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Numerical Analysis Group

Office
Kollegiengebäude Mathematik (20.30)
Room 3.002 (3rd floor)

Address
Karlsruhe Institute of Technology
Institute for Applied and Numerical Mathematics 1
Englerstr. 2
76131 Karlsruhe
Germany

Office hours:

Mon. - Fri.

9 - 12 o'clock

Mon. - Thu.

13 - 16 o'clock

Contact:

Phone: +49 721 608-42061
Fax: +49 721 608-43767
Email:na-sek@math.kit.edu

Numerical multiscale methods, Summer 2017

Current announcements

  • 2017-07-19: Lecture notes updated.
  • 2017-07-18: Added exercise sheet 7.
  • 2017-07-11: Lecture notes updated.
  • Show old announcements.

People

Lectures and exercises will be given by Dr. Dietmar Gallistl and Dr. Christian Stohrer .

Language

In principal in german, upon request the course will be held in english.

Prerequisutes

The course is meant for Master students who are familiar with the basics of finite element methods and numerical methods for differential equations. Some knowledge on functional analysis is helpful.

Content and qualification objectives

The topic of the lecture are numerical multiscale methods presented exemplarily for elliptic problems.

Students know the basic analytical results for existence and uniqueness of the solution of multiscale problems and from homogenization theory. In addition, they know methods for the numerical approximation of multiscale and the homogenized solution. They are able to analyze the convergence of these methods and asses the pros and cons of the different approaches.

The following four chapters are planned:
  • Motivation
  • Analytical fundamentals (basic results from analysis for elliptic partial differential equations and from homogenization theory)
  • Approximation of the homogenized solution - Heterogeneous Multiscale Method
  • Approximation of the multiscale solution - Local Orthogonal Decomposition

Schedule

Weekly hours

3h lecture and 1h problem class (6 credit points)

Lectures and problem classes

Monday, 11:30-13:00 in SR 3.061, buildung 20.30
Tuesday, 11:30-13:00 in SR -1.009, usually in SR 2.059 buildung 20.30
On the following three dates the lecture or problem classes will take place in SR 3.060:
2017-05-30, 2017-06-27, and 2017-07-25.
The exercises take place on the following dates instead of the lecture:
Exercise 1: Tuesday, May 2, 2017
Exercise 2: Monday, May 22, 2017
Exercise 3: Tuesday, May 30, 2017
Exercise 4: Tuesday, June 13, 2017
Exercise 5: Tuesday, June 27, 2017
Exercise 6: Monday, July 10, 2017
Exercise 7: Tuesday, July 25, 2017

Lectures material

Lectures notes

The lecture notes provided here are a draft version, since they are written when the lecture progresses. This includes corrections shortly after the corresponding topic was discussed.

We are grateful for any suggested corrections and improvements.

Exercise sheets

Code examples