Dr. Sining Gong (Michigan State University)

Title:
Structure-Preserving Adaptive-Rank Solvers for the Wigner–Poisson System

Abstract:
The Wigner–Poisson system is a deterministic phase-space model for quantum kinetic transport, but its numerical solution is challenging because of the nonlocal Wigner potential and the high dimensionality of phase space. We develop structure-preserving adaptive-rank methods that exploit low-rank solution structure while retaining key physical properties. The approach combines Strang splitting, semi-Lagrangian transport, structure-preserving Fourier discretization, and sampling-based rank adaptation. For high-dimensional problems, a hierarchical Tucker representation is used together with symmetry-aware compression and global moment correction to preserve real-valuedness, mass, momentum, and total energy. Numerical experiments in 1D1V, 2D2V, and 3D3V demonstrate accurate resolution of kinetic dynamics, strong conservation properties, and approximately linear scaling with the number of grid points per coordinate over the tested rank range. The results demonstrate the potential of adaptive-rank methods for efficient simulation of high-dimensional quantum transport PDEs.