Related papers: A massively parallel semi-Lagrangian solver for th…
Running kinetic plasma physics simulations using grid-based solvers is very demanding both in terms of memory as well as computational cost. This is primarily due to the up to six-dimensional phase space and the associated unfavorable…
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm…
This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field.…
We develop new numerical schemes for Vlasov--Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is…
The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit…
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the…
In this paper, we describe our approach to develop a simulation software application for the fully kinetic Vlasov equation which will be used to explore physics beyond the gyrokinetic model. Simulating the fully kinetic Vlasov equation…
This work concerns the numerical simulation of the Vlasov-Poisson set of equations using semi- Lagrangian methods on Graphical Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented.…
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 plasma configurations. However, a reduction of…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order tensor setting. The proposed scheme retains the high-order…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov--Poisson equation. More specifically, our goal is to compare the performance of the more recently developed…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
In this paper, our goal is to efficiently solve the Vlasov equation on GPUs. A semi-Lagrangian discontinuous Galerkin scheme is used for the discretization. Such kinetic computations are extremely expensive due to the high-dimensional phase…
In this article, we derive a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Grid-based methods for the Vlasov equation have been shown to give accurate results but their use has mostly…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in physical space. The…
We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in…
In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…