SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Discrete probability law obtained by assuming Poisson variable parameter is distributed according to half-normal probability law
Numerical integration of Poisson equation for computer simulated plasma
Interpolation of Poisson equation by method adjusting equations to insure existence of discrete solution
The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.
A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.
Kinetic simulations of collisionless plasmas are computationally challenging due to phase-space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov–Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard-Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.
We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the “complete” loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.
This dataset consists of 1000 records in a single HDF5 file generated from the simulation code available at: https://github.com/lezahlie/esp_simulation. This code implements Poisson’s equations for electrostatics and more can be read about it here: https://en.wikipedia.org/wiki/Poisson%27s_equation#Electrostatics
We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.
Optimum demodulator for poisson processes is determined for signal processing of photon radiation
Coding schemes for data based on Poisson functions
Solutions to Poisson equation and applicability to problems of electrical breakdown due to low pressure gaseous environment
Application of multivariate extended Poisson distributions
Huffman minimum redundancy coding extension to run-length information based on Poisson distribution, including optimization and data compression applications
M-ary detection for optical communication investigated for maximum likelihood detection of one of M Poisson processes in background noise
Estimation in truncated Poisson distributions with concomitant exposure intervals and truncation points
Poisson shot noise process relationship with continuous stochastic intensity as sample function
Techniques for manipulation of long Poisson series also used for SPASM