A direct multigroup-WENO solver for the 2D non-stationary Boltzmann–Poisson system for GaAs devices: GaAs-MESFET

High order accurate weighted essentially non-oscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic partial differential equations and other convection dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, non-oscillatory and sharp discontinuity transitions. The schemes are thus especially suitable for problems containing both strong discontinuities and complex smooth solution features. WENO schemes are robust and do not require the users to tune parameters, thus they are very convenient to use for practitioners. In this paper we review the history and basic formulation of WENO schemes, outline the main ideas in using WENO schemes to solve various hyperbolic partial differential equations and other convection dominated problems, and present a collected sample of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, and computational biology. Finally, we mention a few topics currently being investigated about WENO schemes.

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“…where well accepted rules do not exist for DSMC. See also related work in [49]. We present in Figure 6.…”

Section: Semiconductor Device Simulationmentioning

confidence: 99%

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

Shu¹

2009

SIAM Rev.

808

589

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“…(1)-(4). The advantages of fully deterministic schemes compared to Monte-Carlo solvers available can be summarized analogously to the case of semiclassical Boltzmann-Poisson solvers [12][13][14][23][24][25] as:…”

Section: Introductionmentioning

confidence: 99%

A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs

Abdallah

Cáceres

Carrillo

et al. 2009

Journal of Computational Physics

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“…Four scattering mechanisms are regarded in our study: acoustic deformation potential scattering and nonpolar optical phonons, which are treated in the isotropic approximation (velocity randomizing), and polar optical phonons and impurity scattering, where the dependence on the angle between the initial and final wave vector is considered [8], [9]. Except for the nonpolar optical phonons, all the mechanism are intravalley scattering.…”

Section: Methodsmentioning

confidence: 99%

“…The lowly-doped structure contains three layers of 250nm length (total length: 750nm) [8]. The n + layers are doped with 2 × 10 17 cm −3 .…”

Section: B Device Simulationmentioning

confidence: 99%

A deterministic Boltzmann solver for GaAs devices based on the spherical harmonics expansion

Bieder

Hong

Jungemann

2010

2010 14th International Workshop on Computational Electronics

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A deterministic Boltzmann solver has been developed using a spherical harmonics expansion and is applied to gallium arsenide. The Newton-Raphson scheme is used to solve the nonlinear Boltzmann and Poisson equations. Inclusion of polar optical phonons and their projection onto spherical harmonics is performed. The Pauli exclusion principle is included with the assumption of an isotropic band structure for GaAs. Results are shown for a bulk system and n + -ni-n + structures, which emphasize the impact of the Pauli principle. AC simulations show plasma oscillations of the GaAs devices.

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A direct multigroup-WENO solver for the 2D non-stationary Boltzmann–Poisson system for GaAs devices: GaAs-MESFET

Cited by 14 publications

References 17 publications

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs

A deterministic Boltzmann solver for GaAs devices based on the spherical harmonics expansion

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