Dr. Thomas Müller (Dipl.-Math.)

Abteilung für Angewandte Mathematik
Universität Freiburg
Hermann-Herder-Str. 10
D-79104 Freiburg im Breisgau

 

 

 

Phone	+41 (0)79 4778025
Fax	N/A
Email

 

  

 

Research Interests and Projects

• Analysis, Numerical Analysis and Modelling of dynamical processes on stationary and evolving surfaces
• Nonlinear conservation laws, in particular on time-dependent Riemannian manifolds
• Shallow water equations on the sphere
• Coupling of processes on surfaces with fluid flow in surrounding bulk phases
• Currently, I am working on Project C1 (Dynamics on and of Surfaces ) of the Collaborative Research Centre (Sonderforschungsbereich / Transregio) 71 by the German Research Foundation (Deutsche Forschungsgemeinschaft).

Education

• PhD (Mathematics), University of Freiburg, Supervisor: Dietmar Kröner, (12/2014)
• Diplom in Mathematics with a minor in Physics, University of Freiburg, 06/2010
• Studies at University of Freiburg (03/2003-06/2010) and Ponificia Universidad Católica de Chile (08/2006-07/2007)

Teaching / Lehre

 Wintersemester 2013/14

• Vorlesung: Theorie und Numerik für Systeme von hyperbolischen Erhaltungsgleichungen  [gemeinsam mit Ch. Gersbacher]

Wintersemester 2012/13

• Seminarassistenz: Theorie und Numerik für partielle Differentialgleichungen [Dozent: D. Kröner]

Sommersemester 2012

• Seminarassistenz: Numerik für partielle Differentialgleichungen [Dozent: D. Kröner]

Sommersemester 2011

• Übungen und Assistenz zur Vorlesung: Wissenschaftliches Rechnen und Anwendungen in der Strömungsmechanik [Dozent: R. Klöfkorn]

Wintersemester 2010/11

• Übungen und Assistenz zur Voresung: Theorie und Numerik für partielle Differentialgleichungen III [Dozent: D. Kröner]

 

Prizes, Awards and Scholarships

• Ferndinand-von-Lindemann-Prize 2015 for outstanding Thesis, 10/2015
• Doctoral Scholarship, German National Academic Foundation (Studienstiftung des Deutschen Volkes e.V.), since 01/2013
  
• Finalist for the Best Poster Award (together with C. Gersbacher, A. Pfeiffer, N. Shokina), International Conference on Simulation Technology (SimTech), 06/2011
  
• Alumni-Prize 2010 for excellent Degree and Thesis, 08/2010
  
• Full Scholarship, German National Academic Foundation (Studienstiftung des Deutschen Volkes e.V.), 06/2006-06/2010
  
• Baden-Württemberg-Scholarship, Landesstiftung Baden-Württemberg, 08/2006 - 05/2007
  
• Scholarship for outstanding academic achievement, e-fellows.net, since 11/2005

Publications

• D. Kröner, T. Müller, L. M. Strehlau. Traces for functions of bounded variation on manifolds with applications to conservation laws on manifolds with boundary. SIAM Journal on Mathematical Analysis 47, no. 5, 3944-3962, 2015.

• J. Giesselmann and T. Müller. Estimating the Geometric Error of Finite Volume Schemes for Conservation Laws on Surfaces for generic numerical flux functions. In: Jürgen Fuhrmann, Mario Ohlberger and Christian Rohde (eds.), Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, volume 77 of Springer Proceedings in Mathematics & Statistics, pages 323–331. Springer International Publishing, 2014.

•  J. Giesselmann and T. Müller. Geometric Error of Finite Volume Schemes for Conservation Laws on Evolving Surfaces. Numerische Mathematik 128, no. 3, pp. 489–516, 2014. arXiv

• T. Müller and A. Pfeiffer.
  
  
  
  
  
  
  Well-balanced simulation of geophysical flows via the Shallow Water Equations with bottom topography: Consistency and Numerical Computation. Proceedings of the 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Padova, Italy, 2012. In: Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson (eds.), Hyperbolic Problems: Theory, Numerics, Applications, pp. 801-808, AIMS Ser. Appl. Math. 8, AIMS, Springfield, 2014.

