Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries

DOI10.1016/j.jcp.2018.02.041zbMath1395.65083arXiv1512.09210OpenAlexW2765478332MaRDI QIDQ1656626

José A. Morales Escalante, Irene Martínez Gamba

Publication date: 10 August 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.09210

zbMATH Keywords

reflectionGalerkin schemeboundaryBoltzmann-Poisson systemdiffusivespecular

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Statistical mechanics of semiconductors (82D37) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05)

Related Items

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

Uses Software

• WENO

Cites Work

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• A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano-devices
• Molecular gas dynamics. Theory, techniques, and applications.
• Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Boltzmann equation and its applications
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices
• High field approximations to a Boltzmann-Poisson system and boundary conditions in a semiconductor
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods.
• Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode
• 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods
• Gas-surface interaction and boundary conditions for the Boltzmann equation
• A Drift-Collision Balance for a Boltzmann--Poisson System in Bounded Domains
• Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices