From the 1 of 6 linked papers with an AI index.
6 papers
Performance Evaluation of Stabilized Corrections for Mixed Precision Runge--Kutta Methods
César Herrera, César Herrera, John Driscoll +4
The paper numerically evaluates the runtime and accuracy of stabilized correction techniques for mixed‑precision diagonally implicit Runge‑Kutta methods applied to nonlinear PDEs,…
A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System
Mandela B. Quashie, J. W. Burby, Andrew J. Christlieb +1
We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-ce…
A Semi-Lagrangian Adaptive Rank (SLAR) Method for High-Dimensional Vlasov Dynamics
Nanyi Zheng, William A. Sands, Daniel Hayes +2
We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order…
Moment-enhanced shallow water equations for non-slip boundary conditions
Shiping Zhou, Juntao Huang, Andrew J. Christlieb
The shallow water equations often assume a constant velocity profile along the vertical axis. However, this assumption does not hold in many practical applications. To better appro…
A Particle-In-Cell Method for Plasmas with a Generalized Momentum Formulation, Part III: A Family of Gauge Conserving Methods
Andrew J. Christlieb, William A. Sands, Stephen R. White
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell's equations under…
Hyperbolic Machine Learning Moment Closures for the BGK Equations
Andrew J. Christlieb, Mingchang Ding, Juntao Huang +1
We introduce a hyperbolic closure for the Grad moment expansion of the Bhatnagar-Gross-Krook's (BGK) kinetic model using a neural network (NN) trained on BGK's moment data. This cl…