Stochastic Galerkin Methods for the Boltzmann-Poisson system

By José A. Morales Escalante, Clemens Heitzinger. Journal of Computational Physics, 2019

591 citations recorded by the source corpus.

We study the uncertainty quantification for a Boltzmann-Poisson system that models electron transport in semiconductors and the physical collision mechanisms over the charges. We use the stochastic Galerkin method in order to handle the randomness associated to the problem. The main uncertainty in the Boltzmann equation is knowing the initial condition for a large number of particles, which is why the problem is formulated in terms of a probability density in phase space. The second source of uncertainty, directly related to the quantum nature of the problem, is the collision operator, as its structure in this semi-classical model comes from the quantum scattering matrices operating on the wave function associated to the electron probability density. Additional sources of uncertainty are transport, boundary data, etc. In this study we choose first the phonon energy as a random variable, since its value influences the energy jump appearing in the collision integral for electron-phonon scattering. Then we choose the lattice temperature as a random variable, as it defines the value of the collision operator terms in the case of electron - phonon scattering by being a parameter of the phonon distribution. The random variable for this case is a scalar then. We present our numerical simulations for this last case.

Subfields: Electrical and Electronic Engineering, Materials Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c753e46192e36d1b7de531b6bb4999b93db45f00

Citations in the corpus

• MHD simulations of the magnetorotational instability in a shearing box with zero net flux - I. The issue of convergence (2007, unknown): “We note that there is no reason why this state of af-fairs should not apply when using Godunov codes like ATHENA (Gardiner & Stone 2005a) or RAMSES (Teyssier 2002; Fromang et al. 2006) or other codes making use of hy-perviscosity to stabilise the numerical scheme, like the PENCIL code (Brandenburg…”
• Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS-MP (2005, unknown): “Our formulation of the problem differs from that of Brio & Wu (1988) and Stone & Norman (1992b) only in that we have oriented the transverse component of the magnetic field to have nonzero components along both the Y- and Z-axes in Cartesian geometry.”
• One-to-one direct modeling of experiments and astrophysical scenarios: pushing the envelope on kinetic plasma simulations (2008, unknown): “…to high intensity laser– plasma interactions, with applications to fast ignition [3] and particle acceleration [4–6], the key 0741-3335/08/124034+09$30.00 © 2008 IOP Publishing Ltd Printed in the UK 1 tools for modeling these problems are fully relativistic three-dimensional kinetic codes [7–15].”
• An MHD gadget for cosmological simulations (2008, unknown): “In particular test5A, which is also used in Brio & Wu (1988), was used to show the effects of different numerical treatments.”