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.

• 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

• 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)

• 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

• 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