4 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…
Multilevel Adaptive-Rank Methods for Linear and Nonlinear Systems in the Hierarchical Tucker Format
William A. Sands, Pierson T. Guthrey, Nathan V. Roberts
We develop multilevel adaptive-rank iterative methods for the solution of linear and nonlinear systems arising from high-dimensional partial differential equations. Our contributio…
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…