# Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign

@article{Cassini2021Efficient6V, title={Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign}, author={Fabio Cassini and Lukas Einkemmer}, journal={ArXiv}, year={2021}, volume={abs/2110.13481} }

Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algorithms can drastically reduce the required computational effort, while still accurately resolving important physical features such as filamentation and Landau damping. In this paper, we introduce the Ensign software framework, which facilitates the efficient implementation of dynamical low-rank algorithms on modern…

## Figures and Tables from this paper

## One Citation

A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations

- Physics
- 2022

Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic…

## References

SHOWING 1-10 OF 40 REFERENCES

A Low-Rank Projector-Splitting Integrator for the Vlasov-Poisson Equation

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2018

Numerical simulations in two and four dimensions for linear Landau damping and the two-stream instability highlight the favorable behavior of this numerical method and show that the proposed algorithm is able to drastically reduce the required computational effort.

A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction

- Physics, MathematicsJ. Comput. Phys.
- 2020

This paper considers the Vlasov--Maxwell system and proposes a dynamic low-rank integrator based on Lagrange multipliers which enforces Gauss' law up to machine precision and achieves good behavior for a range of test problems.

An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2021

This paper proposes an efficient dynamical low-rank integrator that can capture the fluid limit – the Navier-Stokes equations – of the Boltzmann-BGK model even in the compressible regime and has the advantage that the rank required to obtain accurate results is significantly reduced compared to the previous state of the art.

On the stability of robust dynamical low-rank approximations for hyperbolic problems

- Mathematics, Computer ScienceArXiv
- 2021

A projector splitting integrator is proposed, based on applying DLRA to the continuous system before performing the discretization, that recovers the classic CFL condition and it is shown that the unconventional integrator has more favorable stability properties.

A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2019

The traditional approach of evaluating numerical methods is misleading, even for short time simulations, and the semi-Lagrangian discontinuous Galerkin scheme shows a moderate improvement in run time for nonlinear Landau damping and a substantial improvement for the two-stream instability.

A Low-Rank Algorithm for Weakly Compressible Flow

- Mathematics, PhysicsSIAM J. Sci. Comput.
- 2019

A numerical method for solving weakly compressible fluid flow based on a dynamical low-rank projector splitting based on the Boltzmann equation with BGK collision term, which results in a set of constant coefficient advection equations.

A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations

- Computer Science, PhysicsJ. Comput. Phys.
- 2021

It is demonstrated with the numerical results that the so-called high-order / low-order (HOLO) algorithm is conservative without sacrificing computational efficiency and accuracy.

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

- Mathematics, Computer ScienceComput. Phys. Commun.
- 2016

We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized…

Sparse Grids for the Vlasov–Poisson Equation

- Computer Science
- 2016

A semi-Lagrangian Vlasov–Poisson solver on a tensor product of two sparse grids is presented and an evaluation algorithm with constant instead of logarithmic complexity per grid point is devised to defeat the problem of poor representation of Gaussians on the sparse grid.

High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code

- Computer Science, PhysicsComput. Phys. Commun.
- 2016

The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization.