5 papers
Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
Jiajia Yu, Jingwei Hu, Fengyan Li +3
Parametrized PDEs with density-valued solutions are often difficult to approximate with classical linear reduced-order models, especially in transport-dominated regimes. We introdu…
A separable and asymptotic-preserving dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system
Shiheng Zhang, Jingwei Hu
We present a dynamical low-rank (DLR) method for the Vlasov-Poisson-Fokker-Planck (VPFP) system. Our main contributions are two-fold: (i) a conservative spatial discretization of t…
Implicit Dynamical Tensor Train Approximation for Kinetic Equations with Stiff Fokker--Planck Collisions
Geshuo Wang, Jingwei Hu
Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. W…
On the stability of the low-rank projector-splitting integrators for hyperbolic and parabolic equations
Shiheng Zhang, Jingwei Hu
We study the stability of a class of dynamical low-rank methods--the projector-splitting integrator (PSI)--applied to linear hyperbolic and parabolic equations. Using a von Neumann…
Asymptotic-Preserving Dynamical Low-Rank Method for the Stiff Nonlinear Boltzmann Equation
Lukas Einkemmer, Jingwei Hu, Shiheng Zhang
In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear i…