5 papers
A Counterexample to Robust Second-Order Convergence of the Strang Projector-Splitting Integrator
Shiheng Zhang
The classical Strang projector-splitting integrator is widely observed to converge with order two, whereas the error analysis that remains uniform as the smallest singular value re…
Scalar-Tracking SAV Schemes with Pullback Corrections for Gradient Flows
Shiheng Zhang, Jie Shen
The scalar auxiliary variable (SAV) method constructs linear, unconditionally energy-stable time discretizations of gradient flows. In a first-order SAV step, eliminating the auxil…
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…
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…