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Dr. rer. nat. Andreas A. Buchheit

 

Building E1 1, Room 3.30

 

Department of Mathematics

Saarland University

PO 15 11 50

D-66041 Saarbrücken

 

Tel.: +49 (0)681 / 302 3811

E-Mail: buchheit@num.uni-sb.de

GitHub, ResearchGate, LinkedIn

 

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. Code examples can be found on my  GitHub repo.

 

Teaching

Published Research

  • Singular Euler-Maclaurin expansion on multidimensional lattices, Andreas A. Buchheit & Torsten Keßler, Nonlinearity 35 3706 (2022) 

  • On the Efficient Computation of Large Scale Singular Sums with Applications to Long-Range Forces in Crystal Lattices, Andreas A. Buchheit and Torsten Keßler, J. Sci. Comput. 90, 53 (2022)

  • On the efficient computation of multidimensional singular sums, Andreas A. Buchheit, Dissertation (2021)

  • Ground state of the Frenkel–Kontorova model with a globally deformable substrate potential, Andreas A. Buchheit and Sergej Rjasanow, Physica D: Nonlinear Phenomena (2019): 132298

  • Master equation for high-precision spectroscopy, Andreas A. Buchheit and Giovanna Morigi,  Phys. Rev. A 94, 042111 (2016) 

  • Critical Analysis of the Born-Markov Master Equation, Andreas A. Buchheit, Masterarbeit (2015) 

  • Dynamik von lasergetriebenen Atomen, Andreas A. Buchheit, Bachelorarbeit (2013)

 

Preprints

  • Exact continuum representation of long-range interacting systems, Andreas A. Buchheit, Torsten Keßler, Peter K. Schuhmacher, and Benedikt Fauseweh, arXiv:2201.11101

 

Impact and Outreach