Prof. Dr. Jan Giesselmann
Contact
giesselmann@mathematik.tu-...
work +49 6151 16-23167
Work
S4|10 108
Dolivostraße 15
64293
Darmstadt
Publications
- Publication list (PDF-File, 49kB)
Research Interests
- Hyperbolic Conservation Laws
- Compressible fluid flows
- Discontinuous Galerkin Methods
- A-priori and a-posteriori error estimators
- Model-adaptation
- Uncertainty Quantification
Teaching
Winter Term 2021/22
- Introduction to Numerical Mathematics (in German)
- Numerical Methods for PDEs (in English)
- BSc Seminar Numerical Mathematics
Summer Term 2021
- Numerical Linear Algebra
- Numerical Mathematics (Math 4 for mech. engineering)
- BSc Seminar Numerics
This is a list of suggestions for Bsc-Thesis topics that I would be happy to supervise. If you are interested in any of these topics please send me a mail. The topic will be made precise once we have discussed your scientific background and interests,
I give links to the literature for each topic. The literature is supposed to convey an impression of what the topic is about. It is not necessary to understand this literature in detail before working on any of the topics.
BSc
- Interpretation of Deep Neural networks as discretised Dynamical Systems. a paper of Weinan E)
- A posteriori error estimates for ordinary differential equations. chapterl 1-3 of this paper by Ch. Makridakis
- Error estimators and adaptivity for numerical solutions to ODEs with singularity chapter 1 and 2 (opens in new tab) in this paper
- From particle models to kinetic equations, see pages 1-12 in this paper (opens in new tab)
- Efficient numerical schemes for large systems of interacting particles Shi Jin, Lei Li und Jian-Guo Liu
- Numerical approximation of ODEs with random initial data and/or random right hand side siehe folgendes Buch
- Strong Stability Preserving numerical scheme, see this paper by Sigal Gottlieb, Chi-Wang Shu und Eitan Tadmor (opens in new tab)
- Application of symplectic schemes to Hamiltonian systems a script by Christian Lubich (opens in new tab)
- Approximating Functions Using Neural Nets Daubechies et al (opens in new tab) Depres, Ancellin
MSc
- Data assimilation for (scalar) hyperbolic conservation laws
- Data assimilation for shallow water equations
- Approximating kinetic relations via machine learning (opens in new tab)
- Stability of systems of hyperbolic conservation laws in one space dimension
- Statistical solutions of hyperbolic conservation laws
- Convergence of moment approximations of kinetic equations (opens in new tab)
- Numerical schemes using the hyperbolic structure of Navier-Stokes-Allen-Cahn equations(For a derivation of the equations see here)
- Solution concepts and approximation schemes for non-conservative hyperbolic equations (opens in new tab)
Winter Term 2020/21
Sommersemester 2020
Winter Term 2019/20
Sommersemester 2018 |
Uncertainty Quantification (RWTH Aachen) |
Mathematische Grundlagen für Computational Engineering Science II (RWTH Aachen) |
Wintersemester 2017/18 |
Mathematische Grundlagen für Computational Engineering Science I (RWTH Aachen) |
Mathematische Grundlagen für Computational Engineering Science V (RWTH Aachen) |
Sommersemester 2017 |
Numerical Methods for Differential Equations (Uni Stuttgart) |
Masterseminar Mehrskalenmodellierung (Uni Stuttgart) |
Wintersemester 2016/17 |
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart) |
Sommersemester 2016 |
Numerical Methods for Differential Equations (Uni Stuttgart) |
Wintersemester 2015/16 |
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart) |
Sommersemester 2015 |
Numerical Methods for Differential Equations (Uni Stuttgart) |
Masterseminar Diskontinuitäten im Kontinuum (Uni Stuttgart) |
Proseminar Iterative Lösungsverfahren (Uni Stuttgart) |
Wintersemester 2014/15 |
Lineare Strukturen (Uni Stuttgart) |
Sommersemester 2014 |
Numerische Methoden des Strömungsmechanik (Uni Stuttgart) |
Wintersemester 2013/14 |
Einführung in die Numerik Partieller Differentialgleichungen (Uni Stuttgart) |
Proseminar Mathematische Modellierung (Uni Stuttgart) |
Sommersemester 2013 |
Numerische Lineare Algebra (Uni Stuttgart) |
Sommersemester 2012 |
Numerical Methods for Differential Equations (Uni Stuttgart) |
Education | |
2001 | Abitur, Widukind Gymnasium Enger |
2006 | Diplom in Mathematics, University of Bielefeld |
2011 | PhD in Mathematics, University of Stuttgart |
2015 | Habilitation in Mathematics, University of Stuttgart |
Academic Career | |
2007 – 2018 | Research and Teaching Assistant, University of Stuttgart |
2011/12 | Postdoc, University of Crete |
2012/13 | Research Assistant, Weierstrass Institute, Berlin |
2013/14 | Associate Professor (not tenured) “Numerical Mathematics”, University of Stuttgart |
2015 – 17 | Associate Professor (not tenured) “Optimisation and Inverse Problems”, University of Stuttgart |
2017/18 |
Associate Professor (not tenured) “Numerical Simulations”, RWTH Aachen University |
since October 2018 | Professor “Mathematics – Numerics”, Technische Universität Darmstadt |
Observer-based data assimilation for time-dependent flows in gas networks (Subproject C05 in SFB-TRR154 funded by German Research Foundation DFG) This is a joint project with Martin Gugat, FAU Erlangen-Nuremberg
EMBFlyer
- EMB_Flyer (PDF-File, 79kB)
Tristan Pryer (Univ. of Bath) and I were organising a minisymposium on “Numerical methods for Hyperbolic Conservation Laws” at Computational Methods in Applied Mathematics that has been postponed to 2021 due to COVID 19.
Some conference videos:
- ICERM Workshop Advances in PDEs: Theory, Computation and Application to CFD (Videos unten auf der Seite)
- CIRM-SMF Week on Inhomogeneous Flows
Dynamical, spatially heterogeneous model adaptation in compressible flows (funded by German research foundation (DFG))
Numerical methods for multi-phase flows with strongly varying Mach numbers Elite-program for Postdocs of Baden-Wuerttemberg Stiftung
Mathematical Modeling of compressible fluids – from wild solutions to data integration – Research Seed Capital of University of Stuttgart and Ministry of Science, Research and Art Baden-Württemberg