Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

Andreas A. Buchheit, Dr. rer. nat.


Gebäude E1.1, Zimmer 3.30

FR Mathematik
Universität des Saarlandes
Postfach 15 11 50
D-66041 Saarbrücken

Tel.: +49 (0)681 / 302 3811
E-Mail: buchheit@num.uni-sb.de

Research interests

I am currently developing the Singular Euler-Maclaurin (SEM) expansion, a method that uses techniques from number theory in order to transform large scale lattice sums into integral and differential operators. In contrast to the standard Euler-Maclaurin expansion, the SEM also converges in the case of singular functions, which are of enormous practical importance, as most physical interaction potentials belong to this class. This opens a way for computing macroscopic crystal dynamics precisely and efficiently independently of particle number. A preprint of our work on the 1D SEM is available under arXiv:2003.12422. Code examples can be found on my GitHub repo.

  • Euler-Maclaurin expansion,
  • Nonlinear partial differential equations,
  • Analytical number theory,
  • Topological solitons,
  • Numerical simulation of condensed matter systems,
  • Numerical simulation of electromagnetic fields,
  • Global optimisation,
  • Integer programming.



  • Ground state of the Frenkel–Kontorova model with a globally deformable substrate potential, Andreas A. Buchheit & Sergej Rjasanow, Physica D: Nonlinear Phenomena (2019): 132298
  • Master equation for high-precision spectroscopy, Andreas A. Buchheit & Giovanna Morigi, Phys. Rev. A 94, 042111 (2016)
  • Critical Analysis of the Born-Markov Master Equation, Andreas A. Buchheit & Giovanna Morigi, Masterarbeit (2015)
  • Dynamik von lasergetriebenen Atomen, Andreas Buchheit & Giovanna Morigi, Bachelorarbeit (2013)


  • Singular Euler-Maclaurin expansion, Andreas A. Buchheit & Torsten Keßler, arXiv:2003.12422
ag/buchheit.txt · Zuletzt geändert: 2021/10/18 09:49 von agrja
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