A low-rank projector-splitting integrator for the Vlasov--Poisson equation

L Einkemmer, C Lubich - SIAM Journal on Scientific Computing, 2018 - SIAM
Many problems encountered in plasma physics require a description by kinetic equations,
which are posed in an up to six-dimensional phase space. A direct discretization of this …

A μ-mode integrator for solving evolution equations in Kronecker form

M Caliari, F Cassini, L Einkemmer, A Ostermann… - Journal of …, 2022 - Elsevier
In this paper, we propose a μ-mode integrator for computing the solution of stiff evolution
equations. The integrator is based on a d-dimensional splitting approach and uses exact …

Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations

N Crouseilles, L Einkemmer, J Massot - Journal of Computational Physics, 2020 - Elsevier
The efficient numerical solution of many kinetic models in plasma physics is impeded by the
stiffness of these systems. Exponential integrators are attractive in this context as they …

[HTML][HTML] LeXInt: Package for exponential integrators employing Leja interpolation

PJ Deka, L Einkemmer, M Tokman - SoftwareX, 2023 - Elsevier
We present a publicly available software for exponential integrators that computes the φ l (z)
functions using polynomial interpolation. The interpolation method at Leja points have …

Exponential integrators for resistive magnetohydrodynamics: Matrix-free Leja interpolation and efficient adaptive time stepping

PJ Deka, L Einkemmer - The Astrophysical Journal Supplement …, 2022 - iopscience.iop.org
We propose a novel algorithm for the temporal integration of the resistive
magnetohydrodynamics (MHD) equations. The approach is based on exponential …

[HTML][HTML] Efficient adaptive step size control for exponential integrators

PJ Deka, L Einkemmer - Computers & Mathematics with Applications, 2022 - Elsevier
Traditional step-size controllers make the tacit assumption that the cost of a time step is
independent of the step size. This is true for explicit and implicit integrators that use direct …

[HTML][HTML] An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs

M Caliari, L Einkemmer, A Moriggl… - Journal of Computational …, 2021 - Elsevier
Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …

Modified lawson methods for vlasov equations

B Boutin, A Crestetto, N Crouseilles, J Massot - SIAM Journal on Scientific …, 2024 - SIAM
In this work, Lawson type numerical methods are studied to solve Vlasov type equations on
a phase space grid. These time integrators are known to satisfy enhanced stability …

Should exponential integrators be used for advection-dominated problems?

L Einkemmer, TH Hoang, A Ostermann - arXiv preprint arXiv:2410.12765, 2024 - arxiv.org
In this paper, we consider the application of exponential integrators to problems that are
advection dominated, either on the entire or on a subset of the domain. In this context, we …

A semi-Lagrangian discontinuous Galerkin method for drift-kinetic simulations on GPUs

L Einkemmer, A Moriggl - SIAM Journal on Scientific Computing, 2024 - SIAM
In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous
Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs) …