## Dr. rer. nat. Torsten Keßler

##### Building E1 1, Room 3.28

##### Department of Mathematics

##### Saarland University

##### PO 15 11 50

##### D-66041 Saarbrücken

##### tel:+49 681 302 2472

##### kessler@num.uni-sb.de

## Research Interests

I work on numerical methods for kinetic equations which provide an intermediate (mesoscopic) description of fluid dynamics that links the microscopic discription by individual particles and the macroscopic description by the Euler or Navier-Stokes equations. To that end, I use a wide range of numerical tools, for instance Galerkin-Petrov methods for the Boltzmann equation that describes the time evolution of a rarefied gas, or Boundary Elements Methods to simulate plasma.

Together with my collegue Andreas Buchheit I have been developing the Singular Euler-Maclaurin method, a tool for the efficient computation of large sums over singular functions that appear in condensed matter physics or quantum mechanics. Our post on the Wolfram Blog gives a concise introduction to our method and discusses the application to a macroscopically large ion chain with 20 billion ions. In collaboration with physicists from the German Aerospace Center we are developing a new understanding of physical systems with long-range interactions.

## Teaching

- Spring 2022 Exercises Numerics of Partial Differential Equations
- Winter 2021/22 Seminar Nonlinear Phenomena
- Spring 2021 Exercises Modeling with Partial Differential
- Winter 2020/21 Seminar Partial differential equations and their applications
- Spring 2020 Exercises Numerics of Partial Differential Equations
- Winter 2019/20 Seminar Numerical methods for Maxwell's equations
- Winter 2018/19 Exercises Modeling with Partial Differential
- Winter 2018/19 Seminar Scientific Computing with
- Winter 2018 Exercises Höhere Mathematik für Ingenieure
- Winter 2017/18 Exercises Höhere Mathematik für Ingenieure III

## Publications

### Kinetic Theory

- T. Keßler, S. Rjasanow: Limit model for the Vlasov-Maxwell system with strong magnetic fields via gyroaveraging, St. Petersburg Mathematical Journal, 2021, 32(4): 753-765
- T. Keßler, S. Rjasanow, S. Weißer: Vlasov-Poisson system tackled by particle simulation utilizing boundary element methods, SIAM Journal on Scientific Computing, 2020, 42(1): B299–B326
- T. Keßler, S. Rjasanow: Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation, Kinetic and Related Models, 2019, 12(3): 507-549

### Large-Scale Singular Lattice Sums

- Andreas A. Buchheit, T. Keßler: On the efficient computation of large scale singular sums with applications to long-range forces in crystal lattices, Journal of Scientific Computing, 2022, 90:53
- Andreas A. Buchheit, T. Keßler: Singular Euler-Maclaurin expansion on multidimensional lattices, Preprint, arxiv:2102.10941

### Condensed Matter Physics

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

### Quantum Computing

- Susanna Kirchhoff, Torsten Keßler, Per J. Liebermann, Elie Assémat, Shai Machnes, Felix Motzoi, and Frank K. Wilhelm: Optimized cross-resonance gate for coupled transmon systems, Physical Review A, 2018, 97:042348

## Theses

- Boundary Integral Equations in Kinetic Plasma Theory, Doctoral thesis, Saarland University, July 2022
- Galerkin-Petrov method for the Boltzmann equation, Master's thesis in applied mathematics, Saarland University, July 2017
- Optimale Realisierung eines Kreuzresonanz-Gatters, Bachelor's thesis in physics, Saarland University, November 2015