• G. Dziuk, D. Kröner, T. Müller. Existence and Uniqueness for scalar conservation laws on moving hypersurfaces. Proceedings of the 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Padova, Italy, 2012. In: Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson (eds.), Hyperbolic Problems: Theory, Numerics, Applications, pp. 775-782, AIMS Ser. Appl. Math. 8, AIMS, Springfield, 2014.

• D. Lengeler and T. Müller. Scalar conservation laws on constant and time-dependent Riemannian manifolds. Journal of Differential Equations 254, pp. 1705–1727, 2013. arXiv

• G. Dziuk, D. Kröner, T. Müller. Scalar conservation laws on moving hypersurfaces. Interfaces and Free Boundaries 15, no. 2, pp. 203-236, 2013. arXiv

• T. Müller and D. Kröner. Related Problems for TV-Estimates for Conservation Laws on Surfaces. Proceedings of the 13th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Beijing, China, 2010. In: Tatsien Li; Song Jiang (eds.) Hyperbolic Problems: Theory, Numerics and Applications (2), pp. 584--592, Ser. Contemp. Appl. Math. CAM 18, Higher Ed. Press, Beijing 2012.

 

Thesis

• T. Müller. Scalar conservation laws on time-dependent Riemannian manifolds - analysis, numerical analysis and numerical simulations, PhD thesis, University of Freiburg, 2014. pdf

• T. Müller. Erhaltungsgleichungen auf Mannigfaltigkeiten. Wohlgestelltheit, Totalvariationsabschätzungen und Numerik.
  Diplom thesis, University of Freiburg, 2009. pdf

 

Talks

• Traces for functions of bounded variation on manifolds with applications to conservation laws on manifolds with boundary
  15th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2014), Rio de Janeiro, Brazil, 07/2014.
• Estimating the Geometric Error of Finite Volume Schemes for Conservation Laws on Surfaces for generic numerical flux functions
  FVCA7 - The International Symposium of Finite Volumes for Complex Applications VII, Berlin, Germany, 06/2012014.
• Scalar conservation laws on constant and time-dependent Riemannian manifolds
  Material Modeling Seminar. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany, 11/2012.

• Well-balanced simulation of geophysical flows via the Shallow Water Equations with bottom topography: Consistency and Numerical Computation
  14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), Padova, Italy, 06/2012.
  
• Conservation Laws on (evolving) Surfaces
  10th Hirschegg Workshop on Conservation Laws, Hirschegg, Austria, 09/2011.
• Simulation of nonlinear transport problems on (evolving) Surfaces
  Oberseminar Angewandte Mathematik, Institut für Angewandte Analysis und Numerische Simulation, Univerity of Stuttgart, Germany, 5/2011.
• Related Problems for TV-Estimates for Conservation Laws on Surfaces
  The 2010 Workshop on the Solution of Partial Differential Equations on the Sphere, Potsdam, Germany, 08/2010.
• Related Problems for TV-Estimates for Conservation Laws on Surfaces
  13th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2010), Beijing, China, 06/2010.
• Erhaltungsgleichungen auf Mannigfaltigkeiten
  Oberseminar Angewandte Mathematik, Section of Applied Mathematics, Univerity of Freiburg, Germany, 01/2010.
• Conservation Laws On Riemannian Manifolds
  9th Hirschegg Workshop on Conservation Laws, Hirschegg, Austria, 09/2009.

 

Poster

• G. Dziuk, D. Kröner, T. Müller. Scalar Conservation Laws on Moving Hypersurfaces.
  Solution of Partial Differential Equations on the Sphere 2012, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 09/2012.
  
• Conservation Laws on (moving) Surfaces.
  Gene Golub SIAM Summer School 2012: Simulation and Supercomputing in the Geosciences, Monterey, California, USA, 07-08/2012.
• C. Gersbacher, T. Müller, A. Pfeiffer, N. Shokina. Large-Scale Simulation of Geophysical Flows.
  International Conference on Simulation Technology (SimTech) 2011, Stuttgart, 06/2011, Finalist for the Best Poster Award.