Legacy display Course

This is an archived course. The content might be broken.

Lecture in SS 2014:

Wissenschaftliches Rechnen II / Scientific Computing II (V3E2/F4E1)

Prof. Dr. Sven Beuchler

Assistant: Bastian Bohn

Scientific Computing is an applied discipline which deals with methods and techniques that are necessary to run computer simulations and experiments to obtain advanced insight into processes which stem from engineering tasks or natural sciences. This particular course enlarges upon finite element methods and introduces adaptive variants for efficient treatment of elliptic partial differential equations. Fast multilevel methods will be the main topic of the second part of the lecture.

Prior knowledge

Wissenschaftliches Rechnen I / Scientific Computing I or alternatively a basic course on numerical treatment of PDEs
D. Braess - Finite Elemente (chapters I-IV)
C. Grossmann, H.-G. Roos, M. Stynes - Numerical Treatment of Partial Differential Equations (chapters 1-4)

Lecture

Times: Tuesdays10:15-11:50 am
Thursdays9:00-10:30 am
Beginning: TuesdayApril 08, 2014
Location: Zeichensaal, We 10
An additional Lecture will take place on 28th of May at 8:30 am (Location: Grosser Hoersaal der Mathematik, We 10).

Consultation hour of Prof. Beuchler: Wednesdays 10:30-11:30 am.

Final Exam

Appointments for the final exam (oral) will be made individually by Prof. Dr. Beuchler.

Lecture Script

The final version of the lecture script can be found here: LectureScript. Username and password can be requested from your tutor.

Tutorial

The tutorial will take place Thursdays after the lecture in the Zeichensaal, We 10.

Exercises

The solution to the exercises are due on the beginning of the lecture on tuesdays. Therefore they have to be submitted Tuesdays, 10:10 am.
For admittance to the final exam you have to score 50% or more points of the overall score.

  1. sheet1.pdf (corrected: 12.04. [Exercise 1: In the inequality which is to prove there should be seminorms on the left hand side!])
  2. sheet2.pdf
  3. sheet3.pdf
  4. sheet4.pdf
  5. sheet5.pdf
  6. sheet6.pdf
  7. sheet7.pdf
    8. Input: SampleGrid_Neumann.txt ,SampleGrid_Neumann2.txt
  8. sheet8.pdf
  9. sheet9.pdf
  10. sheet10.pdf
  11. sheet11.pdf

Literature

FEM
  • D. Braess: Finite Elemente: Theorie, schnelle Loeser und Anwendungen in der Elastizitaetstheorie. Springer
  • C. Grossmann, H.-G. Roos, M. Stynes: Numerical Treatment of Partial Differential Equations, Springer
  • M Langer, U. Jung: Methode der finiten Elemente für Ingenieure: Eine Einführung in die numerischen Grundlagen und Computersimulation. Teubner
  • W. Hackbusch: Theorie und Numerik elliptischer Differentialgleichungen, Teubner
  • S. Brenner, R. Scott: The Mathematical Theory of Finite Element Methods, Springer
  • A. Quateroni, A. Valli: Numerical Approximation of Partial Differential Equations, Springer
Adaptive FEM
  • J. Bey: Finite-Volumen- und Mehrgitter-Verfahren für elliptische Randwertprobleme. Teubner
  • M. Ainsworth, J. Tinsley Oden: A posteriori error estimation in finite element analysis. John Wiley
Domain Decomposition
  • A. Toselli, O. Widlund: Domain Decomposition Methods - Algorithms and Theory. Springer
Multigrid Method
Programming
  • B. Stroustrup: The C++ Programming Language
  • B. Eckel: Thinking in C++ [free to download]
You can borrow books from the Library of Mathematics or the MNL Branch Library for example.