## 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

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.

## 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

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.

## 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)

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.

## 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

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

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.

## Proseminar "B-Splines und NURBS"

### Inhalte

Eine Vorstellung des Proseminars kann unter dem folgenden Link aufgerufen werden.

2 SWS Seminar

### Inhaltliche Voraussetzungen

Formal:

• "Grundlagen der Mathematik"
• einfache Programmierkenntnisse

Informal:

• Keine

## 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

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

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.

## 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

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.