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.

WiSe 23/24 Seminar Computer Algorithms in Applied Mathematics

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

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, Phys. Rev. Research 5, 043065 (2023)

Singular Euler-Maclaurin expansion on multidimensional lattices, Andreas A. Buchheit and 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 und Physiker beschleunigen Simulation von Supraleitern enorm, Saarland University Research News, IDW

Success Story: Simulation of unconventional superconductors, Zentrum für Nationales Hochleistungsrechner NHR@FAU

Wirkung auf die Ferne berechnen, Spektrum der Wissenschaft 08.22, S.24 ff

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