Felix Gruber, M.Sc.

Former Position

From December 2012 to June 2018, I was a doctoral student at the IGPM under the supervision of Prof. Dr. Wolfgang Dahmen.

The topic of my thesis is the design of a stable formulation for radiative transfer problems. It is based on a Discontinuous Petrov–Galerkin formulation for the spatial discretization and a wavelet-based discretization in the transport direction.

Research Interests

• Stability in finite element methods (specifically, Discontinuous Petrov–Galerkin)
• Reduced basis methods
• Sparse grids

Research Work

• Development of a Discontinuous Petrov–Galerkin method for the radiative transfer equation (with Wolfgang Dahmen and Olga Mula)

Publications

• F. Gruber, Adaptive Source Term Iteration: A Stable Formulation for Radiative Transfer, doctoral thesis, 2018. [URL] [PDF]
• W. Dahmen, F. Gruber and O. Mula, An Adaptive Nested Source Term Iteration for Radiative Transfer Equations, 2018. arXiv:1810.07035v1
• F. Gruber, A. Klewinghaus and O. Mula, The DUNE-DPG library for solving PDEs with Discontinuous Petrov–Galerkin finite elements, Archive of Numerical Software 5(1), 2017. DOI: 10.11588/ans.2017.1.27719 [PDF]
• M. Blatt, A. Burchardt, A. Dedner, C. Engwer, J. Fahlke, B. Flemisch, C. Gersbacher, C. Gräser, F. Gruber, C. Grüninger, D. Kempf, R. Klöfkorn, T. Malkmus, S. Müthing, M. Nolte, M. Piatkowski and O. Sander, The Distributed and Unified Numerics Environment, Version 2.4, Archive of Numerical Software 4(100), 2016. DOI: 10.11588/ans.2016.100.26526 [PDF]

Talks

• Adaptive Source Term Iteration: A Stable Formulation for Radiative Transfer
  Doctoral Defense, RWTH Aachen, May 2018
• An Introduction to the Git Version Control System
  IGPM-Oberseminar, Feb. 2018, [sources]
• The Discontinuous Petrov–Galerkin Method for Radiative Transfer Problems
  Lunch Seminar, MathCCES, RWTH Aachen, Jun. 2017
• The Discontinuous Petrov–Galerkin Method for Radiative Transfer Problems
  IGPM-Seminar in Amsterdam, Sep. 2016
• dune-dpg: A Library for Discontinuous Petrov–Galerkin Using Optimal Test Spaces
  Dune User Meeting 2015 in Heidelberg, Sep. 2015
• The Discontinuous Petrov–Galerkin Method—Introduction to Stable Test Spaces and Application to Radiative Transfer Problems
  IGPM-Seminar in Leer, Sep. 2014
• On the Stability of the Discontinuous Petrov–Galerkin Method
  IGPM-Oberseminar, Jun. 2013

Programming Projects

Some of my contributions to free software projects can be found on my GitHub profile.

• dune-dpg: A C++ library for solving transport dominated problems with the Discontinuous Petrov–Galerkin method (C++, Dune), joint work with Angela Klewinghaus and Olga Mula, IGPM, RWTH Aachen
• Implementation of the Discontinuous Petrov–Galerkin method for simple transport problems (C++, deal.II), IGPM, RWTH Aachen
• Implementation of a sparse grid library (C++), IGPM and AVT-PT, RWTH Aachen (funded as an RWTH Undergraduate Funds project)

Master's Thesis

I did my master's thesis in 2012 at the IGPM under the supervision of Prof. Dr. Wolfgang Dahmen.

Title: On the Stability of Discontinuous Petrov–Galerkin Methods

Teaching

• SoSe 2017: Mathematisches Praktikum
• WS 2016/2017: Adaptive Lösungskonzepte
• SoSe 2016: Mathematisches Praktikum
• SoSe 2015: Mathematisches Praktikum
• WS 2014/2015: Numerische Analysis IV
• SoSe 2014: Mathematisches Praktikum
• WS 2013/2014: Numerische Analysis III
• SoSe 2013: Numerische Mathematik (für Elektrotechniker)

Most webpages of older courses have unfortunately been lost in a CMS migration. Some links have been replaced with links to partial copies at the Internet Archive.