Lecture WS08/09 (Modelling and Simulation of Real-Life Problems)



Outline
We present an overview to modeling and simulation of technical processes in real-life problems. The transformation of the physical processes to evolution equations is discussed. We deal with transport and reaction processes, e.g. in groundwater and plasma modeling. The solutions of the evolution equations, which are systems of parabolic and hyperbolic partial differential equations, are done with numerical approximations, e.g. fnite difference and finite volume methods. We present consistency and stability results of these methods. New methods in the field of decomposition schemes, e.g. Operator splitting and waveform relaxation methods, are further discussed. Such methods decou- ple the delicate time and spatial scales of the equations and solve them more efficiently.

Location and Date : RUD 2.009, Thursday 10.00-11.30,

The lectures contain an overview to each model problem and numerical analysis of the discretization and solver methods. A specialization is given to decomposition methods and their analysis is presented. The below topics are done but could be handled in more than only one lecture.

Lectures :



  1. Introduction to Models and Examples. (06.11.08).

  2. Model to Discretization. (13.11.08)

  3. Discretization to Solver. (20.11.08, 27.11.08)

  4. Solver and Decomposition. (4.12.08)

  5. Decomposition Analysis. (11.12.08, 15.01.09)

  6. Applications. (21.01.09).


A manuscript version of the lecture (first version).


[Lecture 1]

[Lecture 2]

[Lecture 3] [Lecture 3 (Remark)]

[Lecture 4]

[Lecture 5] [Lecture 5 (Remarks)]

[Lecture 6]

[Lecture 7]

[Lecture 8] [Lecture 8 (Remarks)]

For further questions and remarks please send a note to Dr. Juergen Geiser,
e-mail : geiser@mathematik.hu-berlin.de