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Open AccessJournal ArticleDOI

A Numerical Method for Kinetic Semiconductor Equations in the Drift-Diffusion Limit

Axel Klar
- 01 Apr 1999 - 
- Vol. 20, Iss: 5, pp 1696-1712
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TLDR
An asymptotic-induced scheme for kinetic semiconductor equations with the diffusion scaling is developed and works uniformly for all ranges of mean free paths.
Abstract
An asymptotic-induced scheme for kinetic semiconductor equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis of the kinetic semiconductor equation. It works uniformly for all ranges of mean free paths. The velocity discretization is done using quadrature points equivalent to a moment expansion method. Numerical results for different physical situations are presented.

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Citations
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Journal ArticleDOI

Implicit-Explicit Runge-Kutta schemes for the Boltzmann-Poisson system for semiconductors

TL;DR: In this article, a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation was developed for the dierent regimes encountered in general semiconductor simulations.
Journal ArticleDOI

Implicit-Explicit Runge-Kutta schemes for the Boltzmann-Poisson system for semiconductors

TL;DR: A class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation with high order time and space discretization schemes which do not suer from the usual parabolic stiness in the diusive limit.
Journal ArticleDOI

Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

TL;DR: Both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling are derived and both are shown to be uniformly convergent and asymptotic-preserving.
Journal ArticleDOI

Projective and telescopic projective integration for the nonlinear BGK and Boltzmann equations

TL;DR: In this article, the authors present high-order, fully explicit projective integration schemes for nonlinear collisional kinetic equations such as the BGK and Boltzmann equation, which first take a few small (inner) steps with a simple, explicit method to damp out the stiff components of the solution.
Journal ArticleDOI

An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

TL;DR: In this article, the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics is solved using the micro-macro decomposition, which couples a kinetic equation with macroscopic ones.
References
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Book

Computational Methods of Neutron Transport

TL;DR: In this paper, a balanced overview of the major methods currently available for obtaining numerical solutions in neutron and gamma ray transport is presented, focusing on methods particularly suited to the complex problems encountered in the analysis of reactors, fusion devices, radiation shielding, and other nuclear systems.
Journal ArticleDOI

The relaxation schemes for systems of conservation laws in arbitrary space dimensions

TL;DR: A linear hyperbolic system is constructed with a stiff lower order term that approximates the original system with a small dissipative correction and can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally.
Book

The Stationary Semiconductor Device Equations

TL;DR: In this article, the authors present a mathematical model of Semiconductor Device Equations and a singular perturbation analysis of the problem of finding the number of parameters of a single SVM.
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