Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis (AMNA)

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Prof. Dr. Matthias Ehrhardt
Prof. Dr. Michael Günther
Prof. Dr. Wil Schilders

Lecture Winter Term 2020/21:

Mimetic numerical methods, including structure preservation and port-Hamiltonian systems
(Advanced Topic)



Schedule
(Start of Lecture ??.10.2020)
 
 Lecture   Mon,  16:15 - 17:45 starting ??.10.2020   Room G.13.18  (not on ??)
 Lecture   Tue,  14:15 - 15:45  starting ??.10.2020   Room G.13.18 
Guest Lecture   ???? by Hans Zwart   Room G.13.18 
Guest Lecture   ???? by Harshit Bansal   Room G.13.18 
 Exercise  Wed,  10:15 - 11:45   Room G.13.18  

Outline of the Lecture


The lecture is suitable for Master and PhD students of mathematics.
The students of economathematics can use it as component AKap.NAaA-a "Selected Topics in Numerical Analysis and Algorithms" in the module of the same name.


Topics of the Lecture:

Numerical methods, nowadays also termed methods from the area of scientific computing, are usually taught in universities in a traditional way. All methods discussed are based on Taylor's series expansions, using no knowledge whatsoever about the problem to be approximated. The advantage is that such methods are generally applicable, the downside is that they are not always as efficient and accurate as desired or even required. Mimetic methods, i.e. methods that mimic properties of the underlying problem and its solutions, are more specific to the problem, and hence bear the promise to produce more accurate solutions, in a more efficient way, often with less computational effort.

From a mathematical point of view, one may say (but it is a vague argument) that mimetic methods restrict solutions to a subspace of possible solutions, with the subspace being much more amenable to the original problem. A common misunderstanding about mimetic methods is that this class of methods is restricted to discretisation processes only. This is not correct: mimetic methods have also been developed for the solution of linear systems, for nonlinear systems, for model order reduction, and other areas.

In this lecture series, the concept of mimetic methods will be explained, and the advantage as compared to traditional methods. We will discuss the construction of mimetic methods for several areas in scientific computing, including discretisation, linear and nonlinear solution techniques and model order reduction, also using port-Hamiltonian systems. We will discuss various industrial applications, most importantly the simulation of semiconductor devices and for drilling applications.

Outline of the lecture: detailed outline of the lecture.


Literature:


Previous knowledge: Analysis I - III, basic knowledge of ordinary differential equations.


Exercises:
For the exercises we recommend ...
Sheets.


Criteria: Regular participation and participation in the exercise groups, as well as reaching 50% of the possible points on the first seven or the remaining exercise sheets and at least 2/3 of the possible points for the practical tasks.




University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

Last modified:   Disclaimer   ehrhardt@math.uni-wuppertal.de