
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
-
SoSe 2023 Vorlesung Programmierung
-
WiSe 22/23 Seminar Numerische Methoden in kondensierter Quantenmaterie
-
SoSe 2021 Seminar Fourier-Analysis
-
WiSe 21/22 Seminar Nichtlineare Phänomene verstehen
-
SoSe 2021 Vorlesung Programmierung
-
WiSe 19/20 Seminar Numerische Methoden für die Maxwellgleichungen
-
SoSe 2019 Vorlesung Programmierung
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 and Emerging Exotic Phases in Unconventional Superconductors, Andreas A. Buchheit, Torsten Keßler, Peter K. Schuhmacher, and Benedikt Fauseweh, arXiv:2201.11101
Impact and Outreach
-
Mathematiker lösen komplexes Problem durch Verallgemeinerung einer 300 Jahre alten Formel, Saarland University Research News, Campus Magazin, IDW
-
The Singular Euler-Maclaurin Expansion: A New Twist to a Centuries Old Problem, Wolfram Blog Entry on the SEM