11 citations · 30 across the 10 of their papers we have counts for
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Computation of anisotropic singular sums from high-order derivatives of Epstein zeta functions
Andreas A. Buchheit, Jonathan K. Busse
The precise and efficient evaluation of large-scale lattice sums involving power-law kernels is a fundamental computational problem in the simulation of classical and quantum syste…
Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics
Andreas A. Buchheit, Jonathan K. Busse, Torsten Keßler +1
We address the efficient computation of power-law-based interaction potentials of homogeneous -dimensional bodies with an infinite -dimensional array of copies, including the…
Epstein zeta method for many-body lattice sums
Andreas A. Buchheit, Jonathan K. Busse
Many-body interactions arise naturally in the perturbative treatment of classical and quantum many-body systems and play a crucial role in the description of condensed matter syste…
Computation and properties of the Epstein zeta function with applications to quantum systems
Andreas A. Buchheit, Jonathan Busse, Ruben Gutendorf
The Epstein zeta function generalises the classical Riemann zeta function to oscillatory lattice sums in higher dimensions and has recently emerged as a key tool in the simulation…
On the computation of lattice sums without translational invariance
Andreas A. Buchheit, Torsten Keßler, Kirill Serkh
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure a…
Singular Euler-Maclaurin expansion on multidimensional lattices
Andreas A. Buchheit, Torsten Keßler
We extend the classical Euler-Maclaurin expansion to sums over multidimensional lattices that involve functions with algebraic singularities. This offers a tool for the precise qua…
Singular Euler-Maclaurin expansion
Andreas A. Buchheit, Torsten Keßler
We present the singular Euler--Maclaurin expansion, a new method for the efficient computation of large singular sums that appear in long-range interacting systems in condensed mat…