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math.NA2025
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…
math.NA2025
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…