7 papers
A Mass, Momentum, and Energy Conserving Semi-Lagrangian Adaptive-Rank (SLAR) Method for the Vlasov-Poisson System
Nanyi Zheng, William A. Sands, Jing-Mei Qiu
We propose a semi-Lagrangian adaptive-rank (SLAR) method that combines the large time-step capability of semi-Lagrangian schemes with the efficiency of adaptive-rank tensor represe…
A Structure-preserving Adaptive-Rank Approach to the High-Dimensional Wigner-Poisson System
Andrew J. Christlieb, Sining Gong, Jing-Mei Qiu +1
The Wigner-Poisson system is a deterministic phase-space model for quantum kinetic electron dynamics, but high-dimensional simulations are limited by the full 3D3V phase space and…
A Semi-Lagrangian Adaptive Rank (SLAR) Method for High-Dimensional Vlasov Dynamics
Nanyi Zheng, William A. Sands, Daniel Hayes +2
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…
An Adaptive-rank Approach with Greedy Sampling for Multi-scale BGK Equations
William A. Sands, Jing-Mei Qiu, Daniel Hayes +1
In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows a…
A Sampling-Based Adaptive Rank Approach to the Wigner-Poisson System
Andrew Christlieb, Sining Gong, Jing-Mei Qiu +1
We develop a mass-conserving, adaptive-rank solver for the 1D1V Wigner-Poisson system. Our work is motivated by applications to the study of the stopping power of particles at…
A Semi-Lagrangian Adaptive-Rank (SLAR) Method for Linear Advection and Nonlinear Vlasov-Poisson System
Nanyi Zheng, Daniel Hayes, Andrew Christlieb +1
High-order semi-Lagrangian methods for kinetic equations have been under rapid development in the past few decades. In this work, we propose a semi-Lagrangian adaptive rank (SLAR)…