Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results

Authors:
Yunxian Liu;Chi-Wang Shu
Affiliations:
School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

In this paper we continue our effort in [Y. Liu, C.-W. Shu, J. Comput. Electron. 3 (2004) 263] for developing local discontinuous Galerkin (LDG) finite element methods to discretize moment models in device simulations. We consider various hydrodynamic (HD) and energy transport (ET) models, which involve not only first derivative convection terms but also second derivative diffusion (heat conduction) terms and a Poisson potential equation. The convection-diffusion system is discretized by the local discontinuous Galerkin (LDG) method. The potential equation for the electric field is also discretized by the LDG method, thus the numerical tool is based on a unified discontinuous Galerkin methodology for different components. We simulate different moment models and different devices to demonstrate the robustness of the algorithm, and also assess the performance of the algorithm with different orders of accuracy. A two-dimensional simulation is also performed for a MESFET device, producing results in agreement with that obtained by the essentially non-oscillatory (ENO) finite difference method.