu den zentralen Themen der Veranstaltung gehören:
- Fehleranalyse: Kondition eines Problems, Stabilität von Algorithmen
- Numerische Verfahren für lineare Gleichungssysteme
- Lineare Ausgleichsprobleme
- Eigenwertprobleme
- Approximationstheorie: Interpolation durch Polynom- oder Spline-Funktionen
- Numerische Integration: Interpolations- und Gaußquadratur
- Numerische Verfahren für nichtlineare Gleichungssysteme
Kontaktzeit
4 SWS Vorlesung
2 SWS Übung
2 SWS Praktikum
Inhaltliche Voraussetzungen
Formal:
- "Grundlagen der Mathematik"
- einfache Programmierkenntnisse
Informal:
- Keine
Angebotsturnus
Die Lehrveranstaltung wird jedes Wintersemester angeboten.
Links / Kontakt
Dozent: Prof. Dr. Bernd Simeon
Hier geht es zum KIS-Eintrag:
Einführung in Numerische Methoden (Vorlesung)
Einführung in Numerische Methoden (Übung)
Einführung in Numerische Methoden (Praktikum)
Hier geht es zum OLAT-Kurs:
TUK Einführung in Numerische Methoden WS 2020/21