Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

Andreas A. Buchheit, Dr. rer. nat.

profile_buchheit.jpg

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.

Teaching

Publications

  • 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)

Preprints

  • 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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