Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation

DOI10.1016/j.jcp.2024.112757arXiv2306.17526OpenAlexW4390806683MaRDI QIDQ6126542

Lukas Einkemmer

Publication date: 9 April 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.17526

zbMATH Keywords

computer simulationcomplexity reductiongyrokineticsdynamical low-rank approximationkinetic Alfvén waves

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Basic linear algebra (15Axx)

Cites Work

• Vlasov simulation of kinetic shear Alfvén waves
• A dynamical low-rank approach to the chemical master equation
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• Dynamical low-rank approximation: Applications and numerical experiments
• A PI stepsize control for the numerical solution of ordinary differential equations
• The semi-Lagrangian method for the numerical resolution of the Vlasov equation
• An adaptive step size controller for iterative implicit methods
• A dynamical adaptive tensor method for the Vlasov-Poisson system
• An almost symmetric Strang splitting scheme for nonlinear evolution equations
• Efficient adaptive step size control for exponential integrators
• Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system
• A rank-adaptive robust integrator for dynamical low-rank approximation
• An unconventional robust integrator for dynamical low-rank approximation
• A low-rank method for two-dimensional time-dependent radiation transport calculations
• An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
• The development of an implicit full \(f\) method for electromagnetic particle simulations of Alfvén waves and energetic particle physics
• A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
• A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations
• A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps
• Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors
• A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction
• A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions
• A projector-splitting integrator for dynamical low-rank approximation
• A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation
• An almost symmetric Strang splitting scheme for the construction of high order composition methods
• A parallel low-rank solver for the six-dimensional Vlasov-Maxwell equations
• Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations
• A robust and conservative dynamical low-rank algorithm
• The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
• Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors
• Control Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers
• Solving Ordinary Differential Equations I
• An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime
• Time Integration of Rank-Constrained Tucker Tensors
• A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation
• Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit
• A Low-Rank Algorithm for Weakly Compressible Flow
• Time Integration of Tensor Trains
• Dynamical Low‐Rank Approximation
• A Semi-Lagrangian Vlasov Solver in Tensor Train Format
• Rank-Adaptive Time Integration of Tree Tensor Networks
• On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems
• A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy
• Efficient 6D Vlasov simulation using the dynamical low-rank framework \texttt{Ensign}
• A dynamical low-rank approach to solve the chemical master equation for biological reaction networks

This page was built for publication: Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation