2 citations · 4 across the 10 of their papers we have counts for
10 papers
Nonnegative Low-Rank Matrix Correction under an Orthogonality Constraint in Conservative Vlasov Simulations
Yue Wu, Stephen Becker, Jingmei Qiu +1
In low-rank numerical methods for Vlasov dynamics, the SVD-type truncation procedure may introduce negative entries into the numerical solution. Such negative values are unphysical…
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 Structure-Preserving Penalization Method for the Single-species Rosenbluth-Fokker-Planck Equation
Hamad El Kahza, Luis Chacón, William Taitano +2
The Rosenbluth-Fokker-Planck (RFP) equation describes Coulomb collisional dynamics within and across species in plasmas. It belongs to the broader class of anisotropic-diffusion-ad…
A Nodal Discontinuous Galerkin Method with Rank-Adaptive Velocity Space Representation for the Multiscale BGK Model
Andres Galindo-Olarte, Joseph Nakao, Mirjeta Pasha +2
A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a rank-adaptive decomposition is applied solely in the velocity subspace, while a full-rank represent…
A review of low-rank methods for time-dependent kinetic simulations
Lukas Einkemmer, Katharina Kormann, Jonas Kusch +2
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised…
Sylvester-Preconditioned Adaptive-Rank Implicit Time Integrators for Advection-Diffusion Equations with Variable Coefficients
Hamad El Kahza, Jing-Mei Qiu, Luis Chacon +1
We consider the adaptive-rank integration of {2D and 3D} time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard f…
High-order Adaptive Rank Integrators for Multi-scale Linear Kinetic Transport Equations in the Hierarchical Tucker Format
William A. Sands, Wei Guo, Jing-Mei Qiu +1
In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is…
A high-order Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for scalar nonlinear conservation laws
Jiajie Chen, Joseph Nakao, Jing-Mei Qiu +1
We present a class of high-order Eulerian-Lagrangian Runge-Kutta finite volume methods that can numerically solve Burgers' equation with shock formations, which could be extended t…
Krylov-based Adaptive-Rank Implicit Time Integrators for Stiff Problems with Application to Nonlinear Fokker-Planck Kinetic Models
Hamad El Kahza, William Taitano, Jing-Mei Qiu +1
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solut…
Reduced Augmentation Implicit Low-rank (RAIL) integrators for advection-diffusion and Fokker-Planck models
Joseph Nakao, Jing-Mei Qiu, Lukas Einkemmer
This paper introduces a novel computational approach termed the Reduced Augmentation Implicit Low-rank (RAIL) method by investigating two predominant research directions in low-ran…