90 citations · 1k across the 88 of their papers we have counts for
8 papers · 2 filters
Exponential Integrators for Resistive Magnetohydrodynamics: Matrix-free Leja Interpolation and Efficient Adaptive Time Stepping
Pranab Deka, Lukas Einkemmer
We propose a novel algorithm for the temporal integration of the resistive magnetohydrodynamics (MHD) equations. The approach is based on exponential Rosenbrock schemes in combinat…
On the stability of robust dynamical low-rank approximations for hyperbolic problems
Jonas Kusch, Lukas Einkemmer, Gianluca Ceruti
The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems that arise in such diverse fields as kinetic transport and uncertainty quantification. Even t…
Dynamical low-rank approximation for Burgers' equation with uncertainty
Jonas Kusch, Gianluca Ceruti, Lukas Einkemmer +1
Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the solution forms shocks leading to oscillatory behaviour in the numerical approximatio…
An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware
Lukas Einkemmer, Alexander Ostermann, Mirko Residori
Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into…
A -mode integrator for solving evolution equations in Kronecker form
Marco Caliari, Fabio Cassini, Lukas Einkemmer +2
In this paper, we propose a -mode integrator for computing the solution of stiff evolution equations. The integrator is based on a -dimensional splitting approach and uses ex…
Efficient adaptive step size control for exponential integrators
Pranab Jyoti Deka, Lukas Einkemmer
Traditional step size controllers make the tacit assumption that the cost of a time step is independent of the step size. This is reasonable for explicit and implicit integrators t…
A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
Lukas Einkemmer, Ilon Joseph
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerge…
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
Lukas Einkemmer, Jingwei Hu, Lexing Ying
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the…