Numerik IV

News and Important Remarks

• Here is the updated time schedule for the oral exams tomorrow.
• Here you can find the time schedule for the oral exams on thursday, the 14th of february. If you either do not find your name on the list, or if it is impossible for you to keep the date assigned to your name, please contact mawolf{at}math.fu-berlin.de.

Dates

General Information

Description

Geometric partial differential equations are describing the evolution of and processes on surfaces. Geometric flows such as the now classical mean curvature flow, Willmore flow, and pdes on moving surfaces are typical examples. In this lecture, we will consider various formulations including phase field models of Allen-Cahn and Cahn-Hilliard type and concentrate on basic numerical techniques such as surface finite element methods, adaptivity, unfitted finite element methods, and efficient numerical solvers.

Target Audience

Advanced students in the Master Program Mathematics. Various possible topics for a Master thesis will come up during this course.

Prerequisites:

Basic knowledge on partial differential equations and their numerical solution (e.g. Numerik III).

Registration

All participants should register at the KVV which is our only data base for organizing this course. Registration at KVV is mandatory to participate in the oral exams. The number of registrations in KVV is also used to justify rooms etc. for this course.

In addition, depending on your program of study, you have to register in the following way:

• BMS students have to register via e-mail at the one-stop office.
• Studierende im Campus Management verwalteter Bachelor- und Masterstudiengänge müssen sich eigenverantwortlich und verbindlich über das Campus Management an- bzw. abmelden. Über Möglichkeiten und Pflichten zur An- und Abmeldung gibt die Homepage des Campus Managements Auskunft. Für Fragen ist ferner eine Hotline unter 838-77777 sowie eine E-Mail-Adresse cm-hotline@fu-berlin.de eingerichtet.
• Für Studierende der Bioinformatik alter Studienordnung ist die Anmeldung im KVV verbindlich. Im Fall eines Rücktritts ist die Abmeldung bis 31.10.2011 im KVV erforderlich.
• Die Anmeldung im KVV ist für Diplom- und Staatsexamenskandidaten alter Studienordnung (nicht Bachelor/Master) ausreichend. Im Falle eines Rücktritts ist keine Abmeldung nötig.

Exercises and Criteria for a Certificate

Tutorial & Exercises

• Exercises will be handed out each Tuesday during the lecture. These exercises are also available electronically on this web page (see below). The first release takes place on October 23, 2012.
• The tutorial offers the possibility to ask questions regarding the presented material. Furthermore future and previous exercises are discussed in the tutorial. The first tutorial takes place on Wednesday, October 17, 2012. To our experience, active participation in the tutorial is not only fundamental for the understanding of the presented material but also for a successful exam.
• The exercises are intended to be solved by teams of two to three members. Please remember to annotate the name of all participating team members on the completed exercises.
• The solutions have to be finished before the tutorial on Wednesday at 14 o'clock in the week after they were handed out. Please hand your exercises in at the beginning of the tutorial. You can also them put into the box with the name 'Wolf' on it, found in the first floor in Arnimallee 3.
• The exercises consist of theoretical problems as well as numerical experiments. Both types of exercises are rated seperately by an appropiate number of either theory points (TP) or programing points (PP). Numerical experiments have to be handled using Matlab (available at the students computer pool at the institute). A complete solution for a numerical experiment consists of a running Matlab code, a program executing the required test runs and protocols of the execution of these test runs. Please deliver your programs by e-mail as well as printed out to the tutor. Don't forget to mention all team members in your e-mails and programs.
• Caution: Delivering a correct and running code without knowing what's going on in the code will be regarded and rated as attempt of deception.

Oral Exam

• There will be an an oral exam at the end of the semester. All students inscribed at KVV for this course are allowed to participate.

Criteria for the Certificate (Übungsschein)

Neccessary and sufficient for a certificate are:

• passing the oral exam
• active participation (50% of all theory points and 50% of all programing points)
• constant participation (85% presence in the tutorial) (suspended since November 1, 2010)

Certificates are graded according to the result of the oral exam.

Exercises

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9
• Exercise 10
• Exercise 11
• Exercise 12

Accompanying Material

Here you can find an Introduction to Viscosity Solutions

Lecture Notes:

Here are the lecture notes for previous course Numerics III

Literature

1. M. Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
2. K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
3. G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
4. J.A. Sethian: Level Set Methods and Fast Marching Methods, Cambridge University Press (1999)
5. T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)

Contact