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Sining Gong

Publications and source records attributed to Sining Gong.

9 recordsLinked to original sources
arXiv2026

A conservative adaptive rank method for the Wigner-Poisson system

We propose a conservative adaptive rank method for the 1D1V Wigner-Poisson system. The method targets a central challenge in deterministic quantum kinetic simulations: reducing the cost of phase-space evolution while preserving the macroscopic invariants needed for physical fidelity. The scheme combines a sampling-based adaptive rank Wigner-Poisson update [7] with a conservative macroscopic correction. A conservative density-momentum solve provides local macroscopic updates, a Fermi-Dirac-type reconstruction transfers them to the kinetic solution, and a global quadratic moment correction enforces the discrete total energy constraint at the kinetic level. Unlike Maxwell-Boltzmann-type corrections commonly used in classical kinetic settings, the reconstruction uses a Fermi-Dirac-type form motivated by the model's quantum-statistical structure. The corrected state is incorporated into an ACA SVD representation, allowing the numerical rank to adapt to the phase-space complexity generated by the nonlocal Wigner operator and self-consistent Poisson field. Numerical experiments for the two-stream instability, strong Landau damping, and bump-on tail instability show that the method captures benchmark Wigner-Poisson dynamics for several values of the quantum parameter H, maintains bounded adaptive ranks, and preserves the specified global discrete invariants with conservation errors near machine precision. We also compare this formulation, which uses local density-momentum correction plus global total energy correction, with a related globally conservative formulation for mass, momentum, and energy [8]. The two approaches produce nearly identical phase-space and diagnostic results for the periodic benchmark test considered here, indicating that both correction strategies are compatible with adaptive rank compression for Wigner-Poisson dynamics in the tested 1D1V periodic setting.

math.NA↗
arXiv2026

An Energy-Conserving Unstaggered Electromagnetic-Potential Particle-in-Cell Method, Part I: Non-relativistic Generalized-Momentum Formulation

We develop an unstaggered, potential-based particle-in-cell method for the nonrelativistic Vlasov-Maxwell system in the Lorenz gauge. The field update is written as a Crank-Nicolson discretization of first-order wave systems for the scalar potential, the vector potential, and their time derivatives. The charge density is not deposited directly; instead, it is advanced from the discrete continuity equation using the current deposited from the particles. This opens up algorithmic flexibility with a range of innovation, including unstaggered mesh layouts that preserve the Lorenz gauge and Gauss's law at the discrete level. In the potential formulation, this source ordering also permits preservation of the Lorenz gauge and Gauss's law at the discrete level. To extend the paradigm to an energy-conserving formulation, we introduce a consistent orbit-averaged scatter, gather, and particle push. For energy consistency, the update of the canonical momentum is modified by replacing the pointwise midpoint derivative of the vector potential with an orbit-averaged discrete gradient of the mesh-interpolated vector potential consistent with the orbit-average maps. This construction satisfies an exact finite-difference chain rule along each particle orbit. As a result, the particle work equals the mesh work appearing in the Crank-Nicolson field-energy balance, yielding exact total-energy conservation up to nonlinear solver tolerance and roundoff. We demonstrate exact energy conservation of the method in 3D on the cold two-stream instability.

math.NA↗
arXiv2026

A Structure-preserving Adaptive-Rank Approach to the High-Dimensional Wigner-Poisson System

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 the nonlocal Wigner potential. We develop a structure-preserving, sampling-based adaptive-rank solver in hierarchical Tucker format for finite-$H$ regimes in which Wigner-Poisson solutions exhibit exploitable low-rank structure. The central difficulty is that adaptive compression can destroy the Fourier-Hermitian tensor symmetry required for a real inverse velocity transform and can break discrete global conservation laws. We address these issues with a Fourier-Hermitian-symmetry-aware sampling and mapping procedure and a global moment correction enforcing mass, momentum, and self-consistent total energy. Numerical tests for two-stream instability and strong Landau damping in 2D2V and 3D3V show roundoff-level conservation, preservation of the real-valued inverse transform, and approximately linear scaling with respect to the number of grid points per coordinate over the tested rank range. The results demonstrate that long-time 3D3V Wigner-Poisson simulations can be performed without assembling the full phase-space tensor.

math.NA↗
arXiv2025

Quantum Kinetic Modeling of KEEN waves in a Warm-Dense Regime

We report a fully kinetic, quantum study of Kinetic Electrostatic Electron Nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrow harmonic locking to the fundamental, and hasten post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner-Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of nonequilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

physics.plasm-ph↗
arXiv2025

A Sampling-Based Adaptive Rank Approach to the Wigner-Poisson System

We develop a mass-conserving, adaptive-rank solver for the 1D1V Wigner-Poisson system. Our work is motivated by applications to the study of the stopping power of $\alpha$ particles at the National Ignition Facility (NIF). In this regime, electrons are in a warm dense state, requiring more than a standard kinetic model. They are hot enough to neglect Pauli exclusion, yet quantum enough to require accounting for uncertainty. The Wigner-Poisson system captures these effects but presents challenges due to its nonlocal nature. Based on a second-order Strang splitting method, we first design a full-rank solver with a structure-preserving Fourier update that ensures the intermediate solutions remain real-valued (up to machine precision), improving upon previous methods. Simulations demonstrate that the solutions exhibit a low rank structure for moderate to high dimensionless Planck constants ($H \ge 0.1$). This observed low rank structure motivates the development of an adaptive-rank solver, built on a Semi-Lagrangian adaptive-rank (SLAR) scheme for advection and an adaptive-rank, structure-preserving Fourier update for the Wigner integral terms, with a rigorous proof of structure-preserving property provided. Our solver achieves $O(N)$ complexity in both storage and computation time, while preserving mass and maintaining momentum accuracy up to the truncation error. The adaptive rank simulations are visually indistinguishable from the full-rank simulations in capturing solution structures. These results highlight the potential of adaptive rank methods for high-dimensional Wigner-Poisson simulations, paving the way toward fully kinetic studies of stopping power in warm dense plasmas.

math.NA↗
arXiv2024

Boundary corrections for kernel approximation to differential operators

Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, [8,9], order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

math.NA↗
arXiv2023

Discrete Elasticity Exact Sequences on Worsey-Farin Splits

We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators representing deformation, incompatibility, and divergence. For each of these component spaces, a corresponding finite element space on Worsey-Farin meshes is exhibited. Unisolvent degrees of freedom are developed for these finite elements, which also yields commuting (cochain) projections on smooth functions. A distinctive feature of the spaces in these complexes is the lack of extrinsic supersmoothness at subsimplices of the mesh. Notably, the complex yields the first (strongly) symmetric stress finite element with no vertex or edge degrees of freedom in three dimensions. Moreover, the lowest order stress space uses only piecewise linear functions which is the lowest feasible polynomial degree for the stress space.

math.NA↗
arXiv2022

Convergence of Lagrange Finite Element Methods for Maxwell Eigenvalue Problem in 3D

We prove convergence of the Maxwell eigenvalue problem using quadratic or higher Lagrange finite elements on Worsey-Farin splits in three dimensions. To do this, we construct two Fortin-like operators to prove uniform convergence of the corresponding source problem. We present numerical experiments to illustrate the theoretical results.

math.NA↗